lecture01.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9e046cf7-e28b-4384-989c-ea8400b58982",
   "metadata": {},
   "source": [
    "# Lecture 1 - Jet tagging with neural networks"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7570366e-3bb2-4741-b300-1f93213b3262",
   "metadata": {},
   "source": [
    "> A first look at training deep neural networks to classify jets in proton-proton collisions."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aef867e4-7f1e-4550-9d06-85cc91a5fffd",
   "metadata": {},
   "source": [
    "## Learning objectives\n",
    "\n",
    "* Understand what jet tagging is and how to frame it as a machine learning task\n",
    "* Understand the main steps needed to train and evaluate a jet tagger\n",
    "* Learn how to download and process data with the 🤗 Datasets library\n",
    "* Gain an introduction to the fastai library and how to push models to the Hugging Face Hub"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32450a59-30d3-4648-92e8-ae41459e5119",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "* Chapter 1 of [_Deep Learning for Coders with fastai & PyTorch_](https://github.com/fastai/fastbook) by Jeremy Howard and Sylvain Gugger.\n",
    "* [_The Machine Learning Landscape of Top Taggers_](https://arxiv.org/abs/1902.09914) by G. Kasieczka et al.\n",
    "* [_How Much Information is in a Jet?_](https://arxiv.org/abs/1704.08249) by K. Datta and A. Larkowski."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13d80ea2-6645-4b6c-90d2-5b661a262088",
   "metadata": {},
   "source": [
    "## The task and data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "312b2adf-e12f-4d19-8012-e00240254e8a",
   "metadata": {},
   "source": [
    "For the first few lectures, we'll be analysing the [_Top Quark Tagging_ dataset](https://huggingface.co/datasets/dl4phys/top_tagging), which is a famous benchmark that's used to compare the performance of jet classification algorithms. The dataset consists of around 2 million Monte Carlo simulated events in proton-proton collisions that have been clustered into jets.\n",
    "\n",
    "Framed as a supervised machine learning task, the goal is to train a model that can classify each jet as either a top-quark signal or quark-gluon background."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a57d2da-ec9c-4e96-abf3-13a497981ef6",
   "metadata": {},
   "source": [
    "```{figure} ./images/jet-tagging.png\n",
    "---\n",
    "scale: 100%\n",
    "name: jet-tagging\n",
    "---\n",
    "Figure reference: [Particle Transformer for Jet Tagging](https://arxiv.org/abs/2202.03772)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c38657cf-a06e-4c6a-93b9-75b56f75d4a2",
   "metadata": {},
   "source": [
    "## Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "286d970b-65f2-42d3-b7a7-6f10adea2cc5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Uncomment and run this cell if using Colab, Kaggle etc\n",
    "# %pip install fastai==2.6.0 datasets git+https://github.com/huggingface/huggingface_hub"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9a2acd62",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Check we have the correct fastai version\n",
    "import fastai\n",
    "\n",
    "assert fastai.__version__ == \"2.6.0\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8db4ada-8e8c-4c24-9b14-59db681a408c",
   "metadata": {},
   "source": [
    "## Import libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "872d0a1a-7a3b-4500-a8cf-f5a36216af97",
   "metadata": {},
   "outputs": [],
   "source": [
    "from datasets import load_dataset\n",
    "from fastai.tabular.all import *\n",
    "from huggingface_hub import from_pretrained_fastai, notebook_login, push_to_hub_fastai\n",
    "from scipy.interpolate import interp1d\n",
    "from sklearn.metrics import accuracy_score, auc, roc_auc_score, roc_curve\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "54801fba-818e-488a-bc03-321519c5ef0e",
   "metadata": {
    "tags": [
     "hide-cell"
    ]
   },
   "outputs": [],
   "source": [
    "import datasets\n",
    "\n",
    "# Suppress logs\n",
    "datasets.logging.set_verbosity_error()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61eea3a0-aa61-4296-b1c1-96271e768c34",
   "metadata": {},
   "source": [
    "## Getting the data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e81bfbfb-16cb-46b8-97ef-53ee7ed890c6",
   "metadata": {},
   "source": [
    "We will use the [🤗 Datasets](https://github.com/huggingface/datasets) library to download and process the datasets that we'll encounter in this course. 🤗 Datasets provides smart caching and allows you to process larger-than-RAM datasets by exploiting a technique called _memory-mapping_ that provides a mapping between RAM and filesystem storage.\n",
    "\n",
    "To download the Top Quark Tagging dataset from the [Hugging Face Hub](https://huggingface.co/datasets/dl4phys/top_tagging), we can use the `load_dataset()` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f0848f0c-5f7b-403f-ba8e-4b7cac30ffdd",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1623294f93e14d7fb4ea54219b0e567a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/3 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "top_tagging_ds = load_dataset(\"dl4phys/top_tagging\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e34096b-7a0b-48f7-8747-9a250851297b",
   "metadata": {},
   "source": [
    "If we look inside our `top_tagging_ds` object"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "bbd76488-8778-4326-93b2-a18d5cf57852",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DatasetDict({\n",
       "    train: Dataset({\n",
       "        features: ['E_0', 'PX_0', 'PY_0', 'PZ_0', 'E_1', 'PX_1', 'PY_1', 'PZ_1', 'E_2', 'PX_2', 'PY_2', 'PZ_2', 'E_3', 'PX_3', 'PY_3', 'PZ_3', 'E_4', 'PX_4', 'PY_4', 'PZ_4', 'E_5', 'PX_5', 'PY_5', 'PZ_5', 'E_6', 'PX_6', 'PY_6', 'PZ_6', 'E_7', 'PX_7', 'PY_7', 'PZ_7', 'E_8', 'PX_8', 'PY_8', 'PZ_8', 'E_9', 'PX_9', 'PY_9', 'PZ_9', 'E_10', 'PX_10', 'PY_10', 'PZ_10', 'E_11', 'PX_11', 'PY_11', 'PZ_11', 'E_12', 'PX_12', 'PY_12', 'PZ_12', 'E_13', 'PX_13', 'PY_13', 'PZ_13', 'E_14', 'PX_14', 'PY_14', 'PZ_14', 'E_15', 'PX_15', 'PY_15', 'PZ_15', 'E_16', 'PX_16', 'PY_16', 'PZ_16', 'E_17', 'PX_17', 'PY_17', 'PZ_17', 'E_18', 'PX_18', 'PY_18', 'PZ_18', 'E_19', 'PX_19', 'PY_19', 'PZ_19', 'E_20', 'PX_20', 'PY_20', 'PZ_20', 'E_21', 'PX_21', 'PY_21', 'PZ_21', 'E_22', 'PX_22', 'PY_22', 'PZ_22', 'E_23', 'PX_23', 'PY_23', 'PZ_23', 'E_24', 'PX_24', 'PY_24', 'PZ_24', 'E_25', 'PX_25', 'PY_25', 'PZ_25', 'E_26', 'PX_26', 'PY_26', 'PZ_26', 'E_27', 'PX_27', 'PY_27', 'PZ_27', 'E_28', 'PX_28', 'PY_28', 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'PX_189', 'PY_189', 'PZ_189', 'E_190', 'PX_190', 'PY_190', 'PZ_190', 'E_191', 'PX_191', 'PY_191', 'PZ_191', 'E_192', 'PX_192', 'PY_192', 'PZ_192', 'E_193', 'PX_193', 'PY_193', 'PZ_193', 'E_194', 'PX_194', 'PY_194', 'PZ_194', 'E_195', 'PX_195', 'PY_195', 'PZ_195', 'E_196', 'PX_196', 'PY_196', 'PZ_196', 'E_197', 'PX_197', 'PY_197', 'PZ_197', 'E_198', 'PX_198', 'PY_198', 'PZ_198', 'E_199', 'PX_199', 'PY_199', 'PZ_199', 'truthE', 'truthPX', 'truthPY', 'truthPZ', 'ttv', 'is_signal_new'],\n",
       "        num_rows: 1211000\n",
       "    })\n",
       "    test: Dataset({\n",
       "        features: ['E_0', 'PX_0', 'PY_0', 'PZ_0', 'E_1', 'PX_1', 'PY_1', 'PZ_1', 'E_2', 'PX_2', 'PY_2', 'PZ_2', 'E_3', 'PX_3', 'PY_3', 'PZ_3', 'E_4', 'PX_4', 'PY_4', 'PZ_4', 'E_5', 'PX_5', 'PY_5', 'PZ_5', 'E_6', 'PX_6', 'PY_6', 'PZ_6', 'E_7', 'PX_7', 'PY_7', 'PZ_7', 'E_8', 'PX_8', 'PY_8', 'PZ_8', 'E_9', 'PX_9', 'PY_9', 'PZ_9', 'E_10', 'PX_10', 'PY_10', 'PZ_10', 'E_11', 'PX_11', 'PY_11', 'PZ_11', 'E_12', 'PX_12', 'PY_12', 'PZ_12', 'E_13', 'PX_13', 'PY_13', 'PZ_13', 'E_14', 'PX_14', 'PY_14', 'PZ_14', 'E_15', 'PX_15', 'PY_15', 'PZ_15', 'E_16', 'PX_16', 'PY_16', 'PZ_16', 'E_17', 'PX_17', 'PY_17', 'PZ_17', 'E_18', 'PX_18', 'PY_18', 'PZ_18', 'E_19', 'PX_19', 'PY_19', 'PZ_19', 'E_20', 'PX_20', 'PY_20', 'PZ_20', 'E_21', 'PX_21', 'PY_21', 'PZ_21', 'E_22', 'PX_22', 'PY_22', 'PZ_22', 'E_23', 'PX_23', 'PY_23', 'PZ_23', 'E_24', 'PX_24', 'PY_24', 'PZ_24', 'E_25', 'PX_25', 'PY_25', 'PZ_25', 'E_26', 'PX_26', 'PY_26', 'PZ_26', 'E_27', 'PX_27', 'PY_27', 'PZ_27', 'E_28', 'PX_28', 'PY_28', 'PZ_28', 'E_29', 'PX_29', 'PY_29', 'PZ_29', 'E_30', 'PX_30', 'PY_30', 'PZ_30', 'E_31', 'PX_31', 'PY_31', 'PZ_31', 'E_32', 'PX_32', 'PY_32', 'PZ_32', 'E_33', 'PX_33', 'PY_33', 'PZ_33', 'E_34', 'PX_34', 'PY_34', 'PZ_34', 'E_35', 'PX_35', 'PY_35', 'PZ_35', 'E_36', 'PX_36', 'PY_36', 'PZ_36', 'E_37', 'PX_37', 'PY_37', 'PZ_37', 'E_38', 'PX_38', 'PY_38', 'PZ_38', 'E_39', 'PX_39', 'PY_39', 'PZ_39', 'E_40', 'PX_40', 'PY_40', 'PZ_40', 'E_41', 'PX_41', 'PY_41', 'PZ_41', 'E_42', 'PX_42', 'PY_42', 'PZ_42', 'E_43', 'PX_43', 'PY_43', 'PZ_43', 'E_44', 'PX_44', 'PY_44', 'PZ_44', 'E_45', 'PX_45', 'PY_45', 'PZ_45', 'E_46', 'PX_46', 'PY_46', 'PZ_46', 'E_47', 'PX_47', 'PY_47', 'PZ_47', 'E_48', 'PX_48', 'PY_48', 'PZ_48', 'E_49', 'PX_49', 'PY_49', 'PZ_49', 'E_50', 'PX_50', 'PY_50', 'PZ_50', 'E_51', 'PX_51', 'PY_51', 'PZ_51', 'E_52', 'PX_52', 'PY_52', 'PZ_52', 'E_53', 'PX_53', 'PY_53', 'PZ_53', 'E_54', 'PX_54', 'PY_54', 'PZ_54', 'E_55', 'PX_55', 'PY_55', 'PZ_55', 'E_56', 'PX_56', 'PY_56', 'PZ_56', 'E_57', 'PX_57', 'PY_57', 'PZ_57', 'E_58', 'PX_58', 'PY_58', 'PZ_58', 'E_59', 'PX_59', 'PY_59', 'PZ_59', 'E_60', 'PX_60', 'PY_60', 'PZ_60', 'E_61', 'PX_61', 'PY_61', 'PZ_61', 'E_62', 'PX_62', 'PY_62', 'PZ_62', 'E_63', 'PX_63', 'PY_63', 'PZ_63', 'E_64', 'PX_64', 'PY_64', 'PZ_64', 'E_65', 'PX_65', 'PY_65', 'PZ_65', 'E_66', 'PX_66', 'PY_66', 'PZ_66', 'E_67', 'PX_67', 'PY_67', 'PZ_67', 'E_68', 'PX_68', 'PY_68', 'PZ_68', 'E_69', 'PX_69', 'PY_69', 'PZ_69', 'E_70', 'PX_70', 'PY_70', 'PZ_70', 'E_71', 'PX_71', 'PY_71', 'PZ_71', 'E_72', 'PX_72', 'PY_72', 'PZ_72', 'E_73', 'PX_73', 'PY_73', 'PZ_73', 'E_74', 'PX_74', 'PY_74', 'PZ_74', 'E_75', 'PX_75', 'PY_75', 'PZ_75', 'E_76', 'PX_76', 'PY_76', 'PZ_76', 'E_77', 'PX_77', 'PY_77', 'PZ_77', 'E_78', 'PX_78', 'PY_78', 'PZ_78', 'E_79', 'PX_79', 'PY_79', 'PZ_79', 'E_80', 'PX_80', 'PY_80', 'PZ_80', 'E_81', 'PX_81', 'PY_81', 'PZ_81', 'E_82', 'PX_82', 'PY_82', 'PZ_82', 'E_83', 'PX_83', 'PY_83', 'PZ_83', 'E_84', 'PX_84', 'PY_84', 'PZ_84', 'E_85', 'PX_85', 'PY_85', 'PZ_85', 'E_86', 'PX_86', 'PY_86', 'PZ_86', 'E_87', 'PX_87', 'PY_87', 'PZ_87', 'E_88', 'PX_88', 'PY_88', 'PZ_88', 'E_89', 'PX_89', 'PY_89', 'PZ_89', 'E_90', 'PX_90', 'PY_90', 'PZ_90', 'E_91', 'PX_91', 'PY_91', 'PZ_91', 'E_92', 'PX_92', 'PY_92', 'PZ_92', 'E_93', 'PX_93', 'PY_93', 'PZ_93', 'E_94', 'PX_94', 'PY_94', 'PZ_94', 'E_95', 'PX_95', 'PY_95', 'PZ_95', 'E_96', 'PX_96', 'PY_96', 'PZ_96', 'E_97', 'PX_97', 'PY_97', 'PZ_97', 'E_98', 'PX_98', 'PY_98', 'PZ_98', 'E_99', 'PX_99', 'PY_99', 'PZ_99', 'E_100', 'PX_100', 'PY_100', 'PZ_100', 'E_101', 'PX_101', 'PY_101', 'PZ_101', 'E_102', 'PX_102', 'PY_102', 'PZ_102', 'E_103', 'PX_103', 'PY_103', 'PZ_103', 'E_104', 'PX_104', 'PY_104', 'PZ_104', 'E_105', 'PX_105', 'PY_105', 'PZ_105', 'E_106', 'PX_106', 'PY_106', 'PZ_106', 'E_107', 'PX_107', 'PY_107', 'PZ_107', 'E_108', 'PX_108', 'PY_108', 'PZ_108', 'E_109', 'PX_109', 'PY_109', 'PZ_109', 'E_110', 'PX_110', 'PY_110', 'PZ_110', 'E_111', 'PX_111', 'PY_111', 'PZ_111', 'E_112', 'PX_112', 'PY_112', 'PZ_112', 'E_113', 'PX_113', 'PY_113', 'PZ_113', 'E_114', 'PX_114', 'PY_114', 'PZ_114', 'E_115', 'PX_115', 'PY_115', 'PZ_115', 'E_116', 'PX_116', 'PY_116', 'PZ_116', 'E_117', 'PX_117', 'PY_117', 'PZ_117', 'E_118', 'PX_118', 'PY_118', 'PZ_118', 'E_119', 'PX_119', 'PY_119', 'PZ_119', 'E_120', 'PX_120', 'PY_120', 'PZ_120', 'E_121', 'PX_121', 'PY_121', 'PZ_121', 'E_122', 'PX_122', 'PY_122', 'PZ_122', 'E_123', 'PX_123', 'PY_123', 'PZ_123', 'E_124', 'PX_124', 'PY_124', 'PZ_124', 'E_125', 'PX_125', 'PY_125', 'PZ_125', 'E_126', 'PX_126', 'PY_126', 'PZ_126', 'E_127', 'PX_127', 'PY_127', 'PZ_127', 'E_128', 'PX_128', 'PY_128', 'PZ_128', 'E_129', 'PX_129', 'PY_129', 'PZ_129', 'E_130', 'PX_130', 'PY_130', 'PZ_130', 'E_131', 'PX_131', 'PY_131', 'PZ_131', 'E_132', 'PX_132', 'PY_132', 'PZ_132', 'E_133', 'PX_133', 'PY_133', 'PZ_133', 'E_134', 'PX_134', 'PY_134', 'PZ_134', 'E_135', 'PX_135', 'PY_135', 'PZ_135', 'E_136', 'PX_136', 'PY_136', 'PZ_136', 'E_137', 'PX_137', 'PY_137', 'PZ_137', 'E_138', 'PX_138', 'PY_138', 'PZ_138', 'E_139', 'PX_139', 'PY_139', 'PZ_139', 'E_140', 'PX_140', 'PY_140', 'PZ_140', 'E_141', 'PX_141', 'PY_141', 'PZ_141', 'E_142', 'PX_142', 'PY_142', 'PZ_142', 'E_143', 'PX_143', 'PY_143', 'PZ_143', 'E_144', 'PX_144', 'PY_144', 'PZ_144', 'E_145', 'PX_145', 'PY_145', 'PZ_145', 'E_146', 'PX_146', 'PY_146', 'PZ_146', 'E_147', 'PX_147', 'PY_147', 'PZ_147', 'E_148', 'PX_148', 'PY_148', 'PZ_148', 'E_149', 'PX_149', 'PY_149', 'PZ_149', 'E_150', 'PX_150', 'PY_150', 'PZ_150', 'E_151', 'PX_151', 'PY_151', 'PZ_151', 'E_152', 'PX_152', 'PY_152', 'PZ_152', 'E_153', 'PX_153', 'PY_153', 'PZ_153', 'E_154', 'PX_154', 'PY_154', 'PZ_154', 'E_155', 'PX_155', 'PY_155', 'PZ_155', 'E_156', 'PX_156', 'PY_156', 'PZ_156', 'E_157', 'PX_157', 'PY_157', 'PZ_157', 'E_158', 'PX_158', 'PY_158', 'PZ_158', 'E_159', 'PX_159', 'PY_159', 'PZ_159', 'E_160', 'PX_160', 'PY_160', 'PZ_160', 'E_161', 'PX_161', 'PY_161', 'PZ_161', 'E_162', 'PX_162', 'PY_162', 'PZ_162', 'E_163', 'PX_163', 'PY_163', 'PZ_163', 'E_164', 'PX_164', 'PY_164', 'PZ_164', 'E_165', 'PX_165', 'PY_165', 'PZ_165', 'E_166', 'PX_166', 'PY_166', 'PZ_166', 'E_167', 'PX_167', 'PY_167', 'PZ_167', 'E_168', 'PX_168', 'PY_168', 'PZ_168', 'E_169', 'PX_169', 'PY_169', 'PZ_169', 'E_170', 'PX_170', 'PY_170', 'PZ_170', 'E_171', 'PX_171', 'PY_171', 'PZ_171', 'E_172', 'PX_172', 'PY_172', 'PZ_172', 'E_173', 'PX_173', 'PY_173', 'PZ_173', 'E_174', 'PX_174', 'PY_174', 'PZ_174', 'E_175', 'PX_175', 'PY_175', 'PZ_175', 'E_176', 'PX_176', 'PY_176', 'PZ_176', 'E_177', 'PX_177', 'PY_177', 'PZ_177', 'E_178', 'PX_178', 'PY_178', 'PZ_178', 'E_179', 'PX_179', 'PY_179', 'PZ_179', 'E_180', 'PX_180', 'PY_180', 'PZ_180', 'E_181', 'PX_181', 'PY_181', 'PZ_181', 'E_182', 'PX_182', 'PY_182', 'PZ_182', 'E_183', 'PX_183', 'PY_183', 'PZ_183', 'E_184', 'PX_184', 'PY_184', 'PZ_184', 'E_185', 'PX_185', 'PY_185', 'PZ_185', 'E_186', 'PX_186', 'PY_186', 'PZ_186', 'E_187', 'PX_187', 'PY_187', 'PZ_187', 'E_188', 'PX_188', 'PY_188', 'PZ_188', 'E_189', 'PX_189', 'PY_189', 'PZ_189', 'E_190', 'PX_190', 'PY_190', 'PZ_190', 'E_191', 'PX_191', 'PY_191', 'PZ_191', 'E_192', 'PX_192', 'PY_192', 'PZ_192', 'E_193', 'PX_193', 'PY_193', 'PZ_193', 'E_194', 'PX_194', 'PY_194', 'PZ_194', 'E_195', 'PX_195', 'PY_195', 'PZ_195', 'E_196', 'PX_196', 'PY_196', 'PZ_196', 'E_197', 'PX_197', 'PY_197', 'PZ_197', 'E_198', 'PX_198', 'PY_198', 'PZ_198', 'E_199', 'PX_199', 'PY_199', 'PZ_199', 'truthE', 'truthPX', 'truthPY', 'truthPZ', 'ttv', 'is_signal_new'],\n",
       "        num_rows: 404000\n",
       "    })\n",
       "    validation: Dataset({\n",
       "        features: ['E_0', 'PX_0', 'PY_0', 'PZ_0', 'E_1', 'PX_1', 'PY_1', 'PZ_1', 'E_2', 'PX_2', 'PY_2', 'PZ_2', 'E_3', 'PX_3', 'PY_3', 'PZ_3', 'E_4', 'PX_4', 'PY_4', 'PZ_4', 'E_5', 'PX_5', 'PY_5', 'PZ_5', 'E_6', 'PX_6', 'PY_6', 'PZ_6', 'E_7', 'PX_7', 'PY_7', 'PZ_7', 'E_8', 'PX_8', 'PY_8', 'PZ_8', 'E_9', 'PX_9', 'PY_9', 'PZ_9', 'E_10', 'PX_10', 'PY_10', 'PZ_10', 'E_11', 'PX_11', 'PY_11', 'PZ_11', 'E_12', 'PX_12', 'PY_12', 'PZ_12', 'E_13', 'PX_13', 'PY_13', 'PZ_13', 'E_14', 'PX_14', 'PY_14', 'PZ_14', 'E_15', 'PX_15', 'PY_15', 'PZ_15', 'E_16', 'PX_16', 'PY_16', 'PZ_16', 'E_17', 'PX_17', 'PY_17', 'PZ_17', 'E_18', 'PX_18', 'PY_18', 'PZ_18', 'E_19', 'PX_19', 'PY_19', 'PZ_19', 'E_20', 'PX_20', 'PY_20', 'PZ_20', 'E_21', 'PX_21', 'PY_21', 'PZ_21', 'E_22', 'PX_22', 'PY_22', 'PZ_22', 'E_23', 'PX_23', 'PY_23', 'PZ_23', 'E_24', 'PX_24', 'PY_24', 'PZ_24', 'E_25', 'PX_25', 'PY_25', 'PZ_25', 'E_26', 'PX_26', 'PY_26', 'PZ_26', 'E_27', 'PX_27', 'PY_27', 'PZ_27', 'E_28', 'PX_28', 'PY_28', 'PZ_28', 'E_29', 'PX_29', 'PY_29', 'PZ_29', 'E_30', 'PX_30', 'PY_30', 'PZ_30', 'E_31', 'PX_31', 'PY_31', 'PZ_31', 'E_32', 'PX_32', 'PY_32', 'PZ_32', 'E_33', 'PX_33', 'PY_33', 'PZ_33', 'E_34', 'PX_34', 'PY_34', 'PZ_34', 'E_35', 'PX_35', 'PY_35', 'PZ_35', 'E_36', 'PX_36', 'PY_36', 'PZ_36', 'E_37', 'PX_37', 'PY_37', 'PZ_37', 'E_38', 'PX_38', 'PY_38', 'PZ_38', 'E_39', 'PX_39', 'PY_39', 'PZ_39', 'E_40', 'PX_40', 'PY_40', 'PZ_40', 'E_41', 'PX_41', 'PY_41', 'PZ_41', 'E_42', 'PX_42', 'PY_42', 'PZ_42', 'E_43', 'PX_43', 'PY_43', 'PZ_43', 'E_44', 'PX_44', 'PY_44', 'PZ_44', 'E_45', 'PX_45', 'PY_45', 'PZ_45', 'E_46', 'PX_46', 'PY_46', 'PZ_46', 'E_47', 'PX_47', 'PY_47', 'PZ_47', 'E_48', 'PX_48', 'PY_48', 'PZ_48', 'E_49', 'PX_49', 'PY_49', 'PZ_49', 'E_50', 'PX_50', 'PY_50', 'PZ_50', 'E_51', 'PX_51', 'PY_51', 'PZ_51', 'E_52', 'PX_52', 'PY_52', 'PZ_52', 'E_53', 'PX_53', 'PY_53', 'PZ_53', 'E_54', 'PX_54', 'PY_54', 'PZ_54', 'E_55', 'PX_55', 'PY_55', 'PZ_55', 'E_56', 'PX_56', 'PY_56', 'PZ_56', 'E_57', 'PX_57', 'PY_57', 'PZ_57', 'E_58', 'PX_58', 'PY_58', 'PZ_58', 'E_59', 'PX_59', 'PY_59', 'PZ_59', 'E_60', 'PX_60', 'PY_60', 'PZ_60', 'E_61', 'PX_61', 'PY_61', 'PZ_61', 'E_62', 'PX_62', 'PY_62', 'PZ_62', 'E_63', 'PX_63', 'PY_63', 'PZ_63', 'E_64', 'PX_64', 'PY_64', 'PZ_64', 'E_65', 'PX_65', 'PY_65', 'PZ_65', 'E_66', 'PX_66', 'PY_66', 'PZ_66', 'E_67', 'PX_67', 'PY_67', 'PZ_67', 'E_68', 'PX_68', 'PY_68', 'PZ_68', 'E_69', 'PX_69', 'PY_69', 'PZ_69', 'E_70', 'PX_70', 'PY_70', 'PZ_70', 'E_71', 'PX_71', 'PY_71', 'PZ_71', 'E_72', 'PX_72', 'PY_72', 'PZ_72', 'E_73', 'PX_73', 'PY_73', 'PZ_73', 'E_74', 'PX_74', 'PY_74', 'PZ_74', 'E_75', 'PX_75', 'PY_75', 'PZ_75', 'E_76', 'PX_76', 'PY_76', 'PZ_76', 'E_77', 'PX_77', 'PY_77', 'PZ_77', 'E_78', 'PX_78', 'PY_78', 'PZ_78', 'E_79', 'PX_79', 'PY_79', 'PZ_79', 'E_80', 'PX_80', 'PY_80', 'PZ_80', 'E_81', 'PX_81', 'PY_81', 'PZ_81', 'E_82', 'PX_82', 'PY_82', 'PZ_82', 'E_83', 'PX_83', 'PY_83', 'PZ_83', 'E_84', 'PX_84', 'PY_84', 'PZ_84', 'E_85', 'PX_85', 'PY_85', 'PZ_85', 'E_86', 'PX_86', 'PY_86', 'PZ_86', 'E_87', 'PX_87', 'PY_87', 'PZ_87', 'E_88', 'PX_88', 'PY_88', 'PZ_88', 'E_89', 'PX_89', 'PY_89', 'PZ_89', 'E_90', 'PX_90', 'PY_90', 'PZ_90', 'E_91', 'PX_91', 'PY_91', 'PZ_91', 'E_92', 'PX_92', 'PY_92', 'PZ_92', 'E_93', 'PX_93', 'PY_93', 'PZ_93', 'E_94', 'PX_94', 'PY_94', 'PZ_94', 'E_95', 'PX_95', 'PY_95', 'PZ_95', 'E_96', 'PX_96', 'PY_96', 'PZ_96', 'E_97', 'PX_97', 'PY_97', 'PZ_97', 'E_98', 'PX_98', 'PY_98', 'PZ_98', 'E_99', 'PX_99', 'PY_99', 'PZ_99', 'E_100', 'PX_100', 'PY_100', 'PZ_100', 'E_101', 'PX_101', 'PY_101', 'PZ_101', 'E_102', 'PX_102', 'PY_102', 'PZ_102', 'E_103', 'PX_103', 'PY_103', 'PZ_103', 'E_104', 'PX_104', 'PY_104', 'PZ_104', 'E_105', 'PX_105', 'PY_105', 'PZ_105', 'E_106', 'PX_106', 'PY_106', 'PZ_106', 'E_107', 'PX_107', 'PY_107', 'PZ_107', 'E_108', 'PX_108', 'PY_108', 'PZ_108', 'E_109', 'PX_109', 'PY_109', 'PZ_109', 'E_110', 'PX_110', 'PY_110', 'PZ_110', 'E_111', 'PX_111', 'PY_111', 'PZ_111', 'E_112', 'PX_112', 'PY_112', 'PZ_112', 'E_113', 'PX_113', 'PY_113', 'PZ_113', 'E_114', 'PX_114', 'PY_114', 'PZ_114', 'E_115', 'PX_115', 'PY_115', 'PZ_115', 'E_116', 'PX_116', 'PY_116', 'PZ_116', 'E_117', 'PX_117', 'PY_117', 'PZ_117', 'E_118', 'PX_118', 'PY_118', 'PZ_118', 'E_119', 'PX_119', 'PY_119', 'PZ_119', 'E_120', 'PX_120', 'PY_120', 'PZ_120', 'E_121', 'PX_121', 'PY_121', 'PZ_121', 'E_122', 'PX_122', 'PY_122', 'PZ_122', 'E_123', 'PX_123', 'PY_123', 'PZ_123', 'E_124', 'PX_124', 'PY_124', 'PZ_124', 'E_125', 'PX_125', 'PY_125', 'PZ_125', 'E_126', 'PX_126', 'PY_126', 'PZ_126', 'E_127', 'PX_127', 'PY_127', 'PZ_127', 'E_128', 'PX_128', 'PY_128', 'PZ_128', 'E_129', 'PX_129', 'PY_129', 'PZ_129', 'E_130', 'PX_130', 'PY_130', 'PZ_130', 'E_131', 'PX_131', 'PY_131', 'PZ_131', 'E_132', 'PX_132', 'PY_132', 'PZ_132', 'E_133', 'PX_133', 'PY_133', 'PZ_133', 'E_134', 'PX_134', 'PY_134', 'PZ_134', 'E_135', 'PX_135', 'PY_135', 'PZ_135', 'E_136', 'PX_136', 'PY_136', 'PZ_136', 'E_137', 'PX_137', 'PY_137', 'PZ_137', 'E_138', 'PX_138', 'PY_138', 'PZ_138', 'E_139', 'PX_139', 'PY_139', 'PZ_139', 'E_140', 'PX_140', 'PY_140', 'PZ_140', 'E_141', 'PX_141', 'PY_141', 'PZ_141', 'E_142', 'PX_142', 'PY_142', 'PZ_142', 'E_143', 'PX_143', 'PY_143', 'PZ_143', 'E_144', 'PX_144', 'PY_144', 'PZ_144', 'E_145', 'PX_145', 'PY_145', 'PZ_145', 'E_146', 'PX_146', 'PY_146', 'PZ_146', 'E_147', 'PX_147', 'PY_147', 'PZ_147', 'E_148', 'PX_148', 'PY_148', 'PZ_148', 'E_149', 'PX_149', 'PY_149', 'PZ_149', 'E_150', 'PX_150', 'PY_150', 'PZ_150', 'E_151', 'PX_151', 'PY_151', 'PZ_151', 'E_152', 'PX_152', 'PY_152', 'PZ_152', 'E_153', 'PX_153', 'PY_153', 'PZ_153', 'E_154', 'PX_154', 'PY_154', 'PZ_154', 'E_155', 'PX_155', 'PY_155', 'PZ_155', 'E_156', 'PX_156', 'PY_156', 'PZ_156', 'E_157', 'PX_157', 'PY_157', 'PZ_157', 'E_158', 'PX_158', 'PY_158', 'PZ_158', 'E_159', 'PX_159', 'PY_159', 'PZ_159', 'E_160', 'PX_160', 'PY_160', 'PZ_160', 'E_161', 'PX_161', 'PY_161', 'PZ_161', 'E_162', 'PX_162', 'PY_162', 'PZ_162', 'E_163', 'PX_163', 'PY_163', 'PZ_163', 'E_164', 'PX_164', 'PY_164', 'PZ_164', 'E_165', 'PX_165', 'PY_165', 'PZ_165', 'E_166', 'PX_166', 'PY_166', 'PZ_166', 'E_167', 'PX_167', 'PY_167', 'PZ_167', 'E_168', 'PX_168', 'PY_168', 'PZ_168', 'E_169', 'PX_169', 'PY_169', 'PZ_169', 'E_170', 'PX_170', 'PY_170', 'PZ_170', 'E_171', 'PX_171', 'PY_171', 'PZ_171', 'E_172', 'PX_172', 'PY_172', 'PZ_172', 'E_173', 'PX_173', 'PY_173', 'PZ_173', 'E_174', 'PX_174', 'PY_174', 'PZ_174', 'E_175', 'PX_175', 'PY_175', 'PZ_175', 'E_176', 'PX_176', 'PY_176', 'PZ_176', 'E_177', 'PX_177', 'PY_177', 'PZ_177', 'E_178', 'PX_178', 'PY_178', 'PZ_178', 'E_179', 'PX_179', 'PY_179', 'PZ_179', 'E_180', 'PX_180', 'PY_180', 'PZ_180', 'E_181', 'PX_181', 'PY_181', 'PZ_181', 'E_182', 'PX_182', 'PY_182', 'PZ_182', 'E_183', 'PX_183', 'PY_183', 'PZ_183', 'E_184', 'PX_184', 'PY_184', 'PZ_184', 'E_185', 'PX_185', 'PY_185', 'PZ_185', 'E_186', 'PX_186', 'PY_186', 'PZ_186', 'E_187', 'PX_187', 'PY_187', 'PZ_187', 'E_188', 'PX_188', 'PY_188', 'PZ_188', 'E_189', 'PX_189', 'PY_189', 'PZ_189', 'E_190', 'PX_190', 'PY_190', 'PZ_190', 'E_191', 'PX_191', 'PY_191', 'PZ_191', 'E_192', 'PX_192', 'PY_192', 'PZ_192', 'E_193', 'PX_193', 'PY_193', 'PZ_193', 'E_194', 'PX_194', 'PY_194', 'PZ_194', 'E_195', 'PX_195', 'PY_195', 'PZ_195', 'E_196', 'PX_196', 'PY_196', 'PZ_196', 'E_197', 'PX_197', 'PY_197', 'PZ_197', 'E_198', 'PX_198', 'PY_198', 'PZ_198', 'E_199', 'PX_199', 'PY_199', 'PZ_199', 'truthE', 'truthPX', 'truthPY', 'truthPZ', 'ttv', 'is_signal_new'],\n",
       "        num_rows: 403000\n",
       "    })\n",
       "})"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "top_tagging_ds"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a872713d-81e7-4267-a39e-cdef8817b5b2",
   "metadata": {},
   "source": [
    "we see it is similar to a Python dictionary, with each key corresponding to a different split. And we can use the usual dictionary syntax to access an individual split:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "02a12082-68a1-4b59-a59f-44544de05e71",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dataset({\n",
       "    features: ['E_0', 'PX_0', 'PY_0', 'PZ_0', 'E_1', 'PX_1', 'PY_1', 'PZ_1', 'E_2', 'PX_2', 'PY_2', 'PZ_2', 'E_3', 'PX_3', 'PY_3', 'PZ_3', 'E_4', 'PX_4', 'PY_4', 'PZ_4', 'E_5', 'PX_5', 'PY_5', 'PZ_5', 'E_6', 'PX_6', 'PY_6', 'PZ_6', 'E_7', 'PX_7', 'PY_7', 'PZ_7', 'E_8', 'PX_8', 'PY_8', 'PZ_8', 'E_9', 'PX_9', 'PY_9', 'PZ_9', 'E_10', 'PX_10', 'PY_10', 'PZ_10', 'E_11', 'PX_11', 'PY_11', 'PZ_11', 'E_12', 'PX_12', 'PY_12', 'PZ_12', 'E_13', 'PX_13', 'PY_13', 'PZ_13', 'E_14', 'PX_14', 'PY_14', 'PZ_14', 'E_15', 'PX_15', 'PY_15', 'PZ_15', 'E_16', 'PX_16', 'PY_16', 'PZ_16', 'E_17', 'PX_17', 'PY_17', 'PZ_17', 'E_18', 'PX_18', 'PY_18', 'PZ_18', 'E_19', 'PX_19', 'PY_19', 'PZ_19', 'E_20', 'PX_20', 'PY_20', 'PZ_20', 'E_21', 'PX_21', 'PY_21', 'PZ_21', 'E_22', 'PX_22', 'PY_22', 'PZ_22', 'E_23', 'PX_23', 'PY_23', 'PZ_23', 'E_24', 'PX_24', 'PY_24', 'PZ_24', 'E_25', 'PX_25', 'PY_25', 'PZ_25', 'E_26', 'PX_26', 'PY_26', 'PZ_26', 'E_27', 'PX_27', 'PY_27', 'PZ_27', 'E_28', 'PX_28', 'PY_28', 'PZ_28', 'E_29', 'PX_29', 'PY_29', 'PZ_29', 'E_30', 'PX_30', 'PY_30', 'PZ_30', 'E_31', 'PX_31', 'PY_31', 'PZ_31', 'E_32', 'PX_32', 'PY_32', 'PZ_32', 'E_33', 'PX_33', 'PY_33', 'PZ_33', 'E_34', 'PX_34', 'PY_34', 'PZ_34', 'E_35', 'PX_35', 'PY_35', 'PZ_35', 'E_36', 'PX_36', 'PY_36', 'PZ_36', 'E_37', 'PX_37', 'PY_37', 'PZ_37', 'E_38', 'PX_38', 'PY_38', 'PZ_38', 'E_39', 'PX_39', 'PY_39', 'PZ_39', 'E_40', 'PX_40', 'PY_40', 'PZ_40', 'E_41', 'PX_41', 'PY_41', 'PZ_41', 'E_42', 'PX_42', 'PY_42', 'PZ_42', 'E_43', 'PX_43', 'PY_43', 'PZ_43', 'E_44', 'PX_44', 'PY_44', 'PZ_44', 'E_45', 'PX_45', 'PY_45', 'PZ_45', 'E_46', 'PX_46', 'PY_46', 'PZ_46', 'E_47', 'PX_47', 'PY_47', 'PZ_47', 'E_48', 'PX_48', 'PY_48', 'PZ_48', 'E_49', 'PX_49', 'PY_49', 'PZ_49', 'E_50', 'PX_50', 'PY_50', 'PZ_50', 'E_51', 'PX_51', 'PY_51', 'PZ_51', 'E_52', 'PX_52', 'PY_52', 'PZ_52', 'E_53', 'PX_53', 'PY_53', 'PZ_53', 'E_54', 'PX_54', 'PY_54', 'PZ_54', 'E_55', 'PX_55', 'PY_55', 'PZ_55', 'E_56', 'PX_56', 'PY_56', 'PZ_56', 'E_57', 'PX_57', 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'E_86', 'PX_86', 'PY_86', 'PZ_86', 'E_87', 'PX_87', 'PY_87', 'PZ_87', 'E_88', 'PX_88', 'PY_88', 'PZ_88', 'E_89', 'PX_89', 'PY_89', 'PZ_89', 'E_90', 'PX_90', 'PY_90', 'PZ_90', 'E_91', 'PX_91', 'PY_91', 'PZ_91', 'E_92', 'PX_92', 'PY_92', 'PZ_92', 'E_93', 'PX_93', 'PY_93', 'PZ_93', 'E_94', 'PX_94', 'PY_94', 'PZ_94', 'E_95', 'PX_95', 'PY_95', 'PZ_95', 'E_96', 'PX_96', 'PY_96', 'PZ_96', 'E_97', 'PX_97', 'PY_97', 'PZ_97', 'E_98', 'PX_98', 'PY_98', 'PZ_98', 'E_99', 'PX_99', 'PY_99', 'PZ_99', 'E_100', 'PX_100', 'PY_100', 'PZ_100', 'E_101', 'PX_101', 'PY_101', 'PZ_101', 'E_102', 'PX_102', 'PY_102', 'PZ_102', 'E_103', 'PX_103', 'PY_103', 'PZ_103', 'E_104', 'PX_104', 'PY_104', 'PZ_104', 'E_105', 'PX_105', 'PY_105', 'PZ_105', 'E_106', 'PX_106', 'PY_106', 'PZ_106', 'E_107', 'PX_107', 'PY_107', 'PZ_107', 'E_108', 'PX_108', 'PY_108', 'PZ_108', 'E_109', 'PX_109', 'PY_109', 'PZ_109', 'E_110', 'PX_110', 'PY_110', 'PZ_110', 'E_111', 'PX_111', 'PY_111', 'PZ_111', 'E_112', 'PX_112', 'PY_112', 'PZ_112', 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'PY_138', 'PZ_138', 'E_139', 'PX_139', 'PY_139', 'PZ_139', 'E_140', 'PX_140', 'PY_140', 'PZ_140', 'E_141', 'PX_141', 'PY_141', 'PZ_141', 'E_142', 'PX_142', 'PY_142', 'PZ_142', 'E_143', 'PX_143', 'PY_143', 'PZ_143', 'E_144', 'PX_144', 'PY_144', 'PZ_144', 'E_145', 'PX_145', 'PY_145', 'PZ_145', 'E_146', 'PX_146', 'PY_146', 'PZ_146', 'E_147', 'PX_147', 'PY_147', 'PZ_147', 'E_148', 'PX_148', 'PY_148', 'PZ_148', 'E_149', 'PX_149', 'PY_149', 'PZ_149', 'E_150', 'PX_150', 'PY_150', 'PZ_150', 'E_151', 'PX_151', 'PY_151', 'PZ_151', 'E_152', 'PX_152', 'PY_152', 'PZ_152', 'E_153', 'PX_153', 'PY_153', 'PZ_153', 'E_154', 'PX_154', 'PY_154', 'PZ_154', 'E_155', 'PX_155', 'PY_155', 'PZ_155', 'E_156', 'PX_156', 'PY_156', 'PZ_156', 'E_157', 'PX_157', 'PY_157', 'PZ_157', 'E_158', 'PX_158', 'PY_158', 'PZ_158', 'E_159', 'PX_159', 'PY_159', 'PZ_159', 'E_160', 'PX_160', 'PY_160', 'PZ_160', 'E_161', 'PX_161', 'PY_161', 'PZ_161', 'E_162', 'PX_162', 'PY_162', 'PZ_162', 'E_163', 'PX_163', 'PY_163', 'PZ_163', 'E_164', 'PX_164', 'PY_164', 'PZ_164', 'E_165', 'PX_165', 'PY_165', 'PZ_165', 'E_166', 'PX_166', 'PY_166', 'PZ_166', 'E_167', 'PX_167', 'PY_167', 'PZ_167', 'E_168', 'PX_168', 'PY_168', 'PZ_168', 'E_169', 'PX_169', 'PY_169', 'PZ_169', 'E_170', 'PX_170', 'PY_170', 'PZ_170', 'E_171', 'PX_171', 'PY_171', 'PZ_171', 'E_172', 'PX_172', 'PY_172', 'PZ_172', 'E_173', 'PX_173', 'PY_173', 'PZ_173', 'E_174', 'PX_174', 'PY_174', 'PZ_174', 'E_175', 'PX_175', 'PY_175', 'PZ_175', 'E_176', 'PX_176', 'PY_176', 'PZ_176', 'E_177', 'PX_177', 'PY_177', 'PZ_177', 'E_178', 'PX_178', 'PY_178', 'PZ_178', 'E_179', 'PX_179', 'PY_179', 'PZ_179', 'E_180', 'PX_180', 'PY_180', 'PZ_180', 'E_181', 'PX_181', 'PY_181', 'PZ_181', 'E_182', 'PX_182', 'PY_182', 'PZ_182', 'E_183', 'PX_183', 'PY_183', 'PZ_183', 'E_184', 'PX_184', 'PY_184', 'PZ_184', 'E_185', 'PX_185', 'PY_185', 'PZ_185', 'E_186', 'PX_186', 'PY_186', 'PZ_186', 'E_187', 'PX_187', 'PY_187', 'PZ_187', 'E_188', 'PX_188', 'PY_188', 'PZ_188', 'E_189', 'PX_189', 'PY_189', 'PZ_189', 'E_190', 'PX_190', 'PY_190', 'PZ_190', 'E_191', 'PX_191', 'PY_191', 'PZ_191', 'E_192', 'PX_192', 'PY_192', 'PZ_192', 'E_193', 'PX_193', 'PY_193', 'PZ_193', 'E_194', 'PX_194', 'PY_194', 'PZ_194', 'E_195', 'PX_195', 'PY_195', 'PZ_195', 'E_196', 'PX_196', 'PY_196', 'PZ_196', 'E_197', 'PX_197', 'PY_197', 'PZ_197', 'E_198', 'PX_198', 'PY_198', 'PZ_198', 'E_199', 'PX_199', 'PY_199', 'PZ_199', 'truthE', 'truthPX', 'truthPY', 'truthPZ', 'ttv', 'is_signal_new'],\n",
       "    num_rows: 1211000\n",
       "})"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "top_tagging_ds[\"train\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "476a057b-2122-4f2c-b99e-6d172ded6b84",
   "metadata": {},
   "source": [
    "The `Dataset` object is one of the core data structures in 🤗 Datasets and behaves like an ordinary Python `list`, so we can query its length:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "d969fce7-e1d9-4efc-bf2e-a484ec9b4700",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1211000"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(top_tagging_ds[\"train\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88673ef4-3f59-4bd0-b7f1-e490c740ddc6",
   "metadata": {},
   "source": [
    "or access a single element by its index:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "44eba391-e7ac-482e-a381-ff62c77d1987",
   "metadata": {
    "tags": [
     "hide-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'E_0': 474.0711364746094,\n",
       " 'PX_0': -250.34703063964844,\n",
       " 'PY_0': -223.65196228027344,\n",
       " 'PZ_0': -334.73809814453125,\n",
       " 'E_1': 103.23623657226562,\n",
       " 'PX_1': -48.8662223815918,\n",
       " 'PY_1': -56.790775299072266,\n",
       " 'PZ_1': -71.0254898071289,\n",
       " 'E_2': 105.25556945800781,\n",
       " 'PX_2': -55.415000915527344,\n",
       " 'PY_2': -49.96888732910156,\n",
       " 'PZ_2': -74.23626708984375,\n",
       " 'E_3': 40.17677688598633,\n",
       " 'PX_3': -21.760696411132812,\n",
       " 'PY_3': -18.71761131286621,\n",
       " 'PZ_3': -28.112215042114258,\n",
       " 'E_4': 22.4285831451416,\n",
       " 'PX_4': -11.835756301879883,\n",
       " 'PY_4': -10.374107360839844,\n",
       " 'PZ_4': -15.979177474975586,\n",
       " 'E_5': 20.334388732910156,\n",
       " 'PX_5': -10.950518608093262,\n",
       " 'PY_5': -9.545439720153809,\n",
       " 'PZ_5': -14.228776931762695,\n",
       " 'E_6': 19.030899047851562,\n",
       " 'PX_6': -10.243264198303223,\n",
       " 'PY_6': -9.004837036132812,\n",
       " 'PZ_6': -13.272662162780762,\n",
       " 'E_7': 13.460596084594727,\n",
       " 'PX_7': -7.3433637619018555,\n",
       " 'PY_7': -6.359743595123291,\n",
       " 'PZ_7': -9.317526817321777,\n",
       " 'E_8': 11.226107597351074,\n",
       " 'PX_8': -5.981515884399414,\n",
       " 'PY_8': -5.456268787384033,\n",
       " 'PZ_8': -7.776637554168701,\n",
       " 'E_9': 10.445060729980469,\n",
       " 'PX_9': -5.460624694824219,\n",
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       " 'PX_199': 0.0,\n",
       " 'PY_199': 0.0,\n",
       " 'PZ_199': 0.0,\n",
       " 'truthE': 0.0,\n",
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       " 'truthPZ': 0.0,\n",
       " 'ttv': 0,\n",
       " 'is_signal_new': 0}"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "top_tagging_ds[\"train\"][0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d87b0645-2d3a-4816-b840-075e8040cdab",
   "metadata": {},
   "source": [
    "Here we see that a single row is repesented as a dictionary where the keys correspond to the column names. Since we won't need the top-quark 4-vector columns, let's remove them along with the `ttv` one:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "327a4c1a-3b98-47ef-9ecd-275059d366f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "top_tagging_ds = top_tagging_ds.remove_columns(\n",
    "    [\"truthE\", \"truthPX\", \"truthPY\", \"truthPZ\", \"ttv\"]\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5df4d94-4116-418d-940e-b2558fa0054f",
   "metadata": {},
   "source": [
    "Although 🤗 Datasets provides a lot of low-level functionality for preprocessing datasets, it is often conventient to convert a `Dataset` object to a Pandas `DataFrame`. To enable the conversion, 🤗 Datasets provides a `set_format()` method that allows us to change the output format of the dataset: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "19f17074-c1e6-459f-a212-6f1ba16cab6d",
   "metadata": {
    "tags": []
   },
   "outputs": [
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       "\n",
       "[5 rows x 801 columns]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Convert output format to DataFrames\n",
    "top_tagging_ds.set_format(\"pandas\")\n",
    "# Create DataFrames for the training and test splits\n",
    "train_df, test_df = top_tagging_ds[\"train\"][:], top_tagging_ds[\"test\"][:]\n",
    "# Peek at first few rows\n",
    "train_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ed98137-8c5d-47da-9868-4a2d7a2cb1a1",
   "metadata": {},
   "source": [
    "As we can see, each row consists of 4-vectors $(E_i, p_{x_i}, p_{y_i}, p_{z_i})$ that correspond to the maximum 200 particles that make up each jet. We can also see that each jet has been padded with zeros, since most won't have 200 particles. We also have an `is_signal_new` column that indicates whether the jet is a top quark signal (1) or QCD background (0).\n",
    "\n",
    "Now that we've had a look at a sample of the raw data, let's take a look at how we can convert it to a format that is suitable for neural networks!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e619bf96-1e95-42ca-875a-970f6c0555ca",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Introducing fastai\n",
    "\n",
    "To train our model, we'll use the [fastai library](https://github.com/fastai/fastai). fastai is the most popular framework for training deep neural networks with PyTorch and provides various application-specific classes for different types of deep learning data structures and architectures. It is also designed with a _layered API_, which means:\n",
    "\n",
    "* We can use high-level components to quickly and easily get state-of-the-art results in standard deep learning domains\n",
    "* Low-level components can be mixed and matched to build new approaches\n",
    "\n",
    "In particular, this approach will allow us in later lessons to use pure PyTorch code to define our models, and then let fastai take care of the training loop (which is often an error-prone process).\n",
    "\n",
    "**Basics of the API**\n",
    "\n",
    "The most common steps one takes when training a model in fastai are:\n",
    "\n",
    "* Create `DataLoaders` to feed batches of data to the model\n",
    "* Create a `Learner` which wraps the architecture, optimizer, and data, and automatically chooses an appropriate loss function where possible\n",
    "* Find a good learning rate\n",
    "* Train your model\n",
    "* Evaluate your model\n",
    "\n",
    "Let's go through each of these steps to build a neural network that can classify top quark jets from the QCD background!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f820a022-ca1e-40ef-8e8b-7007347c7e2c",
   "metadata": {},
   "source": [
    "### From data to DataLoaders"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35e75770-cb9c-44f2-af57-bed0b0548b7a",
   "metadata": {},
   "source": [
    "To wrangle our data in a format that's suitable for training neural nets, we need to create an object called `DataLoaders`. To turn our dataset into a `DataLoaders` object we need to specify:\n",
    "\n",
    "* What type of data we are dealing with (tabular, images, etc)\n",
    "* How to get the examples\n",
    "* How to label each example\n",
    "* How to create the validation set\n",
    "\n",
    "fastai provides a number of classes for different kinds of deep learning datasets and problems. In our case, the data is in a _tabular_ format (i.e. a table of rows and columns), so we can use the `TabularDataLoaders` class:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "7f0f876c-8de0-4185-b803-345e2f3e928e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Downsample to ~0.5 if you're running on Colab / Kaggle which have limited RAM\n",
    "frac_of_samples = 1.0\n",
    "train_df = train_df.sample(int(frac_of_samples * len(train_df)), random_state=42)\n",
    "\n",
    "features = list(train_df.drop(columns=[\"is_signal_new\"]).columns)\n",
    "splits = RandomSplitter(valid_pct=0.20, seed=42)(range_of(train_df))\n",
    "\n",
    "dls = TabularDataLoaders.from_df(\n",
    "    df=train_df,\n",
    "    cont_names=features,\n",
    "    y_names=\"is_signal_new\",\n",
    "    y_block=CategoryBlock,\n",
    "    splits=splits,\n",
    "    bs=1024,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e46e17c6-ec3b-45d0-a68d-3c71ab602e79",
   "metadata": {},
   "source": [
    "Let's unpack this code a bit. The first thing we've specified is which columns of our dataset correspond to _continuous features_ via the `cont_names` argument. To do this, we've simply grabbed all column names from our `DataFrame`, except for the label column `is_signal_new`. Next, we've specified which column is the target in `y_names` and that this is a _categorical feature_ with `CategoryBlock`. Finally we've specified the training and validation splits with `RandomSplitter` and picked a batch size of 1,024 examples.\n",
    "\n",
    "After we've defined a `DataLoaders` object, we can take a look at the data by using the `show_batch()` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "df1a7e20-ed23-40ca-84e2-b960a54d5d83",
   "metadata": {},
   "outputs": [
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       "      <th>PY_96</th>\n",
       "      <th>PZ_96</th>\n",
       "      <th>E_97</th>\n",
       "      <th>PX_97</th>\n",
       "      <th>PY_97</th>\n",
       "      <th>PZ_97</th>\n",
       "      <th>E_98</th>\n",
       "      <th>PX_98</th>\n",
       "      <th>PY_98</th>\n",
       "      <th>PZ_98</th>\n",
       "      <th>E_99</th>\n",
       "      <th>PX_99</th>\n",
       "      <th>PY_99</th>\n",
       "      <th>PZ_99</th>\n",
       "      <th>E_100</th>\n",
       "      <th>PX_100</th>\n",
       "      <th>PY_100</th>\n",
       "      <th>PZ_100</th>\n",
       "      <th>E_101</th>\n",
       "      <th>PX_101</th>\n",
       "      <th>PY_101</th>\n",
       "      <th>PZ_101</th>\n",
       "      <th>E_102</th>\n",
       "      <th>PX_102</th>\n",
       "      <th>PY_102</th>\n",
       "      <th>PZ_102</th>\n",
       "      <th>E_103</th>\n",
       "      <th>PX_103</th>\n",
       "      <th>PY_103</th>\n",
       "      <th>PZ_103</th>\n",
       "      <th>E_104</th>\n",
       "      <th>PX_104</th>\n",
       "      <th>PY_104</th>\n",
       "      <th>PZ_104</th>\n",
       "      <th>E_105</th>\n",
       "      <th>PX_105</th>\n",
       "      <th>PY_105</th>\n",
       "      <th>PZ_105</th>\n",
       "      <th>E_106</th>\n",
       "      <th>PX_106</th>\n",
       "      <th>PY_106</th>\n",
       "      <th>PZ_106</th>\n",
       "      <th>E_107</th>\n",
       "      <th>PX_107</th>\n",
       "      <th>PY_107</th>\n",
       "      <th>PZ_107</th>\n",
       "      <th>E_108</th>\n",
       "      <th>PX_108</th>\n",
       "      <th>PY_108</th>\n",
       "      <th>PZ_108</th>\n",
       "      <th>E_109</th>\n",
       "      <th>PX_109</th>\n",
       "      <th>PY_109</th>\n",
       "      <th>PZ_109</th>\n",
       "      <th>E_110</th>\n",
       "      <th>PX_110</th>\n",
       "      <th>PY_110</th>\n",
       "      <th>PZ_110</th>\n",
       "      <th>E_111</th>\n",
       "      <th>PX_111</th>\n",
       "      <th>PY_111</th>\n",
       "      <th>PZ_111</th>\n",
       "      <th>E_112</th>\n",
       "      <th>PX_112</th>\n",
       "      <th>PY_112</th>\n",
       "      <th>PZ_112</th>\n",
       "      <th>E_113</th>\n",
       "      <th>PX_113</th>\n",
       "      <th>PY_113</th>\n",
       "      <th>PZ_113</th>\n",
       "      <th>E_114</th>\n",
       "      <th>PX_114</th>\n",
       "      <th>PY_114</th>\n",
       "      <th>PZ_114</th>\n",
       "      <th>E_115</th>\n",
       "      <th>PX_115</th>\n",
       "      <th>PY_115</th>\n",
       "      <th>PZ_115</th>\n",
       "      <th>E_116</th>\n",
       "      <th>PX_116</th>\n",
       "      <th>PY_116</th>\n",
       "      <th>PZ_116</th>\n",
       "      <th>E_117</th>\n",
       "      <th>PX_117</th>\n",
       "      <th>PY_117</th>\n",
       "      <th>PZ_117</th>\n",
       "      <th>E_118</th>\n",
       "      <th>PX_118</th>\n",
       "      <th>PY_118</th>\n",
       "      <th>PZ_118</th>\n",
       "      <th>E_119</th>\n",
       "      <th>PX_119</th>\n",
       "      <th>PY_119</th>\n",
       "      <th>PZ_119</th>\n",
       "      <th>E_120</th>\n",
       "      <th>PX_120</th>\n",
       "      <th>PY_120</th>\n",
       "      <th>PZ_120</th>\n",
       "      <th>E_121</th>\n",
       "      <th>PX_121</th>\n",
       "      <th>PY_121</th>\n",
       "      <th>PZ_121</th>\n",
       "      <th>E_122</th>\n",
       "      <th>PX_122</th>\n",
       "      <th>PY_122</th>\n",
       "      <th>PZ_122</th>\n",
       "      <th>E_123</th>\n",
       "      <th>PX_123</th>\n",
       "      <th>PY_123</th>\n",
       "      <th>PZ_123</th>\n",
       "      <th>E_124</th>\n",
       "      <th>PX_124</th>\n",
       "      <th>PY_124</th>\n",
       "      <th>PZ_124</th>\n",
       "      <th>E_125</th>\n",
       "      <th>PX_125</th>\n",
       "      <th>PY_125</th>\n",
       "      <th>PZ_125</th>\n",
       "      <th>E_126</th>\n",
       "      <th>PX_126</th>\n",
       "      <th>PY_126</th>\n",
       "      <th>PZ_126</th>\n",
       "      <th>E_127</th>\n",
       "      <th>PX_127</th>\n",
       "      <th>PY_127</th>\n",
       "      <th>PZ_127</th>\n",
       "      <th>E_128</th>\n",
       "      <th>PX_128</th>\n",
       "      <th>PY_128</th>\n",
       "      <th>PZ_128</th>\n",
       "      <th>E_129</th>\n",
       "      <th>PX_129</th>\n",
       "      <th>PY_129</th>\n",
       "      <th>PZ_129</th>\n",
       "      <th>E_130</th>\n",
       "      <th>PX_130</th>\n",
       "      <th>PY_130</th>\n",
       "      <th>PZ_130</th>\n",
       "      <th>E_131</th>\n",
       "      <th>PX_131</th>\n",
       "      <th>PY_131</th>\n",
       "      <th>PZ_131</th>\n",
       "      <th>E_132</th>\n",
       "      <th>PX_132</th>\n",
       "      <th>PY_132</th>\n",
       "      <th>PZ_132</th>\n",
       "      <th>E_133</th>\n",
       "      <th>PX_133</th>\n",
       "      <th>PY_133</th>\n",
       "      <th>PZ_133</th>\n",
       "      <th>E_134</th>\n",
       "      <th>PX_134</th>\n",
       "      <th>PY_134</th>\n",
       "      <th>PZ_134</th>\n",
       "      <th>E_135</th>\n",
       "      <th>PX_135</th>\n",
       "      <th>PY_135</th>\n",
       "      <th>PZ_135</th>\n",
       "      <th>E_136</th>\n",
       "      <th>PX_136</th>\n",
       "      <th>PY_136</th>\n",
       "      <th>PZ_136</th>\n",
       "      <th>E_137</th>\n",
       "      <th>PX_137</th>\n",
       "      <th>PY_137</th>\n",
       "      <th>PZ_137</th>\n",
       "      <th>E_138</th>\n",
       "      <th>PX_138</th>\n",
       "      <th>PY_138</th>\n",
       "      <th>PZ_138</th>\n",
       "      <th>E_139</th>\n",
       "      <th>PX_139</th>\n",
       "      <th>PY_139</th>\n",
       "      <th>PZ_139</th>\n",
       "      <th>E_140</th>\n",
       "      <th>PX_140</th>\n",
       "      <th>PY_140</th>\n",
       "      <th>PZ_140</th>\n",
       "      <th>E_141</th>\n",
       "      <th>PX_141</th>\n",
       "      <th>PY_141</th>\n",
       "      <th>PZ_141</th>\n",
       "      <th>E_142</th>\n",
       "      <th>PX_142</th>\n",
       "      <th>PY_142</th>\n",
       "      <th>PZ_142</th>\n",
       "      <th>E_143</th>\n",
       "      <th>PX_143</th>\n",
       "      <th>PY_143</th>\n",
       "      <th>PZ_143</th>\n",
       "      <th>E_144</th>\n",
       "      <th>PX_144</th>\n",
       "      <th>PY_144</th>\n",
       "      <th>PZ_144</th>\n",
       "      <th>E_145</th>\n",
       "      <th>PX_145</th>\n",
       "      <th>PY_145</th>\n",
       "      <th>PZ_145</th>\n",
       "      <th>E_146</th>\n",
       "      <th>PX_146</th>\n",
       "      <th>PY_146</th>\n",
       "      <th>PZ_146</th>\n",
       "      <th>E_147</th>\n",
       "      <th>PX_147</th>\n",
       "      <th>PY_147</th>\n",
       "      <th>PZ_147</th>\n",
       "      <th>E_148</th>\n",
       "      <th>PX_148</th>\n",
       "      <th>PY_148</th>\n",
       "      <th>PZ_148</th>\n",
       "      <th>E_149</th>\n",
       "      <th>PX_149</th>\n",
       "      <th>PY_149</th>\n",
       "      <th>PZ_149</th>\n",
       "      <th>E_150</th>\n",
       "      <th>PX_150</th>\n",
       "      <th>PY_150</th>\n",
       "      <th>PZ_150</th>\n",
       "      <th>E_151</th>\n",
       "      <th>PX_151</th>\n",
       "      <th>PY_151</th>\n",
       "      <th>PZ_151</th>\n",
       "      <th>E_152</th>\n",
       "      <th>PX_152</th>\n",
       "      <th>PY_152</th>\n",
       "      <th>PZ_152</th>\n",
       "      <th>E_153</th>\n",
       "      <th>PX_153</th>\n",
       "      <th>PY_153</th>\n",
       "      <th>PZ_153</th>\n",
       "      <th>E_154</th>\n",
       "      <th>PX_154</th>\n",
       "      <th>PY_154</th>\n",
       "      <th>PZ_154</th>\n",
       "      <th>E_155</th>\n",
       "      <th>PX_155</th>\n",
       "      <th>PY_155</th>\n",
       "      <th>PZ_155</th>\n",
       "      <th>E_156</th>\n",
       "      <th>PX_156</th>\n",
       "      <th>PY_156</th>\n",
       "      <th>PZ_156</th>\n",
       "      <th>E_157</th>\n",
       "      <th>PX_157</th>\n",
       "      <th>PY_157</th>\n",
       "      <th>PZ_157</th>\n",
       "      <th>E_158</th>\n",
       "      <th>PX_158</th>\n",
       "      <th>PY_158</th>\n",
       "      <th>PZ_158</th>\n",
       "      <th>E_159</th>\n",
       "      <th>PX_159</th>\n",
       "      <th>PY_159</th>\n",
       "      <th>PZ_159</th>\n",
       "      <th>E_160</th>\n",
       "      <th>PX_160</th>\n",
       "      <th>PY_160</th>\n",
       "      <th>PZ_160</th>\n",
       "      <th>E_161</th>\n",
       "      <th>PX_161</th>\n",
       "      <th>PY_161</th>\n",
       "      <th>PZ_161</th>\n",
       "      <th>E_162</th>\n",
       "      <th>PX_162</th>\n",
       "      <th>PY_162</th>\n",
       "      <th>PZ_162</th>\n",
       "      <th>E_163</th>\n",
       "      <th>PX_163</th>\n",
       "      <th>PY_163</th>\n",
       "      <th>PZ_163</th>\n",
       "      <th>E_164</th>\n",
       "      <th>PX_164</th>\n",
       "      <th>PY_164</th>\n",
       "      <th>PZ_164</th>\n",
       "      <th>E_165</th>\n",
       "      <th>PX_165</th>\n",
       "      <th>PY_165</th>\n",
       "      <th>PZ_165</th>\n",
       "      <th>E_166</th>\n",
       "      <th>PX_166</th>\n",
       "      <th>PY_166</th>\n",
       "      <th>PZ_166</th>\n",
       "      <th>E_167</th>\n",
       "      <th>PX_167</th>\n",
       "      <th>PY_167</th>\n",
       "      <th>PZ_167</th>\n",
       "      <th>E_168</th>\n",
       "      <th>PX_168</th>\n",
       "      <th>PY_168</th>\n",
       "      <th>PZ_168</th>\n",
       "      <th>E_169</th>\n",
       "      <th>PX_169</th>\n",
       "      <th>PY_169</th>\n",
       "      <th>PZ_169</th>\n",
       "      <th>E_170</th>\n",
       "      <th>PX_170</th>\n",
       "      <th>PY_170</th>\n",
       "      <th>PZ_170</th>\n",
       "      <th>E_171</th>\n",
       "      <th>PX_171</th>\n",
       "      <th>PY_171</th>\n",
       "      <th>PZ_171</th>\n",
       "      <th>E_172</th>\n",
       "      <th>PX_172</th>\n",
       "      <th>PY_172</th>\n",
       "      <th>PZ_172</th>\n",
       "      <th>E_173</th>\n",
       "      <th>PX_173</th>\n",
       "      <th>PY_173</th>\n",
       "      <th>PZ_173</th>\n",
       "      <th>E_174</th>\n",
       "      <th>PX_174</th>\n",
       "      <th>PY_174</th>\n",
       "      <th>PZ_174</th>\n",
       "      <th>E_175</th>\n",
       "      <th>PX_175</th>\n",
       "      <th>PY_175</th>\n",
       "      <th>PZ_175</th>\n",
       "      <th>E_176</th>\n",
       "      <th>PX_176</th>\n",
       "      <th>PY_176</th>\n",
       "      <th>PZ_176</th>\n",
       "      <th>E_177</th>\n",
       "      <th>PX_177</th>\n",
       "      <th>PY_177</th>\n",
       "      <th>PZ_177</th>\n",
       "      <th>E_178</th>\n",
       "      <th>PX_178</th>\n",
       "      <th>PY_178</th>\n",
       "      <th>PZ_178</th>\n",
       "      <th>E_179</th>\n",
       "      <th>PX_179</th>\n",
       "      <th>PY_179</th>\n",
       "      <th>PZ_179</th>\n",
       "      <th>E_180</th>\n",
       "      <th>PX_180</th>\n",
       "      <th>PY_180</th>\n",
       "      <th>PZ_180</th>\n",
       "      <th>E_181</th>\n",
       "      <th>PX_181</th>\n",
       "      <th>PY_181</th>\n",
       "      <th>PZ_181</th>\n",
       "      <th>E_182</th>\n",
       "      <th>PX_182</th>\n",
       "      <th>PY_182</th>\n",
       "      <th>PZ_182</th>\n",
       "      <th>E_183</th>\n",
       "      <th>PX_183</th>\n",
       "      <th>PY_183</th>\n",
       "      <th>PZ_183</th>\n",
       "      <th>E_184</th>\n",
       "      <th>PX_184</th>\n",
       "      <th>PY_184</th>\n",
       "      <th>PZ_184</th>\n",
       "      <th>E_185</th>\n",
       "      <th>PX_185</th>\n",
       "      <th>PY_185</th>\n",
       "      <th>PZ_185</th>\n",
       "      <th>E_186</th>\n",
       "      <th>PX_186</th>\n",
       "      <th>PY_186</th>\n",
       "      <th>PZ_186</th>\n",
       "      <th>E_187</th>\n",
       "      <th>PX_187</th>\n",
       "      <th>PY_187</th>\n",
       "      <th>PZ_187</th>\n",
       "      <th>E_188</th>\n",
       "      <th>PX_188</th>\n",
       "      <th>PY_188</th>\n",
       "      <th>PZ_188</th>\n",
       "      <th>E_189</th>\n",
       "      <th>PX_189</th>\n",
       "      <th>PY_189</th>\n",
       "      <th>PZ_189</th>\n",
       "      <th>E_190</th>\n",
       "      <th>PX_190</th>\n",
       "      <th>PY_190</th>\n",
       "      <th>PZ_190</th>\n",
       "      <th>E_191</th>\n",
       "      <th>PX_191</th>\n",
       "      <th>PY_191</th>\n",
       "      <th>PZ_191</th>\n",
       "      <th>E_192</th>\n",
       "      <th>PX_192</th>\n",
       "      <th>PY_192</th>\n",
       "      <th>PZ_192</th>\n",
       "      <th>E_193</th>\n",
       "      <th>PX_193</th>\n",
       "      <th>PY_193</th>\n",
       "      <th>PZ_193</th>\n",
       "      <th>E_194</th>\n",
       "      <th>PX_194</th>\n",
       "      <th>PY_194</th>\n",
       "      <th>PZ_194</th>\n",
       "      <th>E_195</th>\n",
       "      <th>PX_195</th>\n",
       "      <th>PY_195</th>\n",
       "      <th>PZ_195</th>\n",
       "      <th>E_196</th>\n",
       "      <th>PX_196</th>\n",
       "      <th>PY_196</th>\n",
       "      <th>PZ_196</th>\n",
       "      <th>E_197</th>\n",
       "      <th>PX_197</th>\n",
       "      <th>PY_197</th>\n",
       "      <th>PZ_197</th>\n",
       "      <th>E_198</th>\n",
       "      <th>PX_198</th>\n",
       "      <th>PY_198</th>\n",
       "      <th>PZ_198</th>\n",
       "      <th>E_199</th>\n",
       "      <th>PX_199</th>\n",
       "      <th>PY_199</th>\n",
       "      <th>PZ_199</th>\n",
       "      <th>is_signal_new</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>156.651123</td>\n",
       "      <td>147.405258</td>\n",
       "      <td>26.006823</td>\n",
       "      <td>-46.205074</td>\n",
       "      <td>66.166000</td>\n",
       "      <td>61.714252</td>\n",
       "      <td>13.618260</td>\n",
       "      <td>-19.591679</td>\n",
       "      <td>59.187538</td>\n",
       "      <td>43.524006</td>\n",
       "      <td>18.544239</td>\n",
       "      <td>-35.565948</td>\n",
       "      <td>52.280418</td>\n",
       "      <td>39.901722</td>\n",
       "      <td>14.766282</td>\n",
       "      <td>-30.381767</td>\n",
       "      <td>46.479649</td>\n",
       "      <td>37.455952</td>\n",
       "      <td>-4.363357</td>\n",
       "      <td>-27.172979</td>\n",
       "      <td>37.165035</td>\n",
       "      <td>35.369465</td>\n",
       "      <td>1.354363</td>\n",
       "      <td>-11.331660</td>\n",
       "      <td>36.232121</td>\n",
       "      <td>27.362452</td>\n",
       "      <td>10.842762</td>\n",
       "      <td>-21.130484</td>\n",
       "      <td>35.059006</td>\n",
       "      <td>26.817917</td>\n",
       "      <td>10.583280</td>\n",
       "      <td>-19.948118</td>\n",
       "      <td>27.499258</td>\n",
       "      <td>21.504807</td>\n",
       "      <td>-7.419861</td>\n",
       "      <td>-15.449861</td>\n",
       "      <td>24.723345</td>\n",
       "      <td>18.445026</td>\n",
       "      <td>7.439287</td>\n",
       "      <td>-14.686109</td>\n",
       "      <td>21.618416</td>\n",
       "      <td>17.497467</td>\n",
       "      <td>5.555872</td>\n",
       "      <td>-11.416079</td>\n",
       "      <td>20.788595</td>\n",
       "      <td>15.854955</td>\n",
       "      <td>6.082806</td>\n",
       "      <td>-11.991064</td>\n",
       "      <td>18.213100</td>\n",
       "      <td>13.441398</td>\n",
       "      <td>6.698515</td>\n",
       "      <td>-10.304162</td>\n",
       "      <td>12.677663</td>\n",
       "      <td>12.036289</td>\n",
       "      <td>2.944411</td>\n",
       "      <td>-2.679800</td>\n",
       "      <td>12.660934</td>\n",
       "      <td>11.887339</td>\n",
       "      <td>1.900199</td>\n",
       "      <td>-3.921694</td>\n",
       "      <td>9.484063</td>\n",
       "      <td>7.706819</td>\n",
       "      <td>2.073808</td>\n",
       "      <td>-5.123643</td>\n",
       "      <td>8.043362</td>\n",
       "      <td>6.180357</td>\n",
       "      <td>2.354782</td>\n",
       "      <td>-4.577538</td>\n",
       "      <td>7.829610</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>217.770920</td>\n",
       "      <td>112.669815</td>\n",
       "      <td>-55.818962</td>\n",
       "      <td>-177.803070</td>\n",
       "      <td>169.487793</td>\n",
       "      <td>57.047081</td>\n",
       "      <td>-86.189850</td>\n",
       "      <td>-134.324432</td>\n",
       "      <td>79.572060</td>\n",
       "      <td>52.154568</td>\n",
       "      <td>-31.429808</td>\n",
       "      <td>-51.222851</td>\n",
       "      <td>56.272415</td>\n",
       "      <td>34.468712</td>\n",
       "      <td>-25.402637</td>\n",
       "      <td>-36.512993</td>\n",
       "      <td>47.898685</td>\n",
       "      <td>33.165764</td>\n",
       "      <td>-16.905451</td>\n",
       "      <td>-30.141701</td>\n",
       "      <td>38.172230</td>\n",
       "      <td>26.431019</td>\n",
       "      <td>-13.472577</td>\n",
       "      <td>-24.021032</td>\n",
       "      <td>43.246582</td>\n",
       "      <td>14.914506</td>\n",
       "      <td>-23.153084</td>\n",
       "      <td>-33.343048</td>\n",
       "      <td>42.543930</td>\n",
       "      <td>22.392347</td>\n",
       "      <td>-10.330865</td>\n",
       "      <td>-34.667595</td>\n",
       "      <td>32.264137</td>\n",
       "      <td>20.407352</td>\n",
       "      <td>-13.483160</td>\n",
       "      <td>-21.040884</td>\n",
       "      <td>28.707653</td>\n",
       "      <td>18.947687</td>\n",
       "      <td>-11.550921</td>\n",
       "      <td>-18.212378</td>\n",
       "      <td>17.897223</td>\n",
       "      <td>10.066465</td>\n",
       "      <td>-7.947463</td>\n",
       "      <td>-12.482575</td>\n",
       "      <td>15.136470</td>\n",
       "      <td>9.821433</td>\n",
       "      <td>-5.684728</td>\n",
       "      <td>-10.016788</td>\n",
       "      <td>12.714173</td>\n",
       "      <td>7.650305</td>\n",
       "      <td>-4.211721</td>\n",
       "      <td>-9.240370</td>\n",
       "      <td>10.947527</td>\n",
       "      <td>6.395720</td>\n",
       "      <td>-3.739368</td>\n",
       "      <td>-8.059792</td>\n",
       "      <td>9.969221</td>\n",
       "      <td>6.233003</td>\n",
       "      <td>-3.332090</td>\n",
       "      <td>-7.030806</td>\n",
       "      <td>9.037607</td>\n",
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       "      <td>-2.770133</td>\n",
       "      <td>-6.491545</td>\n",
       "      <td>9.774871</td>\n",
       "      <td>3.194082</td>\n",
       "      <td>-5.116557</td>\n",
       "      <td>-7.691995</td>\n",
       "      <td>7.610077</td>\n",
       "      <td>4.280361</td>\n",
       "      <td>-3.379340</td>\n",
       "      <td>-5.307716</td>\n",
       "      <td>7.548386</td>\n",
       "      <td>4.600593</td>\n",
       "      <td>-2.243847</td>\n",
       "      <td>-5.547777</td>\n",
       "      <td>7.722602</td>\n",
       "      <td>4.280883</td>\n",
       "      <td>-2.738911</td>\n",
       "      <td>-5.814722</td>\n",
       "      <td>7.851254</td>\n",
       "      <td>2.219324</td>\n",
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       "      <td>-6.537639</td>\n",
       "      <td>7.487554</td>\n",
       "      <td>3.762560</td>\n",
       "      <td>-2.020533</td>\n",
       "      <td>-6.150126</td>\n",
       "      <td>3.724781</td>\n",
       "      <td>2.421021</td>\n",
       "      <td>-1.775541</td>\n",
       "      <td>-2.204564</td>\n",
       "      <td>3.201555</td>\n",
       "      <td>2.680049</td>\n",
       "      <td>-1.256285</td>\n",
       "      <td>-1.220262</td>\n",
       "      <td>3.649110</td>\n",
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       "      <td>-2.196685</td>\n",
       "      <td>3.758146</td>\n",
       "      <td>2.474789</td>\n",
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       "      <td>2.923555</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>197.560150</td>\n",
       "      <td>-56.235020</td>\n",
       "      <td>167.053986</td>\n",
       "      <td>89.222221</td>\n",
       "      <td>165.007935</td>\n",
       "      <td>-46.307407</td>\n",
       "      <td>140.065323</td>\n",
       "      <td>73.925278</td>\n",
       "      <td>58.558525</td>\n",
       "      <td>7.904080</td>\n",
       "      <td>38.231747</td>\n",
       "      <td>43.645844</td>\n",
       "      <td>24.165867</td>\n",
       "      <td>-7.660753</td>\n",
       "      <td>20.127789</td>\n",
       "      <td>10.962393</td>\n",
       "      <td>31.479214</td>\n",
       "      <td>6.973133</td>\n",
       "      <td>20.029806</td>\n",
       "      <td>23.262056</td>\n",
       "      <td>25.901262</td>\n",
       "      <td>3.065581</td>\n",
       "      <td>17.752800</td>\n",
       "      <td>18.609558</td>\n",
       "      <td>19.532864</td>\n",
       "      <td>2.014424</td>\n",
       "      <td>13.778230</td>\n",
       "      <td>13.698002</td>\n",
       "      <td>15.889723</td>\n",
       "      <td>1.921973</td>\n",
       "      <td>10.279412</td>\n",
       "      <td>11.963403</td>\n",
       "      <td>11.679363</td>\n",
       "      <td>-2.999971</td>\n",
       "      <td>9.845611</td>\n",
       "      <td>5.520113</td>\n",
       "      <td>15.129631</td>\n",
       "      <td>2.799529</td>\n",
       "      <td>9.602891</td>\n",
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       "      <td>-4.385475</td>\n",
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       "      <td>5.414523</td>\n",
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       "      <td>1.402773</td>\n",
       "      <td>7.611049</td>\n",
       "      <td>7.167179</td>\n",
       "      <td>10.266623</td>\n",
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       "      <td>7.162259</td>\n",
       "      <td>7.140145</td>\n",
       "      <td>10.980591</td>\n",
       "      <td>1.992374</td>\n",
       "      <td>7.085339</td>\n",
       "      <td>8.148730</td>\n",
       "      <td>8.134279</td>\n",
       "      <td>-1.721148</td>\n",
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       "      <td>3.951072</td>\n",
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       "      <td>1.322561</td>\n",
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       "      <td>-2.662420</td>\n",
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       "      <td>-4.736222</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
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       "      <td>-158.199081</td>\n",
       "      <td>-190.258362</td>\n",
       "      <td>186.682709</td>\n",
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       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>164.499893</td>\n",
       "      <td>99.829689</td>\n",
       "      <td>114.322830</td>\n",
       "      <td>-63.439232</td>\n",
       "      <td>123.595650</td>\n",
       "      <td>73.272484</td>\n",
       "      <td>87.150879</td>\n",
       "      <td>-48.080688</td>\n",
       "      <td>46.899860</td>\n",
       "      <td>29.951080</td>\n",
       "      <td>30.025049</td>\n",
       "      <td>-20.025631</td>\n",
       "      <td>44.196377</td>\n",
       "      <td>26.861120</td>\n",
       "      <td>30.690706</td>\n",
       "      <td>-17.025875</td>\n",
       "      <td>44.664692</td>\n",
       "      <td>16.855186</td>\n",
       "      <td>30.713501</td>\n",
       "      <td>-27.704121</td>\n",
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       "      <td>18.721317</td>\n",
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       "      <td>31.945690</td>\n",
       "      <td>25.068062</td>\n",
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       "      <td>26.329243</td>\n",
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       "      <td>-12.304070</td>\n",
       "      <td>32.041317</td>\n",
       "      <td>9.733595</td>\n",
       "      <td>22.010416</td>\n",
       "      <td>-21.152889</td>\n",
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       "      <td>15.625027</td>\n",
       "      <td>18.247799</td>\n",
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       "      <td>-13.250886</td>\n",
       "      <td>17.998421</td>\n",
       "      <td>15.480885</td>\n",
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       "      <td>-7.635093</td>\n",
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       "      <td>-4.658664</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>275.454407</td>\n",
       "      <td>-122.148170</td>\n",
       "      <td>245.166122</td>\n",
       "      <td>29.129313</td>\n",
       "      <td>118.976463</td>\n",
       "      <td>-54.020538</td>\n",
       "      <td>103.525024</td>\n",
       "      <td>22.798040</td>\n",
       "      <td>56.767715</td>\n",
       "      <td>-25.233208</td>\n",
       "      <td>50.541958</td>\n",
       "      <td>5.600825</td>\n",
       "      <td>39.765671</td>\n",
       "      <td>-17.675812</td>\n",
       "      <td>35.404541</td>\n",
       "      <td>3.923367</td>\n",
       "      <td>28.905994</td>\n",
       "      <td>-12.309326</td>\n",
       "      <td>25.961252</td>\n",
       "      <td>3.170231</td>\n",
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       "      <td>-7.289474</td>\n",
       "      <td>15.827994</td>\n",
       "      <td>2.166228</td>\n",
       "      <td>15.634098</td>\n",
       "      <td>-6.248994</td>\n",
       "      <td>14.285532</td>\n",
       "      <td>1.139592</td>\n",
       "      <td>13.518690</td>\n",
       "      <td>-4.890047</td>\n",
       "      <td>12.514712</td>\n",
       "      <td>1.491443</td>\n",
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       "      <td>5.872437</td>\n",
       "      <td>1.170002</td>\n",
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       "      <td>4.984735</td>\n",
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       "      <td>-2.154214</td>\n",
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       "      <td>4.855865</td>\n",
       "      <td>-1.840441</td>\n",
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       "      <td>3.889884</td>\n",
       "      <td>0.485834</td>\n",
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       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>195.776382</td>\n",
       "      <td>71.457642</td>\n",
       "      <td>-43.164070</td>\n",
       "      <td>-177.084900</td>\n",
       "      <td>89.740707</td>\n",
       "      <td>31.712599</td>\n",
       "      <td>-42.891129</td>\n",
       "      <td>-72.166870</td>\n",
       "      <td>97.034958</td>\n",
       "      <td>28.485353</td>\n",
       "      <td>-19.710289</td>\n",
       "      <td>-90.641449</td>\n",
       "      <td>105.457581</td>\n",
       "      <td>29.350021</td>\n",
       "      <td>-17.268545</td>\n",
       "      <td>-99.808189</td>\n",
       "      <td>91.525826</td>\n",
       "      <td>26.652744</td>\n",
       "      <td>-18.645784</td>\n",
       "      <td>-85.550819</td>\n",
       "      <td>45.013363</td>\n",
       "      <td>17.892401</td>\n",
       "      <td>-20.705256</td>\n",
       "      <td>-35.740135</td>\n",
       "      <td>67.904793</td>\n",
       "      <td>21.080061</td>\n",
       "      <td>-14.514310</td>\n",
       "      <td>-62.896954</td>\n",
       "      <td>65.139336</td>\n",
       "      <td>19.158308</td>\n",
       "      <td>-13.387456</td>\n",
       "      <td>-60.801876</td>\n",
       "      <td>28.043575</td>\n",
       "      <td>10.094787</td>\n",
       "      <td>-11.583507</td>\n",
       "      <td>-23.459747</td>\n",
       "      <td>33.811947</td>\n",
       "      <td>12.049286</td>\n",
       "      <td>-9.135211</td>\n",
       "      <td>-30.242525</td>\n",
       "      <td>39.968479</td>\n",
       "      <td>11.967908</td>\n",
       "      <td>-7.647948</td>\n",
       "      <td>-37.359837</td>\n",
       "      <td>19.605148</td>\n",
       "      <td>6.826134</td>\n",
       "      <td>-10.283878</td>\n",
       "      <td>-15.231794</td>\n",
       "      <td>19.917049</td>\n",
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       "      <td>-9.450686</td>\n",
       "      <td>-15.656697</td>\n",
       "      <td>26.502373</td>\n",
       "      <td>8.925963</td>\n",
       "      <td>-8.377806</td>\n",
       "      <td>-23.505644</td>\n",
       "      <td>28.139923</td>\n",
       "      <td>10.174318</td>\n",
       "      <td>-6.100360</td>\n",
       "      <td>-25.517134</td>\n",
       "      <td>21.598833</td>\n",
       "      <td>8.947879</td>\n",
       "      <td>-7.567963</td>\n",
       "      <td>-18.143070</td>\n",
       "      <td>32.135963</td>\n",
       "      <td>9.605417</td>\n",
       "      <td>-6.528434</td>\n",
       "      <td>-29.963903</td>\n",
       "      <td>21.106709</td>\n",
       "      <td>7.316864</td>\n",
       "      <td>-8.853605</td>\n",
       "      <td>-17.707916</td>\n",
       "      <td>17.236910</td>\n",
       "      <td>6.328868</td>\n",
       "      <td>-7.247945</td>\n",
       "      <td>-14.301180</td>\n",
       "      <td>22.669622</td>\n",
       "      <td>6.760088</td>\n",
       "      <td>-6.758747</td>\n",
       "      <td>-20.555592</td>\n",
       "      <td>17.584393</td>\n",
       "      <td>6.982410</td>\n",
       "      <td>-5.573163</td>\n",
       "      <td>-15.145845</td>\n",
       "      <td>13.972600</td>\n",
       "      <td>4.864989</td>\n",
       "      <td>-7.329326</td>\n",
       "      <td>-10.855709</td>\n",
       "      <td>14.518909</td>\n",
       "      <td>5.529046</td>\n",
       "      <td>-6.366781</td>\n",
       "      <td>-11.819158</td>\n",
       "      <td>19.141750</td>\n",
       "      <td>6.333881</td>\n",
       "      <td>-5.494456</td>\n",
       "      <td>-17.207541</td>\n",
       "      <td>14.319798</td>\n",
       "      <td>6.128025</td>\n",
       "      <td>-4.859442</td>\n",
       "      <td>-11.995406</td>\n",
       "      <td>18.058144</td>\n",
       "      <td>5.734624</td>\n",
       "      <td>-5.234973</td>\n",
       "      <td>-16.303547</td>\n",
       "      <td>15.012374</td>\n",
       "      <td>5.689663</td>\n",
       "      <td>-3.815546</td>\n",
       "      <td>-13.358171</td>\n",
       "      <td>16.057026</td>\n",
       "      <td>5.201401</td>\n",
       "      <td>-3.606006</td>\n",
       "      <td>-14.757041</td>\n",
       "      <td>14.916764</td>\n",
       "      <td>5.126918</td>\n",
       "      <td>-3.422858</td>\n",
       "      <td>-13.583395</td>\n",
       "      <td>10.874345</td>\n",
       "      <td>4.409315</td>\n",
       "      <td>-3.699378</td>\n",
       "      <td>-9.226262</td>\n",
       "      <td>9.346753</td>\n",
       "      <td>3.026163</td>\n",
       "      <td>-4.479315</td>\n",
       "      <td>-7.624949</td>\n",
       "      <td>11.745160</td>\n",
       "      <td>4.989849</td>\n",
       "      <td>-0.893933</td>\n",
       "      <td>-10.594861</td>\n",
       "      <td>11.756345</td>\n",
       "      <td>4.166164</td>\n",
       "      <td>-1.612040</td>\n",
       "      <td>-10.874559</td>\n",
       "      <td>7.894176</td>\n",
       "      <td>3.271113</td>\n",
       "      <td>-3.024977</td>\n",
       "      <td>-6.516698</td>\n",
       "      <td>9.953744</td>\n",
       "      <td>2.944449</td>\n",
       "      <td>-3.067981</td>\n",
       "      <td>-8.999707</td>\n",
       "      <td>11.413699</td>\n",
       "      <td>3.805331</td>\n",
       "      <td>-1.026229</td>\n",
       "      <td>-10.711622</td>\n",
       "      <td>8.001363</td>\n",
       "      <td>2.741758</td>\n",
       "      <td>-2.334764</td>\n",
       "      <td>-7.145170</td>\n",
       "      <td>8.111948</td>\n",
       "      <td>3.066202</td>\n",
       "      <td>-1.367840</td>\n",
       "      <td>-7.384519</td>\n",
       "      <td>8.008175</td>\n",
       "      <td>2.509926</td>\n",
       "      <td>-2.168585</td>\n",
       "      <td>-7.288922</td>\n",
       "      <td>9.635747</td>\n",
       "      <td>3.264674</td>\n",
       "      <td>-0.398368</td>\n",
       "      <td>-9.057087</td>\n",
       "      <td>6.581693</td>\n",
       "      <td>2.098787</td>\n",
       "      <td>-2.274143</td>\n",
       "      <td>-5.808791</td>\n",
       "      <td>6.415633</td>\n",
       "      <td>2.281583</td>\n",
       "      <td>-1.853963</td>\n",
       "      <td>-5.702415</td>\n",
       "      <td>5.414214</td>\n",
       "      <td>2.242979</td>\n",
       "      <td>-1.897073</td>\n",
       "      <td>-4.547952</td>\n",
       "      <td>6.342005</td>\n",
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       "      <td>-5.663373</td>\n",
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       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>59.403610</td>\n",
       "      <td>41.055508</td>\n",
       "      <td>-33.719429</td>\n",
       "      <td>-26.575066</td>\n",
       "      <td>48.023834</td>\n",
       "      <td>40.540417</td>\n",
       "      <td>-25.325750</td>\n",
       "      <td>-4.622713</td>\n",
       "      <td>47.623581</td>\n",
       "      <td>40.172688</td>\n",
       "      <td>-25.056154</td>\n",
       "      <td>-5.133194</td>\n",
       "      <td>35.076084</td>\n",
       "      <td>34.462933</td>\n",
       "      <td>-4.700911</td>\n",
       "      <td>-4.532028</td>\n",
       "      <td>35.169415</td>\n",
       "      <td>24.306574</td>\n",
       "      <td>-19.963308</td>\n",
       "      <td>-15.733547</td>\n",
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       "      <td>-13.533061</td>\n",
       "      <td>-0.527802</td>\n",
       "      <td>22.762016</td>\n",
       "      <td>21.673370</td>\n",
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       "      <td>-2.388879</td>\n",
       "      <td>21.087252</td>\n",
       "      <td>17.847937</td>\n",
       "      <td>-11.186087</td>\n",
       "      <td>-0.997427</td>\n",
       "      <td>18.204227</td>\n",
       "      <td>17.811428</td>\n",
       "      <td>-2.865510</td>\n",
       "      <td>-2.436343</td>\n",
       "      <td>17.363245</td>\n",
       "      <td>16.520151</td>\n",
       "      <td>-4.841825</td>\n",
       "      <td>-2.263539</td>\n",
       "      <td>15.720620</td>\n",
       "      <td>12.664824</td>\n",
       "      <td>-9.306363</td>\n",
       "      <td>-0.362957</td>\n",
       "      <td>14.507853</td>\n",
       "      <td>10.184656</td>\n",
       "      <td>-8.142515</td>\n",
       "      <td>-6.360033</td>\n",
       "      <td>13.173553</td>\n",
       "      <td>11.744920</td>\n",
       "      <td>-5.335850</td>\n",
       "      <td>-2.669840</td>\n",
       "      <td>12.037468</td>\n",
       "      <td>11.905970</td>\n",
       "      <td>-1.162715</td>\n",
       "      <td>-1.340377</td>\n",
       "      <td>11.400192</td>\n",
       "      <td>9.603645</td>\n",
       "      <td>-6.033511</td>\n",
       "      <td>-1.153745</td>\n",
       "      <td>10.687634</td>\n",
       "      <td>9.820236</td>\n",
       "      <td>-4.214749</td>\n",
       "      <td>-0.156130</td>\n",
       "      <td>10.765874</td>\n",
       "      <td>8.830809</td>\n",
       "      <td>-5.947473</td>\n",
       "      <td>-1.596380</td>\n",
       "      <td>9.998008</td>\n",
       "      <td>9.060877</td>\n",
       "      <td>-3.770721</td>\n",
       "      <td>-1.908486</td>\n",
       "      <td>10.647401</td>\n",
       "      <td>7.320719</td>\n",
       "      <td>-6.443269</td>\n",
       "      <td>-4.272997</td>\n",
       "      <td>9.769657</td>\n",
       "      <td>8.575953</td>\n",
       "      <td>-4.528944</td>\n",
       "      <td>-1.178091</td>\n",
       "      <td>9.726794</td>\n",
       "      <td>9.184681</td>\n",
       "      <td>-2.947534</td>\n",
       "      <td>-1.250682</td>\n",
       "      <td>8.962761</td>\n",
       "      <td>7.351788</td>\n",
       "      <td>-4.951365</td>\n",
       "      <td>-1.329011</td>\n",
       "      <td>9.045572</td>\n",
       "      <td>5.860114</td>\n",
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       "      <td>-4.104985</td>\n",
       "      <td>7.799853</td>\n",
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       "      <td>-3.384279</td>\n",
       "      <td>-1.337398</td>\n",
       "      <td>7.589919</td>\n",
       "      <td>7.217942</td>\n",
       "      <td>-2.322251</td>\n",
       "      <td>-0.339617</td>\n",
       "      <td>6.618104</td>\n",
       "      <td>6.475303</td>\n",
       "      <td>-1.041749</td>\n",
       "      <td>-0.885727</td>\n",
       "      <td>6.445922</td>\n",
       "      <td>5.841820</td>\n",
       "      <td>-2.608860</td>\n",
       "      <td>-0.785435</td>\n",
       "      <td>6.303173</td>\n",
       "      <td>5.880459</td>\n",
       "      <td>-2.012818</td>\n",
       "      <td>-1.048216</td>\n",
       "      <td>6.115631</td>\n",
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       "      <td>-2.389849</td>\n",
       "      <td>-0.387172</td>\n",
       "      <td>6.016768</td>\n",
       "      <td>5.741394</td>\n",
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       "      <td>-0.507951</td>\n",
       "      <td>6.582354</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>151.784470</td>\n",
       "      <td>0.949546</td>\n",
       "      <td>131.392471</td>\n",
       "      <td>75.984489</td>\n",
       "      <td>106.406952</td>\n",
       "      <td>0.097951</td>\n",
       "      <td>92.315750</td>\n",
       "      <td>52.917225</td>\n",
       "      <td>73.209137</td>\n",
       "      <td>1.746257</td>\n",
       "      <td>63.050304</td>\n",
       "      <td>37.164330</td>\n",
       "      <td>73.091263</td>\n",
       "      <td>1.297367</td>\n",
       "      <td>61.928951</td>\n",
       "      <td>38.800182</td>\n",
       "      <td>53.414776</td>\n",
       "      <td>0.531225</td>\n",
       "      <td>45.820644</td>\n",
       "      <td>27.446762</td>\n",
       "      <td>35.558651</td>\n",
       "      <td>0.306147</td>\n",
       "      <td>30.661337</td>\n",
       "      <td>18.005730</td>\n",
       "      <td>27.954166</td>\n",
       "      <td>-0.050373</td>\n",
       "      <td>23.910858</td>\n",
       "      <td>14.481151</td>\n",
       "      <td>14.535252</td>\n",
       "      <td>-0.025319</td>\n",
       "      <td>12.635176</td>\n",
       "      <td>7.185069</td>\n",
       "      <td>14.017663</td>\n",
       "      <td>0.100577</td>\n",
       "      <td>11.907260</td>\n",
       "      <td>7.396075</td>\n",
       "      <td>16.027166</td>\n",
       "      <td>0.939310</td>\n",
       "      <td>11.593787</td>\n",
       "      <td>11.025963</td>\n",
       "      <td>12.076696</td>\n",
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       "      <td>10.127374</td>\n",
       "      <td>6.565596</td>\n",
       "      <td>14.812226</td>\n",
       "      <td>0.261285</td>\n",
       "      <td>9.948937</td>\n",
       "      <td>10.970526</td>\n",
       "      <td>9.939997</td>\n",
       "      <td>0.096975</td>\n",
       "      <td>8.514777</td>\n",
       "      <td>5.127642</td>\n",
       "      <td>9.104223</td>\n",
       "      <td>-0.080639</td>\n",
       "      <td>7.039525</td>\n",
       "      <td>5.772820</td>\n",
       "      <td>7.128007</td>\n",
       "      <td>0.364237</td>\n",
       "      <td>6.171385</td>\n",
       "      <td>3.548216</td>\n",
       "      <td>8.472843</td>\n",
       "      <td>0.282425</td>\n",
       "      <td>5.559115</td>\n",
       "      <td>6.387922</td>\n",
       "      <td>6.245513</td>\n",
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       "      <td>5.436501</td>\n",
       "      <td>3.069250</td>\n",
       "      <td>5.853168</td>\n",
       "      <td>0.487733</td>\n",
       "      <td>4.812369</td>\n",
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       "      <td>6.324660</td>\n",
       "      <td>-0.116454</td>\n",
       "      <td>4.811591</td>\n",
       "      <td>4.103212</td>\n",
       "      <td>4.871553</td>\n",
       "      <td>0.481108</td>\n",
       "      <td>4.298071</td>\n",
       "      <td>2.242130</td>\n",
       "      <td>5.296984</td>\n",
       "      <td>0.249718</td>\n",
       "      <td>4.235509</td>\n",
       "      <td>3.171141</td>\n",
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       "      <td>3.596556</td>\n",
       "      <td>5.233563</td>\n",
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       "      <td>3.384312</td>\n",
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       "      <td>3.254965</td>\n",
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    "This looks like the format we want: we have a matrix of numerical features encoded in the 4-vectors, along with a target denoted by the `is_signal_new` column."
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  {
   "cell_type": "markdown",
   "id": "b94bdc16-7c76-4504-8783-0802b756d85a",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Create a Learner"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e8da4e7-482c-41a0-85d4-409332091774",
   "metadata": {},
   "source": [
    "We can now create the `Learner` for this data. fastai provides various application-specific learner classes, each of which come with a set of good defaults for training. In our case, we'll use the `tabular_learner` class:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "c2260657-e576-43c9-b8dc-7a9bac376e06",
   "metadata": {},
   "outputs": [],
   "source": [
    "learn = tabular_learner(\n",
    "    dls, layers=[200, 200, 50, 50], metrics=[accuracy, RocAucBinary()]\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "606cad43-2d4a-4040-89eb-6941d725cee3",
   "metadata": {},
   "source": [
    "By default, `tabular_learner` creates a neural network with two hidden layers and 200 and 100 activations each. This works great for small datasets, but since our dataset is quite large, we've increased the depth of the network by adding two more layers. This also matches the architecture chosen in Section 3.2.2 of [_The Machine Learning Landscape of Top Taggers_](https://arxiv.org/abs/1902.09914) review that we'll compare to later.\n",
    "\n",
    "We've also provided two common classification metrics to track during training: accuracy and the Area Under the ROC Curve (ROC AUC). We'll look at ROC AUC in more detail later, so for now let's take a look at our network with the `summary()` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "0527cd48-316a-494f-8ff1-9efc7e153fd6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "    /* Turns off some styling */\n",
       "    progress {\n",
       "        /* gets rid of default border in Firefox and Opera. */\n",
       "        border: none;\n",
       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "        background-size: auto;\n",
       "    }\n",
       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
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       "    }\n",
       "</style>\n"
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     "data": {
      "text/plain": [
       "TabularModel (Input shape: 1024 x 0)\n",
       "============================================================================\n",
       "Layer (type)         Output Shape         Param #    Trainable \n",
       "============================================================================\n",
       "                     1024 x 800          \n",
       "BatchNorm1d                               1600       True      \n",
       "____________________________________________________________________________\n",
       "                     1024 x 200          \n",
       "Linear                                    160000     True      \n",
       "ReLU                                                           \n",
       "BatchNorm1d                               400        True      \n",
       "Linear                                    40000      True      \n",
       "ReLU                                                           \n",
       "BatchNorm1d                               400        True      \n",
       "____________________________________________________________________________\n",
       "                     1024 x 50           \n",
       "Linear                                    10000      True      \n",
       "ReLU                                                           \n",
       "BatchNorm1d                               100        True      \n",
       "Linear                                    2500       True      \n",
       "ReLU                                                           \n",
       "BatchNorm1d                               100        True      \n",
       "____________________________________________________________________________\n",
       "                     1024 x 2            \n",
       "Linear                                    102        True      \n",
       "____________________________________________________________________________\n",
       "\n",
       "Total params: 215,202\n",
       "Total trainable params: 215,202\n",
       "Total non-trainable params: 0\n",
       "\n",
       "Optimizer used: <function Adam at 0x7faa1ad5e790>\n",
       "Loss function: FlattenedLoss of CrossEntropyLoss()\n",
       "\n",
       "Callbacks:\n",
       "  - TrainEvalCallback\n",
       "  - Recorder\n",
       "  - ProgressCallback"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "learn.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6257d53c-30e0-4739-a634-8441fb36bb91",
   "metadata": {},
   "source": [
    "Here we can see that this particular network has around 215,000 parameters - although this sounds like a lot, it's actually a very small model by modern standards (e.g. in natural language processing, some models have hundreds of billions of parameters!)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a822240-e8c5-4560-88e5-cccae83d7a9a",
   "metadata": {},
   "source": [
    "### Find a good learning rate"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d142f032-6764-4d67-91cc-ce56c88f64d7",
   "metadata": {},
   "source": [
    "The learning rate is one of the most important hyperparameters involved in training neural networks, so it's important to make sure you've picked a good one. We'll see in the next lesson exactly how this parameter impacts training, but for now it is enough to know that:\n",
    "\n",
    "* If our learning rate is too low, it will take a long time to train the model and there is a good chance of overfitting.\n",
    "* If our learning rate is too high, the training process can diverge.\n",
    "\n",
    "To handle these two extremes, fastai provides a _learning rate finder_ that tracks the loss as we increase the learning rate. You can see this in action by using the `lr_find()` method of any `Learner`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "f1cd3ea0-df09-43e0-82a0-1db33bdc29a4",
   "metadata": {},
   "outputs": [
    {
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       "\n",
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       "    progress {\n",
       "        /* gets rid of default border in Firefox and Opera. */\n",
       "        border: none;\n",
       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "        background-size: auto;\n",
       "    }\n",
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    {
     "data": {
      "text/plain": [
       "SuggestedLRs(valley=0.0006918309954926372)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "learn.lr_find()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5aac905b-9bd3-460e-bf79-70c806d9ccf4",
   "metadata": {},
   "source": [
    "From this curve we can see that the loss hits a minimum around a learning rate of $3 \\times 10^{-1}$, so we should select a learning rate lower than this point. The `lr_find()` method provides a handy heuristic to pick the learning rate 1-2 orders of magnitude less than the minimum, as indicated by the orange dot. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "766ad957-ff12-4cd5-b2b8-6aa35c9b9450",
   "metadata": {},
   "source": [
    "### Train your model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af6b834e-e597-49f4-bfb7-30c48ac0b29d",
   "metadata": {},
   "source": [
    "In the above learning rate plot, it appears a learning rate of around $10^{-3}$ would be good, so let's choose that and train our models for 3 epochs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "55669c54-12f5-4a76-a4b6-88c31fc6895a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "    /* Turns off some styling */\n",
       "    progress {\n",
       "        /* gets rid of default border in Firefox and Opera. */\n",
       "        border: none;\n",
       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "        background-size: auto;\n",
       "    }\n",
       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "        background: #F44336;\n",
       "    }\n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>accuracy</th>\n",
       "      <th>roc_auc_score</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0.512565</td>\n",
       "      <td>0.511615</td>\n",
       "      <td>0.732775</td>\n",
       "      <td>0.809289</td>\n",
       "      <td>00:20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>0.419058</td>\n",
       "      <td>0.404574</td>\n",
       "      <td>0.810632</td>\n",
       "      <td>0.891700</td>\n",
       "      <td>00:20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>0.381482</td>\n",
       "      <td>0.372323</td>\n",
       "      <td>0.830776</td>\n",
       "      <td>0.907655</td>\n",
       "      <td>00:20</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "learn.fit_one_cycle(n_epoch=3, lr_max=1e-3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e630b0a-7ae9-4f77-b0e3-291f976e73e8",
   "metadata": {},
   "source": [
    "Once the model is trained, we can view the results in various ways. A simple approach is to use the `show_results()` method to compare the model errors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "4949435c-9b95-4bad-8c9f-bfc2f1306494",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "    /* Turns off some styling */\n",
       "    progress {\n",
       "        /* gets rid of default border in Firefox and Opera. */\n",
       "        border: none;\n",
       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "        background-size: auto;\n",
       "    }\n",
       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "        background: #F44336;\n",
       "    }\n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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     "metadata": {},
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       "      <th>PY_3</th>\n",
       "      <th>PZ_3</th>\n",
       "      <th>E_4</th>\n",
       "      <th>PX_4</th>\n",
       "      <th>PY_4</th>\n",
       "      <th>PZ_4</th>\n",
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       "      <th>PY_5</th>\n",
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       "      <th>PX_14</th>\n",
       "      <th>PY_14</th>\n",
       "      <th>PZ_14</th>\n",
       "      <th>E_15</th>\n",
       "      <th>PX_15</th>\n",
       "      <th>PY_15</th>\n",
       "      <th>PZ_15</th>\n",
       "      <th>E_16</th>\n",
       "      <th>PX_16</th>\n",
       "      <th>PY_16</th>\n",
       "      <th>PZ_16</th>\n",
       "      <th>E_17</th>\n",
       "      <th>PX_17</th>\n",
       "      <th>PY_17</th>\n",
       "      <th>PZ_17</th>\n",
       "      <th>E_18</th>\n",
       "      <th>PX_18</th>\n",
       "      <th>PY_18</th>\n",
       "      <th>PZ_18</th>\n",
       "      <th>E_19</th>\n",
       "      <th>PX_19</th>\n",
       "      <th>PY_19</th>\n",
       "      <th>PZ_19</th>\n",
       "      <th>E_20</th>\n",
       "      <th>PX_20</th>\n",
       "      <th>PY_20</th>\n",
       "      <th>PZ_20</th>\n",
       "      <th>E_21</th>\n",
       "      <th>PX_21</th>\n",
       "      <th>PY_21</th>\n",
       "      <th>PZ_21</th>\n",
       "      <th>E_22</th>\n",
       "      <th>PX_22</th>\n",
       "      <th>PY_22</th>\n",
       "      <th>PZ_22</th>\n",
       "      <th>E_23</th>\n",
       "      <th>PX_23</th>\n",
       "      <th>PY_23</th>\n",
       "      <th>PZ_23</th>\n",
       "      <th>E_24</th>\n",
       "      <th>PX_24</th>\n",
       "      <th>PY_24</th>\n",
       "      <th>PZ_24</th>\n",
       "      <th>E_25</th>\n",
       "      <th>PX_25</th>\n",
       "      <th>PY_25</th>\n",
       "      <th>PZ_25</th>\n",
       "      <th>E_26</th>\n",
       "      <th>PX_26</th>\n",
       "      <th>PY_26</th>\n",
       "      <th>PZ_26</th>\n",
       "      <th>E_27</th>\n",
       "      <th>PX_27</th>\n",
       "      <th>PY_27</th>\n",
       "      <th>PZ_27</th>\n",
       "      <th>E_28</th>\n",
       "      <th>PX_28</th>\n",
       "      <th>PY_28</th>\n",
       "      <th>PZ_28</th>\n",
       "      <th>E_29</th>\n",
       "      <th>PX_29</th>\n",
       "      <th>PY_29</th>\n",
       "      <th>PZ_29</th>\n",
       "      <th>E_30</th>\n",
       "      <th>PX_30</th>\n",
       "      <th>PY_30</th>\n",
       "      <th>PZ_30</th>\n",
       "      <th>E_31</th>\n",
       "      <th>PX_31</th>\n",
       "      <th>PY_31</th>\n",
       "      <th>PZ_31</th>\n",
       "      <th>E_32</th>\n",
       "      <th>PX_32</th>\n",
       "      <th>PY_32</th>\n",
       "      <th>PZ_32</th>\n",
       "      <th>E_33</th>\n",
       "      <th>PX_33</th>\n",
       "      <th>PY_33</th>\n",
       "      <th>PZ_33</th>\n",
       "      <th>E_34</th>\n",
       "      <th>PX_34</th>\n",
       "      <th>PY_34</th>\n",
       "      <th>PZ_34</th>\n",
       "      <th>E_35</th>\n",
       "      <th>PX_35</th>\n",
       "      <th>PY_35</th>\n",
       "      <th>PZ_35</th>\n",
       "      <th>E_36</th>\n",
       "      <th>PX_36</th>\n",
       "      <th>PY_36</th>\n",
       "      <th>PZ_36</th>\n",
       "      <th>E_37</th>\n",
       "      <th>PX_37</th>\n",
       "      <th>PY_37</th>\n",
       "      <th>PZ_37</th>\n",
       "      <th>E_38</th>\n",
       "      <th>PX_38</th>\n",
       "      <th>PY_38</th>\n",
       "      <th>PZ_38</th>\n",
       "      <th>E_39</th>\n",
       "      <th>PX_39</th>\n",
       "      <th>PY_39</th>\n",
       "      <th>PZ_39</th>\n",
       "      <th>E_40</th>\n",
       "      <th>PX_40</th>\n",
       "      <th>PY_40</th>\n",
       "      <th>PZ_40</th>\n",
       "      <th>E_41</th>\n",
       "      <th>PX_41</th>\n",
       "      <th>PY_41</th>\n",
       "      <th>PZ_41</th>\n",
       "      <th>E_42</th>\n",
       "      <th>PX_42</th>\n",
       "      <th>PY_42</th>\n",
       "      <th>PZ_42</th>\n",
       "      <th>E_43</th>\n",
       "      <th>PX_43</th>\n",
       "      <th>PY_43</th>\n",
       "      <th>PZ_43</th>\n",
       "      <th>E_44</th>\n",
       "      <th>PX_44</th>\n",
       "      <th>PY_44</th>\n",
       "      <th>PZ_44</th>\n",
       "      <th>E_45</th>\n",
       "      <th>PX_45</th>\n",
       "      <th>PY_45</th>\n",
       "      <th>PZ_45</th>\n",
       "      <th>E_46</th>\n",
       "      <th>PX_46</th>\n",
       "      <th>PY_46</th>\n",
       "      <th>PZ_46</th>\n",
       "      <th>E_47</th>\n",
       "      <th>PX_47</th>\n",
       "      <th>PY_47</th>\n",
       "      <th>PZ_47</th>\n",
       "      <th>E_48</th>\n",
       "      <th>PX_48</th>\n",
       "      <th>PY_48</th>\n",
       "      <th>PZ_48</th>\n",
       "      <th>E_49</th>\n",
       "      <th>PX_49</th>\n",
       "      <th>PY_49</th>\n",
       "      <th>PZ_49</th>\n",
       "      <th>E_50</th>\n",
       "      <th>PX_50</th>\n",
       "      <th>PY_50</th>\n",
       "      <th>PZ_50</th>\n",
       "      <th>E_51</th>\n",
       "      <th>PX_51</th>\n",
       "      <th>PY_51</th>\n",
       "      <th>PZ_51</th>\n",
       "      <th>E_52</th>\n",
       "      <th>PX_52</th>\n",
       "      <th>PY_52</th>\n",
       "      <th>PZ_52</th>\n",
       "      <th>E_53</th>\n",
       "      <th>PX_53</th>\n",
       "      <th>PY_53</th>\n",
       "      <th>PZ_53</th>\n",
       "      <th>E_54</th>\n",
       "      <th>PX_54</th>\n",
       "      <th>PY_54</th>\n",
       "      <th>PZ_54</th>\n",
       "      <th>E_55</th>\n",
       "      <th>PX_55</th>\n",
       "      <th>PY_55</th>\n",
       "      <th>PZ_55</th>\n",
       "      <th>E_56</th>\n",
       "      <th>PX_56</th>\n",
       "      <th>PY_56</th>\n",
       "      <th>PZ_56</th>\n",
       "      <th>E_57</th>\n",
       "      <th>PX_57</th>\n",
       "      <th>PY_57</th>\n",
       "      <th>PZ_57</th>\n",
       "      <th>E_58</th>\n",
       "      <th>PX_58</th>\n",
       "      <th>PY_58</th>\n",
       "      <th>PZ_58</th>\n",
       "      <th>E_59</th>\n",
       "      <th>PX_59</th>\n",
       "      <th>PY_59</th>\n",
       "      <th>PZ_59</th>\n",
       "      <th>E_60</th>\n",
       "      <th>PX_60</th>\n",
       "      <th>PY_60</th>\n",
       "      <th>PZ_60</th>\n",
       "      <th>E_61</th>\n",
       "      <th>PX_61</th>\n",
       "      <th>PY_61</th>\n",
       "      <th>PZ_61</th>\n",
       "      <th>E_62</th>\n",
       "      <th>PX_62</th>\n",
       "      <th>PY_62</th>\n",
       "      <th>PZ_62</th>\n",
       "      <th>E_63</th>\n",
       "      <th>PX_63</th>\n",
       "      <th>PY_63</th>\n",
       "      <th>PZ_63</th>\n",
       "      <th>E_64</th>\n",
       "      <th>PX_64</th>\n",
       "      <th>PY_64</th>\n",
       "      <th>PZ_64</th>\n",
       "      <th>E_65</th>\n",
       "      <th>PX_65</th>\n",
       "      <th>PY_65</th>\n",
       "      <th>PZ_65</th>\n",
       "      <th>E_66</th>\n",
       "      <th>PX_66</th>\n",
       "      <th>PY_66</th>\n",
       "      <th>PZ_66</th>\n",
       "      <th>E_67</th>\n",
       "      <th>PX_67</th>\n",
       "      <th>PY_67</th>\n",
       "      <th>PZ_67</th>\n",
       "      <th>E_68</th>\n",
       "      <th>PX_68</th>\n",
       "      <th>PY_68</th>\n",
       "      <th>PZ_68</th>\n",
       "      <th>E_69</th>\n",
       "      <th>PX_69</th>\n",
       "      <th>PY_69</th>\n",
       "      <th>PZ_69</th>\n",
       "      <th>E_70</th>\n",
       "      <th>PX_70</th>\n",
       "      <th>PY_70</th>\n",
       "      <th>PZ_70</th>\n",
       "      <th>E_71</th>\n",
       "      <th>PX_71</th>\n",
       "      <th>PY_71</th>\n",
       "      <th>PZ_71</th>\n",
       "      <th>E_72</th>\n",
       "      <th>PX_72</th>\n",
       "      <th>PY_72</th>\n",
       "      <th>PZ_72</th>\n",
       "      <th>E_73</th>\n",
       "      <th>PX_73</th>\n",
       "      <th>PY_73</th>\n",
       "      <th>PZ_73</th>\n",
       "      <th>E_74</th>\n",
       "      <th>PX_74</th>\n",
       "      <th>PY_74</th>\n",
       "      <th>PZ_74</th>\n",
       "      <th>E_75</th>\n",
       "      <th>PX_75</th>\n",
       "      <th>PY_75</th>\n",
       "      <th>PZ_75</th>\n",
       "      <th>E_76</th>\n",
       "      <th>PX_76</th>\n",
       "      <th>PY_76</th>\n",
       "      <th>PZ_76</th>\n",
       "      <th>E_77</th>\n",
       "      <th>PX_77</th>\n",
       "      <th>PY_77</th>\n",
       "      <th>PZ_77</th>\n",
       "      <th>E_78</th>\n",
       "      <th>PX_78</th>\n",
       "      <th>PY_78</th>\n",
       "      <th>PZ_78</th>\n",
       "      <th>E_79</th>\n",
       "      <th>PX_79</th>\n",
       "      <th>PY_79</th>\n",
       "      <th>PZ_79</th>\n",
       "      <th>E_80</th>\n",
       "      <th>PX_80</th>\n",
       "      <th>PY_80</th>\n",
       "      <th>PZ_80</th>\n",
       "      <th>E_81</th>\n",
       "      <th>PX_81</th>\n",
       "      <th>PY_81</th>\n",
       "      <th>PZ_81</th>\n",
       "      <th>E_82</th>\n",
       "      <th>PX_82</th>\n",
       "      <th>PY_82</th>\n",
       "      <th>PZ_82</th>\n",
       "      <th>E_83</th>\n",
       "      <th>PX_83</th>\n",
       "      <th>PY_83</th>\n",
       "      <th>PZ_83</th>\n",
       "      <th>E_84</th>\n",
       "      <th>PX_84</th>\n",
       "      <th>PY_84</th>\n",
       "      <th>PZ_84</th>\n",
       "      <th>E_85</th>\n",
       "      <th>PX_85</th>\n",
       "      <th>PY_85</th>\n",
       "      <th>PZ_85</th>\n",
       "      <th>E_86</th>\n",
       "      <th>PX_86</th>\n",
       "      <th>PY_86</th>\n",
       "      <th>PZ_86</th>\n",
       "      <th>E_87</th>\n",
       "      <th>PX_87</th>\n",
       "      <th>PY_87</th>\n",
       "      <th>PZ_87</th>\n",
       "      <th>E_88</th>\n",
       "      <th>PX_88</th>\n",
       "      <th>PY_88</th>\n",
       "      <th>PZ_88</th>\n",
       "      <th>E_89</th>\n",
       "      <th>PX_89</th>\n",
       "      <th>PY_89</th>\n",
       "      <th>PZ_89</th>\n",
       "      <th>E_90</th>\n",
       "      <th>PX_90</th>\n",
       "      <th>PY_90</th>\n",
       "      <th>PZ_90</th>\n",
       "      <th>E_91</th>\n",
       "      <th>PX_91</th>\n",
       "      <th>PY_91</th>\n",
       "      <th>PZ_91</th>\n",
       "      <th>E_92</th>\n",
       "      <th>PX_92</th>\n",
       "      <th>PY_92</th>\n",
       "      <th>PZ_92</th>\n",
       "      <th>E_93</th>\n",
       "      <th>PX_93</th>\n",
       "      <th>PY_93</th>\n",
       "      <th>PZ_93</th>\n",
       "      <th>E_94</th>\n",
       "      <th>PX_94</th>\n",
       "      <th>PY_94</th>\n",
       "      <th>PZ_94</th>\n",
       "      <th>E_95</th>\n",
       "      <th>PX_95</th>\n",
       "      <th>PY_95</th>\n",
       "      <th>PZ_95</th>\n",
       "      <th>E_96</th>\n",
       "      <th>PX_96</th>\n",
       "      <th>PY_96</th>\n",
       "      <th>PZ_96</th>\n",
       "      <th>E_97</th>\n",
       "      <th>PX_97</th>\n",
       "      <th>PY_97</th>\n",
       "      <th>PZ_97</th>\n",
       "      <th>E_98</th>\n",
       "      <th>PX_98</th>\n",
       "      <th>PY_98</th>\n",
       "      <th>PZ_98</th>\n",
       "      <th>E_99</th>\n",
       "      <th>PX_99</th>\n",
       "      <th>PY_99</th>\n",
       "      <th>PZ_99</th>\n",
       "      <th>E_100</th>\n",
       "      <th>PX_100</th>\n",
       "      <th>PY_100</th>\n",
       "      <th>PZ_100</th>\n",
       "      <th>E_101</th>\n",
       "      <th>PX_101</th>\n",
       "      <th>PY_101</th>\n",
       "      <th>PZ_101</th>\n",
       "      <th>E_102</th>\n",
       "      <th>PX_102</th>\n",
       "      <th>PY_102</th>\n",
       "      <th>PZ_102</th>\n",
       "      <th>E_103</th>\n",
       "      <th>PX_103</th>\n",
       "      <th>PY_103</th>\n",
       "      <th>PZ_103</th>\n",
       "      <th>E_104</th>\n",
       "      <th>PX_104</th>\n",
       "      <th>PY_104</th>\n",
       "      <th>PZ_104</th>\n",
       "      <th>E_105</th>\n",
       "      <th>PX_105</th>\n",
       "      <th>PY_105</th>\n",
       "      <th>PZ_105</th>\n",
       "      <th>E_106</th>\n",
       "      <th>PX_106</th>\n",
       "      <th>PY_106</th>\n",
       "      <th>PZ_106</th>\n",
       "      <th>E_107</th>\n",
       "      <th>PX_107</th>\n",
       "      <th>PY_107</th>\n",
       "      <th>PZ_107</th>\n",
       "      <th>E_108</th>\n",
       "      <th>PX_108</th>\n",
       "      <th>PY_108</th>\n",
       "      <th>PZ_108</th>\n",
       "      <th>E_109</th>\n",
       "      <th>PX_109</th>\n",
       "      <th>PY_109</th>\n",
       "      <th>PZ_109</th>\n",
       "      <th>E_110</th>\n",
       "      <th>PX_110</th>\n",
       "      <th>PY_110</th>\n",
       "      <th>PZ_110</th>\n",
       "      <th>E_111</th>\n",
       "      <th>PX_111</th>\n",
       "      <th>PY_111</th>\n",
       "      <th>PZ_111</th>\n",
       "      <th>E_112</th>\n",
       "      <th>PX_112</th>\n",
       "      <th>PY_112</th>\n",
       "      <th>PZ_112</th>\n",
       "      <th>E_113</th>\n",
       "      <th>PX_113</th>\n",
       "      <th>PY_113</th>\n",
       "      <th>PZ_113</th>\n",
       "      <th>E_114</th>\n",
       "      <th>PX_114</th>\n",
       "      <th>PY_114</th>\n",
       "      <th>PZ_114</th>\n",
       "      <th>E_115</th>\n",
       "      <th>PX_115</th>\n",
       "      <th>PY_115</th>\n",
       "      <th>PZ_115</th>\n",
       "      <th>E_116</th>\n",
       "      <th>PX_116</th>\n",
       "      <th>PY_116</th>\n",
       "      <th>PZ_116</th>\n",
       "      <th>E_117</th>\n",
       "      <th>PX_117</th>\n",
       "      <th>PY_117</th>\n",
       "      <th>PZ_117</th>\n",
       "      <th>E_118</th>\n",
       "      <th>PX_118</th>\n",
       "      <th>PY_118</th>\n",
       "      <th>PZ_118</th>\n",
       "      <th>E_119</th>\n",
       "      <th>PX_119</th>\n",
       "      <th>PY_119</th>\n",
       "      <th>PZ_119</th>\n",
       "      <th>E_120</th>\n",
       "      <th>PX_120</th>\n",
       "      <th>PY_120</th>\n",
       "      <th>PZ_120</th>\n",
       "      <th>E_121</th>\n",
       "      <th>PX_121</th>\n",
       "      <th>PY_121</th>\n",
       "      <th>PZ_121</th>\n",
       "      <th>E_122</th>\n",
       "      <th>PX_122</th>\n",
       "      <th>PY_122</th>\n",
       "      <th>PZ_122</th>\n",
       "      <th>E_123</th>\n",
       "      <th>PX_123</th>\n",
       "      <th>PY_123</th>\n",
       "      <th>PZ_123</th>\n",
       "      <th>E_124</th>\n",
       "      <th>PX_124</th>\n",
       "      <th>PY_124</th>\n",
       "      <th>PZ_124</th>\n",
       "      <th>E_125</th>\n",
       "      <th>PX_125</th>\n",
       "      <th>PY_125</th>\n",
       "      <th>PZ_125</th>\n",
       "      <th>E_126</th>\n",
       "      <th>PX_126</th>\n",
       "      <th>PY_126</th>\n",
       "      <th>PZ_126</th>\n",
       "      <th>E_127</th>\n",
       "      <th>PX_127</th>\n",
       "      <th>PY_127</th>\n",
       "      <th>PZ_127</th>\n",
       "      <th>E_128</th>\n",
       "      <th>PX_128</th>\n",
       "      <th>PY_128</th>\n",
       "      <th>PZ_128</th>\n",
       "      <th>E_129</th>\n",
       "      <th>PX_129</th>\n",
       "      <th>PY_129</th>\n",
       "      <th>PZ_129</th>\n",
       "      <th>E_130</th>\n",
       "      <th>PX_130</th>\n",
       "      <th>PY_130</th>\n",
       "      <th>PZ_130</th>\n",
       "      <th>E_131</th>\n",
       "      <th>PX_131</th>\n",
       "      <th>PY_131</th>\n",
       "      <th>PZ_131</th>\n",
       "      <th>E_132</th>\n",
       "      <th>PX_132</th>\n",
       "      <th>PY_132</th>\n",
       "      <th>PZ_132</th>\n",
       "      <th>E_133</th>\n",
       "      <th>PX_133</th>\n",
       "      <th>PY_133</th>\n",
       "      <th>PZ_133</th>\n",
       "      <th>E_134</th>\n",
       "      <th>PX_134</th>\n",
       "      <th>PY_134</th>\n",
       "      <th>PZ_134</th>\n",
       "      <th>E_135</th>\n",
       "      <th>PX_135</th>\n",
       "      <th>PY_135</th>\n",
       "      <th>PZ_135</th>\n",
       "      <th>E_136</th>\n",
       "      <th>PX_136</th>\n",
       "      <th>PY_136</th>\n",
       "      <th>PZ_136</th>\n",
       "      <th>E_137</th>\n",
       "      <th>PX_137</th>\n",
       "      <th>PY_137</th>\n",
       "      <th>PZ_137</th>\n",
       "      <th>E_138</th>\n",
       "      <th>PX_138</th>\n",
       "      <th>PY_138</th>\n",
       "      <th>PZ_138</th>\n",
       "      <th>E_139</th>\n",
       "      <th>PX_139</th>\n",
       "      <th>PY_139</th>\n",
       "      <th>PZ_139</th>\n",
       "      <th>E_140</th>\n",
       "      <th>PX_140</th>\n",
       "      <th>PY_140</th>\n",
       "      <th>PZ_140</th>\n",
       "      <th>E_141</th>\n",
       "      <th>PX_141</th>\n",
       "      <th>PY_141</th>\n",
       "      <th>PZ_141</th>\n",
       "      <th>E_142</th>\n",
       "      <th>PX_142</th>\n",
       "      <th>PY_142</th>\n",
       "      <th>PZ_142</th>\n",
       "      <th>E_143</th>\n",
       "      <th>PX_143</th>\n",
       "      <th>PY_143</th>\n",
       "      <th>PZ_143</th>\n",
       "      <th>E_144</th>\n",
       "      <th>PX_144</th>\n",
       "      <th>PY_144</th>\n",
       "      <th>PZ_144</th>\n",
       "      <th>E_145</th>\n",
       "      <th>PX_145</th>\n",
       "      <th>PY_145</th>\n",
       "      <th>PZ_145</th>\n",
       "      <th>E_146</th>\n",
       "      <th>PX_146</th>\n",
       "      <th>PY_146</th>\n",
       "      <th>PZ_146</th>\n",
       "      <th>E_147</th>\n",
       "      <th>PX_147</th>\n",
       "      <th>PY_147</th>\n",
       "      <th>PZ_147</th>\n",
       "      <th>E_148</th>\n",
       "      <th>PX_148</th>\n",
       "      <th>PY_148</th>\n",
       "      <th>PZ_148</th>\n",
       "      <th>E_149</th>\n",
       "      <th>PX_149</th>\n",
       "      <th>PY_149</th>\n",
       "      <th>PZ_149</th>\n",
       "      <th>E_150</th>\n",
       "      <th>PX_150</th>\n",
       "      <th>PY_150</th>\n",
       "      <th>PZ_150</th>\n",
       "      <th>E_151</th>\n",
       "      <th>PX_151</th>\n",
       "      <th>PY_151</th>\n",
       "      <th>PZ_151</th>\n",
       "      <th>E_152</th>\n",
       "      <th>PX_152</th>\n",
       "      <th>PY_152</th>\n",
       "      <th>PZ_152</th>\n",
       "      <th>E_153</th>\n",
       "      <th>PX_153</th>\n",
       "      <th>PY_153</th>\n",
       "      <th>PZ_153</th>\n",
       "      <th>E_154</th>\n",
       "      <th>PX_154</th>\n",
       "      <th>PY_154</th>\n",
       "      <th>PZ_154</th>\n",
       "      <th>E_155</th>\n",
       "      <th>PX_155</th>\n",
       "      <th>PY_155</th>\n",
       "      <th>PZ_155</th>\n",
       "      <th>E_156</th>\n",
       "      <th>PX_156</th>\n",
       "      <th>PY_156</th>\n",
       "      <th>PZ_156</th>\n",
       "      <th>E_157</th>\n",
       "      <th>PX_157</th>\n",
       "      <th>PY_157</th>\n",
       "      <th>PZ_157</th>\n",
       "      <th>E_158</th>\n",
       "      <th>PX_158</th>\n",
       "      <th>PY_158</th>\n",
       "      <th>PZ_158</th>\n",
       "      <th>E_159</th>\n",
       "      <th>PX_159</th>\n",
       "      <th>PY_159</th>\n",
       "      <th>PZ_159</th>\n",
       "      <th>E_160</th>\n",
       "      <th>PX_160</th>\n",
       "      <th>PY_160</th>\n",
       "      <th>PZ_160</th>\n",
       "      <th>E_161</th>\n",
       "      <th>PX_161</th>\n",
       "      <th>PY_161</th>\n",
       "      <th>PZ_161</th>\n",
       "      <th>E_162</th>\n",
       "      <th>PX_162</th>\n",
       "      <th>PY_162</th>\n",
       "      <th>PZ_162</th>\n",
       "      <th>E_163</th>\n",
       "      <th>PX_163</th>\n",
       "      <th>PY_163</th>\n",
       "      <th>PZ_163</th>\n",
       "      <th>E_164</th>\n",
       "      <th>PX_164</th>\n",
       "      <th>PY_164</th>\n",
       "      <th>PZ_164</th>\n",
       "      <th>E_165</th>\n",
       "      <th>PX_165</th>\n",
       "      <th>PY_165</th>\n",
       "      <th>PZ_165</th>\n",
       "      <th>E_166</th>\n",
       "      <th>PX_166</th>\n",
       "      <th>PY_166</th>\n",
       "      <th>PZ_166</th>\n",
       "      <th>E_167</th>\n",
       "      <th>PX_167</th>\n",
       "      <th>PY_167</th>\n",
       "      <th>PZ_167</th>\n",
       "      <th>E_168</th>\n",
       "      <th>PX_168</th>\n",
       "      <th>PY_168</th>\n",
       "      <th>PZ_168</th>\n",
       "      <th>E_169</th>\n",
       "      <th>PX_169</th>\n",
       "      <th>PY_169</th>\n",
       "      <th>PZ_169</th>\n",
       "      <th>E_170</th>\n",
       "      <th>PX_170</th>\n",
       "      <th>PY_170</th>\n",
       "      <th>PZ_170</th>\n",
       "      <th>E_171</th>\n",
       "      <th>PX_171</th>\n",
       "      <th>PY_171</th>\n",
       "      <th>PZ_171</th>\n",
       "      <th>E_172</th>\n",
       "      <th>PX_172</th>\n",
       "      <th>PY_172</th>\n",
       "      <th>PZ_172</th>\n",
       "      <th>E_173</th>\n",
       "      <th>PX_173</th>\n",
       "      <th>PY_173</th>\n",
       "      <th>PZ_173</th>\n",
       "      <th>E_174</th>\n",
       "      <th>PX_174</th>\n",
       "      <th>PY_174</th>\n",
       "      <th>PZ_174</th>\n",
       "      <th>E_175</th>\n",
       "      <th>PX_175</th>\n",
       "      <th>PY_175</th>\n",
       "      <th>PZ_175</th>\n",
       "      <th>E_176</th>\n",
       "      <th>PX_176</th>\n",
       "      <th>PY_176</th>\n",
       "      <th>PZ_176</th>\n",
       "      <th>E_177</th>\n",
       "      <th>PX_177</th>\n",
       "      <th>PY_177</th>\n",
       "      <th>PZ_177</th>\n",
       "      <th>E_178</th>\n",
       "      <th>PX_178</th>\n",
       "      <th>PY_178</th>\n",
       "      <th>PZ_178</th>\n",
       "      <th>E_179</th>\n",
       "      <th>PX_179</th>\n",
       "      <th>PY_179</th>\n",
       "      <th>PZ_179</th>\n",
       "      <th>E_180</th>\n",
       "      <th>PX_180</th>\n",
       "      <th>PY_180</th>\n",
       "      <th>PZ_180</th>\n",
       "      <th>E_181</th>\n",
       "      <th>PX_181</th>\n",
       "      <th>PY_181</th>\n",
       "      <th>PZ_181</th>\n",
       "      <th>E_182</th>\n",
       "      <th>PX_182</th>\n",
       "      <th>PY_182</th>\n",
       "      <th>PZ_182</th>\n",
       "      <th>E_183</th>\n",
       "      <th>PX_183</th>\n",
       "      <th>PY_183</th>\n",
       "      <th>PZ_183</th>\n",
       "      <th>E_184</th>\n",
       "      <th>PX_184</th>\n",
       "      <th>PY_184</th>\n",
       "      <th>PZ_184</th>\n",
       "      <th>E_185</th>\n",
       "      <th>PX_185</th>\n",
       "      <th>PY_185</th>\n",
       "      <th>PZ_185</th>\n",
       "      <th>E_186</th>\n",
       "      <th>PX_186</th>\n",
       "      <th>PY_186</th>\n",
       "      <th>PZ_186</th>\n",
       "      <th>E_187</th>\n",
       "      <th>PX_187</th>\n",
       "      <th>PY_187</th>\n",
       "      <th>PZ_187</th>\n",
       "      <th>E_188</th>\n",
       "      <th>PX_188</th>\n",
       "      <th>PY_188</th>\n",
       "      <th>PZ_188</th>\n",
       "      <th>E_189</th>\n",
       "      <th>PX_189</th>\n",
       "      <th>PY_189</th>\n",
       "      <th>PZ_189</th>\n",
       "      <th>E_190</th>\n",
       "      <th>PX_190</th>\n",
       "      <th>PY_190</th>\n",
       "      <th>PZ_190</th>\n",
       "      <th>E_191</th>\n",
       "      <th>PX_191</th>\n",
       "      <th>PY_191</th>\n",
       "      <th>PZ_191</th>\n",
       "      <th>E_192</th>\n",
       "      <th>PX_192</th>\n",
       "      <th>PY_192</th>\n",
       "      <th>PZ_192</th>\n",
       "      <th>E_193</th>\n",
       "      <th>PX_193</th>\n",
       "      <th>PY_193</th>\n",
       "      <th>PZ_193</th>\n",
       "      <th>E_194</th>\n",
       "      <th>PX_194</th>\n",
       "      <th>PY_194</th>\n",
       "      <th>PZ_194</th>\n",
       "      <th>E_195</th>\n",
       "      <th>PX_195</th>\n",
       "      <th>PY_195</th>\n",
       "      <th>PZ_195</th>\n",
       "      <th>E_196</th>\n",
       "      <th>PX_196</th>\n",
       "      <th>PY_196</th>\n",
       "      <th>PZ_196</th>\n",
       "      <th>E_197</th>\n",
       "      <th>PX_197</th>\n",
       "      <th>PY_197</th>\n",
       "      <th>PZ_197</th>\n",
       "      <th>E_198</th>\n",
       "      <th>PX_198</th>\n",
       "      <th>PY_198</th>\n",
       "      <th>PZ_198</th>\n",
       "      <th>E_199</th>\n",
       "      <th>PX_199</th>\n",
       "      <th>PY_199</th>\n",
       "      <th>PZ_199</th>\n",
       "      <th>is_signal_new</th>\n",
       "      <th>is_signal_new_pred</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>55.373371</td>\n",
       "      <td>15.447829</td>\n",
       "      <td>-53.108967</td>\n",
       "      <td>2.648058</td>\n",
       "      <td>39.483627</td>\n",
       "      <td>9.879107</td>\n",
       "      <td>-38.208023</td>\n",
       "      <td>1.227653</td>\n",
       "      <td>39.344952</td>\n",
       "      <td>28.682394</td>\n",
       "      <td>-26.352501</td>\n",
       "      <td>5.557986</td>\n",
       "      <td>34.630009</td>\n",
       "      <td>25.825630</td>\n",
       "      <td>-22.191050</td>\n",
       "      <td>6.311225</td>\n",
       "      <td>31.741671</td>\n",
       "      <td>22.453880</td>\n",
       "      <td>-22.047646</td>\n",
       "      <td>4.154309</td>\n",
       "      <td>28.607065</td>\n",
       "      <td>20.475050</td>\n",
       "      <td>-19.632759</td>\n",
       "      <td>3.700181</td>\n",
       "      <td>31.330889</td>\n",
       "      <td>12.412865</td>\n",
       "      <td>-21.484344</td>\n",
       "      <td>19.130299</td>\n",
       "      <td>22.874287</td>\n",
       "      <td>16.306553</td>\n",
       "      <td>-15.693566</td>\n",
       "      <td>3.322846</td>\n",
       "      <td>21.684135</td>\n",
       "      <td>11.369366</td>\n",
       "      <td>-17.951180</td>\n",
       "      <td>4.323710</td>\n",
       "      <td>20.443676</td>\n",
       "      <td>5.001358</td>\n",
       "      <td>-19.806828</td>\n",
       "      <td>0.787326</td>\n",
       "      <td>18.971832</td>\n",
       "      <td>14.148410</td>\n",
       "      <td>-12.157228</td>\n",
       "      <td>3.457565</td>\n",
       "      <td>22.302622</td>\n",
       "      <td>7.657867</td>\n",
       "      <td>-16.329651</td>\n",
       "      <td>13.118936</td>\n",
       "      <td>22.506207</td>\n",
       "      <td>8.257535</td>\n",
       "      <td>-15.369576</td>\n",
       "      <td>14.216842</td>\n",
       "      <td>17.488396</td>\n",
       "      <td>12.562215</td>\n",
       "      <td>-11.999881</td>\n",
       "      <td>2.009378</td>\n",
       "      <td>17.286680</td>\n",
       "      <td>12.460367</td>\n",
       "      <td>-11.671321</td>\n",
       "      <td>2.710874</td>\n",
       "      <td>15.806683</td>\n",
       "      <td>9.301882</td>\n",
       "      <td>-12.139855</td>\n",
       "      <td>3.993762</td>\n",
       "      <td>16.524759</td>\n",
       "      <td>6.189622</td>\n",
       "      <td>-11.225109</td>\n",
       "      <td>10.428478</td>\n",
       "      <td>10.510235</td>\n",
       "      <td>7.613899</td>\n",
       "      <td>-7.113340</td>\n",
       "      <td>1.376215</td>\n",
       "      <td>10.505521</td>\n",
       "      <td>6.357656</td>\n",
       "      <td>-7.655622</td>\n",
       "      <td>3.367139</td>\n",
       "      <td>8.879970</td>\n",
       "      <td>2.345350</td>\n",
       "      <td>-8.521793</td>\n",
       "      <td>0.855708</td>\n",
       "      <td>7.796289</td>\n",
       "      <td>2.116827</td>\n",
       "      <td>-7.502737</td>\n",
       "      <td>0.100512</td>\n",
       "      <td>7.792163</td>\n",
       "      <td>5.807485</td>\n",
       "      <td>-5.111705</td>\n",
       "      <td>0.928112</td>\n",
       "      <td>8.909110</td>\n",
       "      <td>3.027786</td>\n",
       "      <td>-6.752189</td>\n",
       "      <td>4.961118</td>\n",
       "      <td>7.138719</td>\n",
       "      <td>1.478972</td>\n",
       "      <td>-6.924917</td>\n",
       "      <td>-0.905249</td>\n",
       "      <td>7.019392</td>\n",
       "      <td>1.748098</td>\n",
       "      <td>-6.797865</td>\n",
       "      <td>0.071055</td>\n",
       "      <td>6.291604</td>\n",
       "      <td>4.547145</td>\n",
       "      <td>-3.957447</td>\n",
       "      <td>-1.801769</td>\n",
       "      <td>5.986259</td>\n",
       "      <td>4.363632</td>\n",
       "      <td>-4.026358</td>\n",
       "      <td>0.763186</td>\n",
       "      <td>7.380098</td>\n",
       "      <td>2.547143</td>\n",
       "      <td>-5.351652</td>\n",
       "      <td>4.397468</td>\n",
       "      <td>5.743817</td>\n",
       "      <td>0.075045</td>\n",
       "      <td>-5.278041</td>\n",
       "      <td>2.264527</td>\n",
       "      <td>6.931075</td>\n",
       "      <td>2.999568</td>\n",
       "      <td>-4.256332</td>\n",
       "      <td>4.574497</td>\n",
       "      <td>7.232418</td>\n",
       "      <td>1.939481</td>\n",
       "      <td>-4.349987</td>\n",
       "      <td>5.442784</td>\n",
       "      <td>5.510406</td>\n",
       "      <td>2.592241</td>\n",
       "      <td>-3.626578</td>\n",
       "      <td>3.239258</td>\n",
       "      <td>4.339673</td>\n",
       "      <td>2.618227</td>\n",
       "      <td>-3.349735</td>\n",
       "      <td>-0.870016</td>\n",
       "      <td>4.239345</td>\n",
       "      <td>3.116243</td>\n",
       "      <td>-2.873728</td>\n",
       "      <td>-0.052541</td>\n",
       "      <td>5.080171</td>\n",
       "      <td>1.750966</td>\n",
       "      <td>-3.859296</td>\n",
       "      <td>2.801444</td>\n",
       "      <td>5.380709</td>\n",
       "      <td>2.247479</td>\n",
       "      <td>-3.541767</td>\n",
       "      <td>3.369979</td>\n",
       "      <td>5.361376</td>\n",
       "      <td>1.817439</td>\n",
       "      <td>-3.761746</td>\n",
       "      <td>3.360140</td>\n",
       "      <td>4.103991</td>\n",
       "      <td>2.657733</td>\n",
       "      <td>-2.794918</td>\n",
       "      <td>1.402720</td>\n",
       "      <td>3.818110</td>\n",
       "      <td>2.906654</td>\n",
       "      <td>-2.466961</td>\n",
       "      <td>-0.208396</td>\n",
       "      <td>4.390255</td>\n",
       "      <td>1.492041</td>\n",
       "      <td>-3.327362</td>\n",
       "      <td>2.444753</td>\n",
       "      <td>3.485384</td>\n",
       "      <td>2.404282</td>\n",
       "      <td>-2.507123</td>\n",
       "      <td>-0.285769</td>\n",
       "      <td>3.187455</td>\n",
       "      <td>1.371662</td>\n",
       "      <td>-2.873592</td>\n",
       "      <td>-0.144521</td>\n",
       "      <td>3.490748</td>\n",
       "      <td>1.988637</td>\n",
       "      <td>-2.472357</td>\n",
       "      <td>1.455369</td>\n",
       "      <td>4.097678</td>\n",
       "      <td>2.209598</td>\n",
       "      <td>-2.229547</td>\n",
       "      <td>2.633963</td>\n",
       "      <td>3.930950</td>\n",
       "      <td>2.172712</td>\n",
       "      <td>-2.055131</td>\n",
       "      <td>2.551103</td>\n",
       "      <td>3.562002</td>\n",
       "      <td>1.982498</td>\n",
       "      <td>-2.168933</td>\n",
       "      <td>2.013279</td>\n",
       "      <td>3.120360</td>\n",
       "      <td>1.434136</td>\n",
       "      <td>-2.554029</td>\n",
       "      <td>-1.075563</td>\n",
       "      <td>2.888219</td>\n",
       "      <td>1.857622</td>\n",
       "      <td>-2.140393</td>\n",
       "      <td>-0.556570</td>\n",
       "      <td>2.678831</td>\n",
       "      <td>2.034264</td>\n",
       "      <td>-1.711286</td>\n",
       "      <td>0.330761</td>\n",
       "      <td>2.630311</td>\n",
       "      <td>1.963093</td>\n",
       "      <td>-1.706802</td>\n",
       "      <td>0.389398</td>\n",
       "      <td>3.244133</td>\n",
       "      <td>1.065371</td>\n",
       "      <td>-2.351692</td>\n",
       "      <td>1.964417</td>\n",
       "      <td>2.638533</td>\n",
       "      <td>1.724679</td>\n",
       "      <td>-1.895686</td>\n",
       "      <td>-0.627464</td>\n",
       "      <td>2.543895</td>\n",
       "      <td>2.038069</td>\n",
       "      <td>-1.515647</td>\n",
       "      <td>0.143134</td>\n",
       "      <td>3.280566</td>\n",
       "      <td>1.412071</td>\n",
       "      <td>-1.966430</td>\n",
       "      <td>2.213893</td>\n",
       "      <td>2.566380</td>\n",
       "      <td>1.855283</td>\n",
       "      <td>-1.529425</td>\n",
       "      <td>-0.897268</td>\n",
       "      <td>2.289888</td>\n",
       "      <td>1.568115</td>\n",
       "      <td>-1.578431</td>\n",
       "      <td>0.541439</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>85.271927</td>\n",
       "      <td>18.985689</td>\n",
       "      <td>80.161728</td>\n",
       "      <td>-22.021387</td>\n",
       "      <td>35.494274</td>\n",
       "      <td>14.089288</td>\n",
       "      <td>27.902519</td>\n",
       "      <td>16.816210</td>\n",
       "      <td>35.372967</td>\n",
       "      <td>5.981579</td>\n",
       "      <td>24.812439</td>\n",
       "      <td>24.491024</td>\n",
       "      <td>25.733261</td>\n",
       "      <td>9.897063</td>\n",
       "      <td>22.975033</td>\n",
       "      <td>6.032969</td>\n",
       "      <td>28.182434</td>\n",
       "      <td>10.784863</td>\n",
       "      <td>21.934576</td>\n",
       "      <td>14.028923</td>\n",
       "      <td>18.519686</td>\n",
       "      <td>4.554176</td>\n",
       "      <td>17.492123</td>\n",
       "      <td>-4.032852</td>\n",
       "      <td>17.722200</td>\n",
       "      <td>8.807404</td>\n",
       "      <td>15.307701</td>\n",
       "      <td>1.476581</td>\n",
       "      <td>16.917294</td>\n",
       "      <td>6.332823</td>\n",
       "      <td>15.572810</td>\n",
       "      <td>1.891498</td>\n",
       "      <td>24.142254</td>\n",
       "      <td>4.088970</td>\n",
       "      <td>16.139261</td>\n",
       "      <td>17.482935</td>\n",
       "      <td>18.184538</td>\n",
       "      <td>7.623066</td>\n",
       "      <td>14.188622</td>\n",
       "      <td>8.440929</td>\n",
       "      <td>14.736913</td>\n",
       "      <td>7.184424</td>\n",
       "      <td>12.294654</td>\n",
       "      <td>3.795013</td>\n",
       "      <td>14.942549</td>\n",
       "      <td>4.855879</td>\n",
       "      <td>12.715952</td>\n",
       "      <td>6.164801</td>\n",
       "      <td>13.729703</td>\n",
       "      <td>6.076223</td>\n",
       "      <td>11.742292</td>\n",
       "      <td>3.701733</td>\n",
       "      <td>12.704572</td>\n",
       "      <td>6.494713</td>\n",
       "      <td>10.371592</td>\n",
       "      <td>3.413933</td>\n",
       "      <td>15.580447</td>\n",
       "      <td>2.845028</td>\n",
       "      <td>9.984985</td>\n",
       "      <td>11.617065</td>\n",
       "      <td>9.553916</td>\n",
       "      <td>2.127168</td>\n",
       "      <td>8.981367</td>\n",
       "      <td>-2.467289</td>\n",
       "      <td>9.804935</td>\n",
       "      <td>3.186309</td>\n",
       "      <td>8.343896</td>\n",
       "      <td>4.045191</td>\n",
       "      <td>8.694020</td>\n",
       "      <td>3.851479</td>\n",
       "      <td>7.770153</td>\n",
       "      <td>0.613865</td>\n",
       "      <td>8.243057</td>\n",
       "      <td>5.284256</td>\n",
       "      <td>5.934836</td>\n",
       "      <td>2.191428</td>\n",
       "      <td>8.779967</td>\n",
       "      <td>3.985839</td>\n",
       "      <td>6.611471</td>\n",
       "      <td>4.182028</td>\n",
       "      <td>7.933362</td>\n",
       "      <td>4.407343</td>\n",
       "      <td>5.780066</td>\n",
       "      <td>3.178741</td>\n",
       "      <td>7.105115</td>\n",
       "      <td>3.368708</td>\n",
       "      <td>5.879133</td>\n",
       "      <td>2.137819</td>\n",
       "      <td>5.970509</td>\n",
       "      <td>2.737379</td>\n",
       "      <td>5.242725</td>\n",
       "      <td>0.817049</td>\n",
       "      <td>6.051137</td>\n",
       "      <td>2.366136</td>\n",
       "      <td>5.302313</td>\n",
       "      <td>1.703857</td>\n",
       "      <td>5.901711</td>\n",
       "      <td>3.073598</td>\n",
       "      <td>4.855549</td>\n",
       "      <td>1.344184</td>\n",
       "      <td>6.272639</td>\n",
       "      <td>4.037410</td>\n",
       "      <td>3.992417</td>\n",
       "      <td>2.665695</td>\n",
       "      <td>6.232912</td>\n",
       "      <td>5.105202</td>\n",
       "      <td>2.319947</td>\n",
       "      <td>2.721020</td>\n",
       "      <td>7.341536</td>\n",
       "      <td>1.614292</td>\n",
       "      <td>5.363025</td>\n",
       "      <td>4.746595</td>\n",
       "      <td>6.145093</td>\n",
       "      <td>4.572462</td>\n",
       "      <td>2.929341</td>\n",
       "      <td>2.876407</td>\n",
       "      <td>5.856678</td>\n",
       "      <td>2.805473</td>\n",
       "      <td>4.596078</td>\n",
       "      <td>2.303491</td>\n",
       "      <td>5.343754</td>\n",
       "      <td>2.587870</td>\n",
       "      <td>4.635347</td>\n",
       "      <td>0.610072</td>\n",
       "      <td>5.468257</td>\n",
       "      <td>2.527618</td>\n",
       "      <td>4.632632</td>\n",
       "      <td>1.432377</td>\n",
       "      <td>6.032536</td>\n",
       "      <td>4.560538</td>\n",
       "      <td>2.457248</td>\n",
       "      <td>3.091102</td>\n",
       "      <td>5.207212</td>\n",
       "      <td>1.688362</td>\n",
       "      <td>4.861693</td>\n",
       "      <td>-0.792737</td>\n",
       "      <td>5.531978</td>\n",
       "      <td>2.484682</td>\n",
       "      <td>4.359250</td>\n",
       "      <td>2.329393</td>\n",
       "      <td>5.121120</td>\n",
       "      <td>1.059114</td>\n",
       "      <td>4.798028</td>\n",
       "      <td>-1.443289</td>\n",
       "      <td>4.850181</td>\n",
       "      <td>2.497190</td>\n",
       "      <td>4.136650</td>\n",
       "      <td>0.420032</td>\n",
       "      <td>6.786995</td>\n",
       "      <td>1.429670</td>\n",
       "      <td>4.304793</td>\n",
       "      <td>5.048573</td>\n",
       "      <td>5.556354</td>\n",
       "      <td>1.293891</td>\n",
       "      <td>4.277099</td>\n",
       "      <td>3.302323</td>\n",
       "      <td>4.906525</td>\n",
       "      <td>3.403742</td>\n",
       "      <td>2.785759</td>\n",
       "      <td>2.174414</td>\n",
       "      <td>4.229742</td>\n",
       "      <td>3.379346</td>\n",
       "      <td>2.434534</td>\n",
       "      <td>-0.737415</td>\n",
       "      <td>4.091139</td>\n",
       "      <td>1.765958</td>\n",
       "      <td>3.664821</td>\n",
       "      <td>0.433472</td>\n",
       "      <td>4.395818</td>\n",
       "      <td>2.131417</td>\n",
       "      <td>3.452122</td>\n",
       "      <td>1.692080</td>\n",
       "      <td>3.884586</td>\n",
       "      <td>1.596526</td>\n",
       "      <td>3.251563</td>\n",
       "      <td>1.403015</td>\n",
       "      <td>4.026021</td>\n",
       "      <td>3.060858</td>\n",
       "      <td>1.747410</td>\n",
       "      <td>1.945906</td>\n",
       "      <td>3.470460</td>\n",
       "      <td>0.785172</td>\n",
       "      <td>3.339807</td>\n",
       "      <td>-0.522771</td>\n",
       "      <td>3.551084</td>\n",
       "      <td>2.793807</td>\n",
       "      <td>1.822081</td>\n",
       "      <td>1.218547</td>\n",
       "      <td>3.460228</td>\n",
       "      <td>2.306340</td>\n",
       "      <td>2.393177</td>\n",
       "      <td>0.962641</td>\n",
       "      <td>3.458021</td>\n",
       "      <td>1.377673</td>\n",
       "      <td>2.960962</td>\n",
       "      <td>1.136938</td>\n",
       "      <td>3.495999</td>\n",
       "      <td>2.029963</td>\n",
       "      <td>2.312546</td>\n",
       "      <td>1.659335</td>\n",
       "      <td>3.475843</td>\n",
       "      <td>2.760226</td>\n",
       "      <td>1.258267</td>\n",
       "      <td>1.696881</td>\n",
       "      <td>3.245294</td>\n",
       "      <td>1.344248</td>\n",
       "      <td>2.667978</td>\n",
       "      <td>1.267608</td>\n",
       "      <td>2.962028</td>\n",
       "      <td>1.531076</td>\n",
       "      <td>2.519693</td>\n",
       "      <td>-0.283835</td>\n",
       "      <td>3.051412</td>\n",
       "      <td>1.687248</td>\n",
       "      <td>2.174260</td>\n",
       "      <td>1.317916</td>\n",
       "      <td>2.512844</td>\n",
       "      <td>1.686045</td>\n",
       "      <td>1.779321</td>\n",
       "      <td>0.552860</td>\n",
       "      <td>2.689137</td>\n",
       "      <td>1.730874</td>\n",
       "      <td>1.711585</td>\n",
       "      <td>1.142807</td>\n",
       "      <td>2.823017</td>\n",
       "      <td>0.768076</td>\n",
       "      <td>2.290710</td>\n",
       "      <td>1.460183</td>\n",
       "      <td>2.411201</td>\n",
       "      <td>1.448410</td>\n",
       "      <td>1.926455</td>\n",
       "      <td>0.069062</td>\n",
       "      <td>3.871706</td>\n",
       "      <td>0.444843</td>\n",
       "      <td>2.284927</td>\n",
       "      <td>3.093757</td>\n",
       "      <td>2.409937</td>\n",
       "      <td>1.518276</td>\n",
       "      <td>1.763376</td>\n",
       "      <td>0.627008</td>\n",
       "      <td>2.762771</td>\n",
       "      <td>0.450254</td>\n",
       "      <td>2.190216</td>\n",
       "      <td>1.622692</td>\n",
       "      <td>2.339598</td>\n",
       "      <td>1.109260</td>\n",
       "      <td>1.935902</td>\n",
       "      <td>0.703949</td>\n",
       "      <td>2.320295</td>\n",
       "      <td>1.870794</td>\n",
       "      <td>1.161824</td>\n",
       "      <td>0.730795</td>\n",
       "      <td>2.191975</td>\n",
       "      <td>1.253329</td>\n",
       "      <td>1.720387</td>\n",
       "      <td>0.523628</td>\n",
       "      <td>2.147218</td>\n",
       "      <td>1.241978</td>\n",
       "      <td>1.723932</td>\n",
       "      <td>0.309991</td>\n",
       "      <td>2.067152</td>\n",
       "      <td>0.668318</td>\n",
       "      <td>1.797967</td>\n",
       "      <td>0.770573</td>\n",
       "      <td>2.486211</td>\n",
       "      <td>0.976978</td>\n",
       "      <td>1.561115</td>\n",
       "      <td>1.670233</td>\n",
       "      <td>1.853210</td>\n",
       "      <td>0.693731</td>\n",
       "      <td>1.705928</td>\n",
       "      <td>0.207205</td>\n",
       "      <td>1.954812</td>\n",
       "      <td>1.041473</td>\n",
       "      <td>1.383678</td>\n",
       "      <td>0.906673</td>\n",
       "      <td>1.887233</td>\n",
       "      <td>0.418697</td>\n",
       "      <td>1.644984</td>\n",
       "      <td>-0.824846</td>\n",
       "      <td>1.756695</td>\n",
       "      <td>0.891352</td>\n",
       "      <td>1.399602</td>\n",
       "      <td>0.576703</td>\n",
       "      <td>2.784866</td>\n",
       "      <td>0.735156</td>\n",
       "      <td>1.483188</td>\n",
       "      <td>2.239459</td>\n",
       "      <td>2.572018</td>\n",
       "      <td>0.816908</td>\n",
       "      <td>1.401982</td>\n",
       "      <td>1.995592</td>\n",
       "      <td>1.613443</td>\n",
       "      <td>0.533463</td>\n",
       "      <td>1.495458</td>\n",
       "      <td>0.286742</td>\n",
       "      <td>1.677924</td>\n",
       "      <td>0.851383</td>\n",
       "      <td>1.336842</td>\n",
       "      <td>0.550843</td>\n",
       "      <td>1.746369</td>\n",
       "      <td>0.290088</td>\n",
       "      <td>1.536734</td>\n",
       "      <td>0.777240</td>\n",
       "      <td>2.353512</td>\n",
       "      <td>0.480571</td>\n",
       "      <td>1.473505</td>\n",
       "      <td>1.771117</td>\n",
       "      <td>2.081337</td>\n",
       "      <td>0.122754</td>\n",
       "      <td>1.513445</td>\n",
       "      <td>1.423510</td>\n",
       "      <td>1.590024</td>\n",
       "      <td>0.158424</td>\n",
       "      <td>1.482136</td>\n",
       "      <td>0.553488</td>\n",
       "      <td>1.504820</td>\n",
       "      <td>0.578757</td>\n",
       "      <td>1.343526</td>\n",
       "      <td>0.352794</td>\n",
       "      <td>1.503309</td>\n",
       "      <td>0.523185</td>\n",
       "      <td>1.351987</td>\n",
       "      <td>0.397927</td>\n",
       "      <td>1.831516</td>\n",
       "      <td>0.319156</td>\n",
       "      <td>1.346600</td>\n",
       "      <td>1.199692</td>\n",
       "      <td>1.556591</td>\n",
       "      <td>0.420901</td>\n",
       "      <td>1.305272</td>\n",
       "      <td>0.736263</td>\n",
       "      <td>1.166046</td>\n",
       "      <td>-0.175975</td>\n",
       "      <td>1.152045</td>\n",
       "      <td>0.038587</td>\n",
       "      <td>1.352714</td>\n",
       "      <td>1.022639</td>\n",
       "      <td>0.551004</td>\n",
       "      <td>0.693138</td>\n",
       "      <td>1.228763</td>\n",
       "      <td>0.139722</td>\n",
       "      <td>1.110641</td>\n",
       "      <td>-0.506768</td>\n",
       "      <td>1.227743</td>\n",
       "      <td>0.433013</td>\n",
       "      <td>0.974023</td>\n",
       "      <td>0.609207</td>\n",
       "      <td>1.074988</td>\n",
       "      <td>0.600248</td>\n",
       "      <td>0.867498</td>\n",
       "      <td>0.206761</td>\n",
       "      <td>1.761592</td>\n",
       "      <td>0.317861</td>\n",
       "      <td>0.975899</td>\n",
       "      <td>1.431710</td>\n",
       "      <td>1.121050</td>\n",
       "      <td>0.744424</td>\n",
       "      <td>0.605544</td>\n",
       "      <td>0.579571</td>\n",
       "      <td>0.931303</td>\n",
       "      <td>0.605460</td>\n",
       "      <td>0.700810</td>\n",
       "      <td>0.098024</td>\n",
       "      <td>0.870360</td>\n",
       "      <td>0.526842</td>\n",
       "      <td>0.679842</td>\n",
       "      <td>0.133338</td>\n",
       "      <td>1.094996</td>\n",
       "      <td>0.182765</td>\n",
       "      <td>0.839526</td>\n",
       "      <td>0.67883</td>\n",
       "      <td>0.869425</td>\n",
       "      <td>0.694774</td>\n",
       "      <td>0.499537</td>\n",
       "      <td>0.153792</td>\n",
       "      <td>0.80607</td>\n",
       "      <td>0.43132</td>\n",
       "      <td>0.671326</td>\n",
       "      <td>-0.114161</td>\n",
       "      <td>0.757981</td>\n",
       "      <td>0.123427</td>\n",
       "      <td>0.695199</td>\n",
       "      <td>-0.27568</td>\n",
       "      <td>0.774677</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
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       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>179.563461</td>\n",
       "      <td>-78.816872</td>\n",
       "      <td>-144.127274</td>\n",
       "      <td>72.513924</td>\n",
       "      <td>57.747158</td>\n",
       "      <td>-21.012482</td>\n",
       "      <td>-47.169498</td>\n",
       "      <td>25.850504</td>\n",
       "      <td>57.541145</td>\n",
       "      <td>-21.817780</td>\n",
       "      <td>-46.437847</td>\n",
       "      <td>26.047922</td>\n",
       "      <td>31.984177</td>\n",
       "      <td>-10.522673</td>\n",
       "      <td>-23.974773</td>\n",
       "      <td>18.370390</td>\n",
       "      <td>28.503929</td>\n",
       "      <td>-19.214449</td>\n",
       "      <td>-16.230444</td>\n",
       "      <td>13.410877</td>\n",
       "      <td>23.305548</td>\n",
       "      <td>-8.522502</td>\n",
       "      <td>-19.122160</td>\n",
       "      <td>10.240045</td>\n",
       "      <td>20.502831</td>\n",
       "      <td>-13.593023</td>\n",
       "      <td>-12.078649</td>\n",
       "      <td>9.471115</td>\n",
       "      <td>19.289295</td>\n",
       "      <td>-10.553767</td>\n",
       "      <td>-13.188070</td>\n",
       "      <td>9.315028</td>\n",
       "      <td>17.299089</td>\n",
       "      <td>-7.465109</td>\n",
       "      <td>-14.635800</td>\n",
       "      <td>5.415163</td>\n",
       "      <td>18.352409</td>\n",
       "      <td>-12.133499</td>\n",
       "      <td>-11.023665</td>\n",
       "      <td>8.250330</td>\n",
       "      <td>15.409149</td>\n",
       "      <td>-5.652246</td>\n",
       "      <td>-13.209612</td>\n",
       "      <td>5.567778</td>\n",
       "      <td>14.739727</td>\n",
       "      <td>-9.908389</td>\n",
       "      <td>-8.232552</td>\n",
       "      <td>7.162993</td>\n",
       "      <td>13.606773</td>\n",
       "      <td>-6.493807</td>\n",
       "      <td>-10.264329</td>\n",
       "      <td>6.133376</td>\n",
       "      <td>15.646438</td>\n",
       "      <td>-4.733969</td>\n",
       "      <td>-11.113035</td>\n",
       "      <td>9.944899</td>\n",
       "      <td>13.769272</td>\n",
       "      <td>-4.598180</td>\n",
       "      <td>-10.381672</td>\n",
       "      <td>7.789125</td>\n",
       "      <td>11.078214</td>\n",
       "      <td>-4.109962</td>\n",
       "      <td>-8.905683</td>\n",
       "      <td>5.150132</td>\n",
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       "      <td>-6.905755</td>\n",
       "      <td>-6.393700</td>\n",
       "      <td>4.514797</td>\n",
       "      <td>10.234579</td>\n",
       "      <td>-4.340665</td>\n",
       "      <td>-7.756525</td>\n",
       "      <td>5.073615</td>\n",
       "      <td>9.574831</td>\n",
       "      <td>-4.906097</td>\n",
       "      <td>-6.998511</td>\n",
       "      <td>4.316070</td>\n",
       "      <td>8.875442</td>\n",
       "      <td>-5.893004</td>\n",
       "      <td>-5.258232</td>\n",
       "      <td>4.049315</td>\n",
       "      <td>8.183035</td>\n",
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       "      <td>-6.941494</td>\n",
       "      <td>3.057940</td>\n",
       "      <td>8.138783</td>\n",
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       "      <td>8.431035</td>\n",
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       "      <td>-5.768741</td>\n",
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       "      <td>-6.377074</td>\n",
       "      <td>2.687901</td>\n",
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       "      <td>-6.148635</td>\n",
       "      <td>3.689528</td>\n",
       "      <td>9.050841</td>\n",
       "      <td>-4.024401</td>\n",
       "      <td>-5.112267</td>\n",
       "      <td>6.291792</td>\n",
       "      <td>6.475564</td>\n",
       "      <td>-2.130436</td>\n",
       "      <td>-4.853968</td>\n",
       "      <td>3.719296</td>\n",
       "      <td>6.063044</td>\n",
       "      <td>-3.251853</td>\n",
       "      <td>-4.128994</td>\n",
       "      <td>3.022806</td>\n",
       "      <td>5.670615</td>\n",
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       "      <td>6.102602</td>\n",
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       "      <td>-1.995948</td>\n",
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       "      <td>-4.083933</td>\n",
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       "      <td>-3.229809</td>\n",
       "      <td>3.485993</td>\n",
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       "      <td>-1.483754</td>\n",
       "      <td>-3.725301</td>\n",
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       "      <td>4.351503</td>\n",
       "      <td>-3.004162</td>\n",
       "      <td>-2.549451</td>\n",
       "      <td>1.846860</td>\n",
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       "      <td>-3.204675</td>\n",
       "      <td>-2.168622</td>\n",
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       "      <td>-2.686709</td>\n",
       "      <td>2.147989</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>102.676163</td>\n",
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       "      <td>29.939236</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>142.923752</td>\n",
       "      <td>78.678352</td>\n",
       "      <td>99.938553</td>\n",
       "      <td>65.185890</td>\n",
       "      <td>72.991386</td>\n",
       "      <td>68.257805</td>\n",
       "      <td>24.202347</td>\n",
       "      <td>9.102827</td>\n",
       "      <td>38.014297</td>\n",
       "      <td>35.750080</td>\n",
       "      <td>12.087891</td>\n",
       "      <td>4.571796</td>\n",
       "      <td>35.611473</td>\n",
       "      <td>33.123123</td>\n",
       "      <td>11.181815</td>\n",
       "      <td>6.782530</td>\n",
       "      <td>29.437706</td>\n",
       "      <td>25.464855</td>\n",
       "      <td>7.476874</td>\n",
       "      <td>12.736403</td>\n",
       "      <td>26.011148</td>\n",
       "      <td>24.477785</td>\n",
       "      <td>8.453134</td>\n",
       "      <td>2.441799</td>\n",
       "      <td>25.178915</td>\n",
       "      <td>23.511496</td>\n",
       "      <td>8.387461</td>\n",
       "      <td>3.292090</td>\n",
       "      <td>26.343893</td>\n",
       "      <td>22.708706</td>\n",
       "      <td>7.349658</td>\n",
       "      <td>11.148897</td>\n",
       "      <td>14.659115</td>\n",
       "      <td>13.821280</td>\n",
       "      <td>4.732279</td>\n",
       "      <td>1.211350</td>\n",
       "      <td>12.022038</td>\n",
       "      <td>11.286951</td>\n",
       "      <td>3.723090</td>\n",
       "      <td>1.809071</td>\n",
       "      <td>11.740626</td>\n",
       "      <td>11.090772</td>\n",
       "      <td>3.692733</td>\n",
       "      <td>1.095822</td>\n",
       "      <td>11.710329</td>\n",
       "      <td>10.720157</td>\n",
       "      <td>4.432101</td>\n",
       "      <td>1.602043</td>\n",
       "      <td>11.045879</td>\n",
       "      <td>9.710128</td>\n",
       "      <td>2.566499</td>\n",
       "      <td>4.597603</td>\n",
       "      <td>10.035184</td>\n",
       "      <td>9.327897</td>\n",
       "      <td>3.396616</td>\n",
       "      <td>1.469095</td>\n",
       "      <td>9.884888</td>\n",
       "      <td>8.961467</td>\n",
       "      <td>2.712603</td>\n",
       "      <td>3.169369</td>\n",
       "      <td>8.882207</td>\n",
       "      <td>7.292553</td>\n",
       "      <td>1.885134</td>\n",
       "      <td>4.707286</td>\n",
       "      <td>6.543412</td>\n",
       "      <td>6.489433</td>\n",
       "      <td>-0.837826</td>\n",
       "      <td>-0.039319</td>\n",
       "      <td>6.999748</td>\n",
       "      <td>6.033854</td>\n",
       "      <td>1.952853</td>\n",
       "      <td>2.962336</td>\n",
       "      <td>6.257664</td>\n",
       "      <td>5.496066</td>\n",
       "      <td>2.890849</td>\n",
       "      <td>0.771110</td>\n",
       "      <td>7.793723</td>\n",
       "      <td>5.734364</td>\n",
       "      <td>1.738196</td>\n",
       "      <td>4.983760</td>\n",
       "      <td>4.510467</td>\n",
       "      <td>4.178370</td>\n",
       "      <td>1.598105</td>\n",
       "      <td>0.575843</td>\n",
       "      <td>4.782681</td>\n",
       "      <td>4.108604</td>\n",
       "      <td>1.113110</td>\n",
       "      <td>2.180458</td>\n",
       "      <td>4.182361</td>\n",
       "      <td>3.912849</td>\n",
       "      <td>1.477021</td>\n",
       "      <td>-0.012807</td>\n",
       "      <td>4.109838</td>\n",
       "      <td>4.077982</td>\n",
       "      <td>0.468581</td>\n",
       "      <td>-0.203135</td>\n",
       "      <td>3.711725</td>\n",
       "      <td>3.349799</td>\n",
       "      <td>1.546700</td>\n",
       "      <td>0.404313</td>\n",
       "      <td>4.168599</td>\n",
       "      <td>3.340050</td>\n",
       "      <td>1.566669</td>\n",
       "      <td>1.940832</td>\n",
       "      <td>4.268133</td>\n",
       "      <td>3.465314</td>\n",
       "      <td>1.210372</td>\n",
       "      <td>2.177971</td>\n",
       "      <td>4.612126</td>\n",
       "      <td>2.487145</td>\n",
       "      <td>2.594614</td>\n",
       "      <td>2.890294</td>\n",
       "      <td>3.607978</td>\n",
       "      <td>3.168864</td>\n",
       "      <td>1.666775</td>\n",
       "      <td>0.444598</td>\n",
       "      <td>3.494550</td>\n",
       "      <td>1.425179</td>\n",
       "      <td>3.127082</td>\n",
       "      <td>0.634120</td>\n",
       "      <td>3.491037</td>\n",
       "      <td>3.115516</td>\n",
       "      <td>0.857281</td>\n",
       "      <td>1.321350</td>\n",
       "      <td>3.215504</td>\n",
       "      <td>1.748195</td>\n",
       "      <td>2.689125</td>\n",
       "      <td>-0.227790</td>\n",
       "      <td>3.137908</td>\n",
       "      <td>2.968556</td>\n",
       "      <td>1.016842</td>\n",
       "      <td>0.013167</td>\n",
       "      <td>3.484559</td>\n",
       "      <td>2.057550</td>\n",
       "      <td>2.275903</td>\n",
       "      <td>1.651939</td>\n",
       "      <td>2.793626</td>\n",
       "      <td>2.571566</td>\n",
       "      <td>1.040875</td>\n",
       "      <td>0.328598</td>\n",
       "      <td>2.581538</td>\n",
       "      <td>1.263143</td>\n",
       "      <td>2.250417</td>\n",
       "      <td>0.066577</td>\n",
       "      <td>3.051403</td>\n",
       "      <td>1.363279</td>\n",
       "      <td>2.085111</td>\n",
       "      <td>1.762057</td>\n",
       "      <td>2.360827</td>\n",
       "      <td>1.616907</td>\n",
       "      <td>1.685841</td>\n",
       "      <td>0.342134</td>\n",
       "      <td>2.474930</td>\n",
       "      <td>1.347824</td>\n",
       "      <td>1.682887</td>\n",
       "      <td>1.215131</td>\n",
       "      <td>1.996616</td>\n",
       "      <td>1.705726</td>\n",
       "      <td>1.037443</td>\n",
       "      <td>0.026195</td>\n",
       "      <td>1.940771</td>\n",
       "      <td>1.925673</td>\n",
       "      <td>-0.095188</td>\n",
       "      <td>-0.222073</td>\n",
       "      <td>1.953383</td>\n",
       "      <td>1.835132</td>\n",
       "      <td>0.535860</td>\n",
       "      <td>-0.401062</td>\n",
       "      <td>2.335166</td>\n",
       "      <td>1.851506</td>\n",
       "      <td>0.128525</td>\n",
       "      <td>1.417182</td>\n",
       "      <td>1.739371</td>\n",
       "      <td>1.590491</td>\n",
       "      <td>0.703631</td>\n",
       "      <td>0.025517</td>\n",
       "      <td>1.747788</td>\n",
       "      <td>1.568626</td>\n",
       "      <td>0.640641</td>\n",
       "      <td>0.428663</td>\n",
       "      <td>1.702729</td>\n",
       "      <td>1.054443</td>\n",
       "      <td>1.319898</td>\n",
       "      <td>0.212849</td>\n",
       "      <td>1.675363</td>\n",
       "      <td>1.218332</td>\n",
       "      <td>1.108690</td>\n",
       "      <td>0.305474</td>\n",
       "      <td>1.422847</td>\n",
       "      <td>1.390380</td>\n",
       "      <td>-0.218373</td>\n",
       "      <td>-0.208926</td>\n",
       "      <td>1.494798</td>\n",
       "      <td>0.871027</td>\n",
       "      <td>0.889037</td>\n",
       "      <td>0.827856</td>\n",
       "      <td>1.229201</td>\n",
       "      <td>1.005900</td>\n",
       "      <td>0.556967</td>\n",
       "      <td>0.434615</td>\n",
       "      <td>1.132050</td>\n",
       "      <td>0.610936</td>\n",
       "      <td>0.893196</td>\n",
       "      <td>0.332407</td>\n",
       "      <td>1.326933</td>\n",
       "      <td>0.782299</td>\n",
       "      <td>0.727508</td>\n",
       "      <td>0.787079</td>\n",
       "      <td>1.065655</td>\n",
       "      <td>0.966104</td>\n",
       "      <td>0.292436</td>\n",
       "      <td>0.341678</td>\n",
       "      <td>1.136415</td>\n",
       "      <td>0.824682</td>\n",
       "      <td>0.569743</td>\n",
       "      <td>0.535474</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.0</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "learn.show_results()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11269ab4-6c51-4daa-ac7c-b3160d1963aa",
   "metadata": {},
   "source": [
    "Here we can see that model made a handful of errors, which is expected since our accuracy is only around 82%. However, evaluating our model’s predictions on the same data it was trained on is almost always a recipe for disaster! Why? The problem is that the model may memorise the structure of the data it sees and fail to provide good predictions when shown new data. Let's see how we can evaluate our model on examples from the _test set_ that it has never seen."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27e1675a-52a4-4fe4-b8c7-4fb5bb31f57b",
   "metadata": {},
   "source": [
    "### Evaluate your model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b4b0d46-f442-413d-8a30-a00a41c8de68",
   "metadata": {},
   "source": [
    "The learners in fastai are equipped with `predict()` and `get_preds()` methods that allow one to evaluae the model on new data. To use them, we'll need a new `DataLoader` which we can create by simply passing in a `DataFrame` of the test events:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "40f2fa5a-6761-4976-8175-b63f658f5759",
   "metadata": {},
   "outputs": [],
   "source": [
    "test_dl = learn.dls.test_dl(test_items=test_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa86813d-83aa-453a-835c-220698516e4b",
   "metadata": {},
   "source": [
    "Now that we have a `DataLoader`, it's a simple matter to compute the predictions with the `get_preds()` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "dc011f96-f75a-4666-ba2b-3d80a0032b8b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "    /* Turns off some styling */\n",
       "    progress {\n",
       "        /* gets rid of default border in Firefox and Opera. */\n",
       "        border: none;\n",
       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "        background-size: auto;\n",
       "    }\n",
       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "        background: #F44336;\n",
       "    }\n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "preds, targs = learn.get_preds(dl=test_dl)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05b8ed39-d766-4662-b021-d8549d220ea9",
   "metadata": {},
   "source": [
    "Let's take a look at the first few values of `preds` and `targs`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "3ba166be-3034-442f-bc4e-66a494d431a5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([[0.9980, 0.0020],\n",
       "         [0.6680, 0.3320],\n",
       "         [0.8597, 0.1403],\n",
       "         [0.4682, 0.5318],\n",
       "         [0.9532, 0.0468]]),\n",
       " tensor([[0],\n",
       "         [0],\n",
       "         [0],\n",
       "         [0],\n",
       "         [0]], dtype=torch.int8))"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preds[:5], targs[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a98a2d2-92c9-4105-b4ed-20a369a27dd5",
   "metadata": {},
   "source": [
    "Here we can see that they are _tensors_. In PyTorch, a tensor is similar to the arrays that you may be familiar with in Numpy. Tensors have a rank that can be inspected by using the `size()` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "4dca8e49-3204-4422-b2a1-c00fb63c3898",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([404000, 2]), torch.Size([404000, 1]))"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preds.size(), targs.size()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8eab468f-dbab-49ab-817a-aa09f7d22d5e",
   "metadata": {},
   "source": [
    "In this case, we see that `preds` is a rank-2 tensor (i.e. a matrix), while `targs` is rank-1 (a vector). Note that each dimension in `preds` corresponds to the _probabilities_ of the model for the two classes (signal vs background). We can visualise the distribution of the probabilities for each class by filtering the `preds` tensor according to the ground truch labels and then plotting the result as a histogram:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "a2a9c8c6-fa90-4d54-bb5f-d17ca1f780bc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "signal_test = preds[:, 1][targs.flatten() == 1].numpy()\n",
    "background_test = preds[:, 1][targs.flatten() == 0].numpy()\n",
    "\n",
    "plt.hist(signal_test, histtype=\"step\", bins=20, range=(0, 1), label=\"Signal\")\n",
    "plt.hist(background_test, histtype=\"step\", bins=20, range=(0, 1), label=\"Background\")\n",
    "plt.xlabel(\"Probability\")\n",
    "plt.ylabel(\"Events/bin\")\n",
    "plt.yscale(\"log\")\n",
    "plt.xlim(0, 1)\n",
    "plt.legend(loc=\"lower right\", frameon=False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e648326c-9cf7-42f7-b53e-eaee0663b5b1",
   "metadata": {},
   "source": [
    "We see that although the model assigns high (low) probabilities to the signal (background) events, a fair amount of the signal events overlap with background ones.  To handle this, one usually defines a \"cut\" or threshold that only includes events above that value. For example, if define the cut at 0, then all the events are counted and the signal efficiency $\\epsilon_S$ and background efficiency $\\epsilon_B$ are both 1. As we increase the cut, we reject more and more background events and the result is a curve with $\\epsilon_{B,S}$ ranging from 0 to 1. \n",
    "\n",
    "This curve is equivalent to the Reciever Operating Characteristic (ROC) curve which plots the true positive rate\n",
    "\n",
    "$$ \\mathrm{TPR} = \\frac{\\mathrm{TP}}{\\mathrm{TP} + \\mathrm{FP}} \\,, \\qquad \\mathrm{TP\\, (FP)} = \\mathrm{number\\, of\\, true\\, (false) \\,positives}\\,, $$\n",
    "\n",
    "against the false positive rate FPR, where the FPR is the ratio of negative instances that are incorrectly classified as positive. In general there is a tradeoff between these two quantities: the higher the TPR, the more false positives (FPR) the classifier produces.\n",
    "\n",
    "To visualise the ROC curve for our model's predictions, we can use the handy `roc_curve()` function from scikit-learn:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "f9b7f8be-9052-4ea2-a934-252287270494",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# fpr = epsilon_B, tpr = epsilon_S\n",
    "fpr, tpr, thresholds = roc_curve(y_true=targs, y_score=preds[:, 1])\n",
    "\n",
    "plt.plot(fpr, tpr)\n",
    "plt.plot([0, 1], [0, 1], ls=\"--\", color=\"k\")\n",
    "plt.xlabel(r\"$\\epsilon_B$\")\n",
    "plt.ylabel(r\"$\\epsilon_S$\")\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b08279d-c668-44e4-9ff7-4899a9399fc4",
   "metadata": {},
   "source": [
    "A perfect classifier would have a ROC curve with all signal and background events correctly identified, i.e. an Area Under the Curve (AUC) of 1. Let's compute this area along with the accuracy on the test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "3a2fbae1-2d9e-4cef-9fa8-037798ace714",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.8314\n",
      "AUC: 0.9077\n"
     ]
    }
   ],
   "source": [
    "acc_test = accuracy_score(targs, preds.argmax(dim=-1))\n",
    "auc_test = auc(fpr, tpr)\n",
    "print(f\"Accuracy: {acc_test:.4f}\")\n",
    "print(f\"AUC: {auc_test:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4833e3f-3f3e-4118-9685-8943be0e7324",
   "metadata": {},
   "source": [
    "Since the AUC is dominated by values at large $\\epsilon_B$, it is common to also report the background rejection at a fixed signal efficiency (often 30%). We can do that by defining an interpolating function across the `tpr` and `fpr` values as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "6278fd5e-9ddf-4cd6-b270-7698f2aa3406",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Backround rejection at signal efficiency 0.3: 42.233\n"
     ]
    }
   ],
   "source": [
    "background_eff = interp1d(tpr, fpr)\n",
    "background_eff_at_30 = background_eff(0.3)\n",
    "print(f\"Backround rejection at signal efficiency 0.3: {1/background_eff_at_30:0.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81b8576f-dab8-4bb9-a33a-ad2fbf814073",
   "metadata": {},
   "source": [
    "Comparing these results again the [_The Machine Learning Landscape of Top Taggers_](https://arxiv.org/abs/1902.09914) review, shows that our baseline model falls short of the models in the review, which get a typical accuracy of 93% and an AUC of 98%. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc7ada3a-c68b-4922-a488-a01fbe76c77c",
   "metadata": {},
   "source": [
    "```{figure} ./images/top-tagging-scores.png\n",
    "---\n",
    "scale: 25%\n",
    "name: top-landscape\n",
    "---\n",
    "Figure reference: [The Machine Learning Landscape of Top Taggers](https://arxiv.org/abs/1902.09914)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17cefc83-3533-4349-9b54-67388dcff91d",
   "metadata": {},
   "source": [
    "Let's see if we can train a better model by choosing a clever representation of the input data! Before doing that, let's collect this evaluation logic in a function that we can reuse later:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "8d3864d1-11a7-41cb-9eb8-6dd7eefcda87",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_metrics(learn, test_df):\n",
    "    test_dl = learn.dls.test_dl(test_items=test_df)\n",
    "    preds, targs = learn.get_preds(dl=test_dl)\n",
    "    fpr, tpr, _ = roc_curve(y_true=targs, y_score=preds[:, 1])\n",
    "    acc_test = accuracy_score(targs, preds.argmax(dim=-1))\n",
    "    auc_test = auc(fpr, tpr)\n",
    "    background_eff = interp1d(tpr, fpr)\n",
    "    background_eff_at_30 = background_eff(0.3)\n",
    "\n",
    "    print(f\"Accuracy: {acc_test:.4f}\")\n",
    "    print(f\"AUC: {auc_test:.4f}\")\n",
    "    print(\n",
    "        f\"Backround rejection at signal efficiency 0.3: {1/background_eff_at_30:0.3f}\"\n",
    "    )\n",
    "    return fpr, tpr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "7edcc719-d565-4d44-8487-60858b812da4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "    /* Turns off some styling */\n",
       "    progress {\n",
       "        /* gets rid of default border in Firefox and Opera. */\n",
       "        border: none;\n",
       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "        background-size: auto;\n",
       "    }\n",
       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "        background: #F44336;\n",
       "    }\n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.8314\n",
      "AUC: 0.9077\n",
      "Backround rejection at signal efficiency 0.3: 42.233\n"
     ]
    }
   ],
   "source": [
    "fpr_baseline, tpr_baseline = compute_metrics(learn, test_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca6fd041-3bd5-497a-a095-b78624766a40",
   "metadata": {},
   "source": [
    "## Jet representations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fec0fa8c-d73b-41eb-b252-b955d21e3d8b",
   "metadata": {},
   "source": [
    "In any machine learning problem, how we represent the data often has a large impact on the performance of the models we train. For jet tagging, the most common approaches one finds in the literature include:\n",
    "\n",
    "* **Jets as images.** A jet image is a pixelated grayscale image, where the pixel intensity represents the energy (or transverse momentum) of all particles that deposited energy in a particular location in the $\\eta-\\phi$ plane. Typically, _convolutional neural networks (CNNs)_ are used to process the images and we'll ecplore these architectures in a future lesson.\n",
    "* **Jets as sequences.** Here the idea is to order the particles in a jet (usually by $p_T$) and use sequence-based architectures like _recurrent neural networks (RNNs)._\n",
    "* **Jets as graphs.** This approach treats each jet as a generic graph of nodes and edges. Graph neural networks (which we'll also encounter later in the course) excel on this tpe of data.\n",
    "* **Jets as sets.** A generalisation of the previous representations, this approach simply treats each jets as an unordered collection or point cloud of 4-vectors.\n",
    "* **Theory-inspired representations.** Instead of representing the jets in formats to match specific neural network architectures, these approaches use results on IR safety from QCD to represent the jets as a simplified set of features. Fully-connected neural networks are then trained on these features.\n",
    "\n",
    "You can find more details about each representation in a nice [review article](https://arxiv.org/abs/1709.04464) from 2017. \n",
    "\n",
    "```{figure} ./images/jets.png\n",
    "---\n",
    "scale: 40%\n",
    "name: jet-substructure\n",
    "---\n",
    "Figure reference: [Jet Substructure at the Large Hadron Collider](https://arxiv.org/abs/1709.04464)\n",
    "```\n",
    "\n",
    "In this lesson and the next, we'll use one of the theory-inspired representations called $N$-subjettiness. Let's take a look."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d70b6cf-c13d-48a1-a737-dbf75a873cc4",
   "metadata": {},
   "source": [
    "### Representing jets with $N$-subjettiness observables"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "471be338-08e1-4ee6-84a5-44055613aac1",
   "metadata": {},
   "source": [
    "$N$-subjettiness observables quantify how much of the radiation in a jet is aligned along different subjet axes. Although originally used for analytic approaches to distinguish different decays and event topologies, these observable can also be used as inputs for machine learning models and provide strong discriminating power. \n",
    "\n",
    "To be precise, an $N$-subjettiness observable $\\tau_N^{(\\beta)}$ measures the radiation about $N$ axes in the jet according to an angular exponent $\\beta>0$:\n",
    "\n",
    "$$ \\tau_N^{(\\beta)} = \\frac{1}{p_{T,J}} \\sum_{i\\in J} p_{T,i} \\min \\left\\{ R_{1,i}^\\beta, R_{1,i}^\\beta, \\ldots , R_{1,i}^\\beta \\right\\} $$\n",
    "\n",
    "Here $p_{T,J}$ is the transverse momentum of the jet, $p_{T,i}$ is the transverse momentum of particle $i$ in the jet, and $R_{K,i}$ is the distance in the $\\eta-\\phi$ plane of particle $i$ to axis $K$.\n",
    "\n",
    "To measure substructure in a jet, one thus needs to measure a suitable number of $N$-subjettiness observables. In practice this is done by specifying the corrdinates of $M$-body phase space in terms of $3M - 4$ $N$-subjettiness observables:\n",
    "\n",
    "$$ \\left\\{ \\tau_1^{(0.5)}, \\tau_1^{(1)}, \\tau_1^{(2)}, \\tau_2^{(0.5)}, \\tau_2^{(1)}, \\tau_2^{(2)}, \\ldots , \\tau_{m-1}^{(0.5)}, \\tau_{m-1}^{(1)}, \\tau_{m-1}^{(2)} \\right\\} $$\n",
    "\n",
    "To see how we can use this basis as features for a neural network, we have computed $N$-subjettiness observables up through 6-body phase space using the [pyjet library](https://github.com/scikit-hep/pyjet). You can download these features via the `load_dataset()` function as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "9f0a5389-e6f5-4e89-a2b6-e6d2b143ccf3",
   "metadata": {
    "tags": [
     "hide-output"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Downloading and preparing dataset parquet/dl4phys--top_tagging_nsubjettiness to /home/lewis/.cache/huggingface/datasets/parquet/dl4phys--top_tagging_nsubjettiness-d7eca4f13187c4c4/0.0.0/0b6d5799bb726b24ad7fc7be720c170d8e497f575d02d47537de9a5bac074901...\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0eb7609a5da042e195902698628bf802",
       "version_major": 2,
       "version_minor": 0
      },
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "27e1e8ac1f8845a8a28da4c763170e86",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Downloading data:   0%|          | 0.00/198M [00:00<?, ?B/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "909ba8220d63435f95aa67890ae47a62",
       "version_major": 2,
       "version_minor": 0
      },
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       "Downloading data:   0%|          | 0.00/69.9M [00:00<?, ?B/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ac60722c230644cb849cf27f71ba62e8",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Downloading data:   0%|          | 0.00/69.7M [00:00<?, ?B/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "09de513d9c6f4b279c3307bcfa20631f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset parquet downloaded and prepared to /home/lewis/.cache/huggingface/datasets/parquet/dl4phys--top_tagging_nsubjettiness-d7eca4f13187c4c4/0.0.0/0b6d5799bb726b24ad7fc7be720c170d8e497f575d02d47537de9a5bac074901. Subsequent calls will reuse this data.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "bb8635431fc14b1a9af60a06e47d9b4f",
       "version_major": 2,
       "version_minor": 0
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nsubjet_ds = load_dataset(\"dl4phys/top_tagging_nsubjettiness\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e253591-66c7-4483-b9e1-65ffdf6f3fc0",
   "metadata": {},
   "source": [
    "As before, we'll convert our `Dataset` object to a pandas `DataFrame`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "498662cc-e3fa-4244-8a5a-ddccacf5cb54",
   "metadata": {},
   "outputs": [
    {
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       "      <th>pT</th>\n",
       "      <th>mass</th>\n",
       "      <th>tau_1_0.5</th>\n",
       "      <th>tau_1_1</th>\n",
       "      <th>tau_1_2</th>\n",
       "      <th>tau_2_0.5</th>\n",
       "      <th>tau_2_1</th>\n",
       "      <th>tau_2_2</th>\n",
       "      <th>tau_3_0.5</th>\n",
       "      <th>tau_3_1</th>\n",
       "      <th>...</th>\n",
       "      <th>tau_4_0.5</th>\n",
       "      <th>tau_4_1</th>\n",
       "      <th>tau_4_2</th>\n",
       "      <th>tau_5_0.5</th>\n",
       "      <th>tau_5_1</th>\n",
       "      <th>tau_5_2</th>\n",
       "      <th>tau_6_0.5</th>\n",
       "      <th>tau_6_1</th>\n",
       "      <th>tau_6_2</th>\n",
       "      <th>label</th>\n",
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       "           pT        mass  tau_1_0.5   tau_1_1   tau_1_2  tau_2_0.5   tau_2_1  \\\n",
       "0  543.633944   25.846792   0.165122  0.032661  0.002262   0.048830  0.003711   \n",
       "1  452.411860   13.388679   0.162938  0.027598  0.000876   0.095902  0.015461   \n",
       "2  429.495258   32.021091   0.244436  0.065901  0.005557   0.155202  0.038807   \n",
       "3  512.675443    6.684734   0.102580  0.011369  0.000170   0.086306  0.007760   \n",
       "4  527.956859  133.985415   0.407009  0.191839  0.065169   0.291460  0.105479   \n",
       "\n",
       "    tau_2_2  tau_3_0.5   tau_3_1  ...  tau_4_0.5   tau_4_1   tau_4_2  \\\n",
       "0  0.000044   0.030994  0.001630  ...   0.024336  0.001115  0.000008   \n",
       "1  0.000506   0.079750  0.009733  ...   0.056854  0.005454  0.000072   \n",
       "2  0.002762   0.123285  0.025339  ...   0.078205  0.012678  0.000567   \n",
       "3  0.000071   0.068169  0.005386  ...   0.044705  0.002376  0.000008   \n",
       "4  0.029753   0.209341  0.049187  ...   0.143768  0.033249  0.003689   \n",
       "\n",
       "   tau_5_0.5   tau_5_1       tau_5_2  tau_6_0.5   tau_6_1       tau_6_2  label  \n",
       "0   0.004252  0.000234  7.706005e-07   0.000000  0.000000  0.000000e+00      0  \n",
       "1   0.044211  0.004430  6.175314e-05   0.037458  0.003396  3.670517e-05      0  \n",
       "2   0.052374  0.005935  9.395772e-05   0.037572  0.002932  2.237277e-05      0  \n",
       "3   0.027895  0.001364  4.400042e-06   0.009012  0.000379  6.731099e-07      0  \n",
       "4   0.135407  0.029054  2.593460e-03   0.110805  0.023179  2.202088e-03      0  \n",
       "\n",
       "[5 rows x 21 columns]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nsubjet_ds.set_format(\"pandas\")\n",
    "train_df, test_df = nsubjet_ds[\"train\"][:], nsubjet_ds[\"test\"][:]\n",
    "train_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4183e5aa-ae86-42d2-93d1-f24d5d505014",
   "metadata": {},
   "source": [
    "Following Section 3.2.2 of [_The Machine Learning Landscape of Top Taggers_](https://arxiv.org/abs/1902.09914) revie, we've also included the jet mass and jet $p_T$ as input variables to allow the network to learn physical scales. \n",
    "\n",
    "Let's now train a model using these features. As before, we need to first define our `DataLoaders` object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "71e06501-8d8b-47ee-8acc-4d461ca3148f",
   "metadata": {},
   "outputs": [],
   "source": [
    "features = list(train_df.drop(columns=[\"label\"]).columns)\n",
    "splits = RandomSplitter(valid_pct=0.20, seed=42)(range_of(train_df))\n",
    "\n",
    "dls = TabularDataLoaders.from_df(\n",
    "    df=train_df,\n",
    "    cont_names=features,\n",
    "    y_names=\"label\",\n",
    "    y_block=CategoryBlock,\n",
    "    splits=splits,\n",
    "    bs=1024,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b79f3601-5e7e-4473-acba-27518febffc4",
   "metadata": {},
   "source": [
    "And just like before it's a good idea to sanity check your data is formatted correctly with the `show_batch()` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "a92d54ec-8961-4862-8c2b-f0a945b00a21",
   "metadata": {},
   "outputs": [
    {
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       "      <th>mass</th>\n",
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       "      <th>tau_1_2</th>\n",
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       "      <td>0.040518</td>\n",
       "      <td>0.130512</td>\n",
       "      <td>0.023113</td>\n",
       "      <td>0.001422</td>\n",
       "      <td>0.114296</td>\n",
       "      <td>0.017393</td>\n",
       "      <td>0.000718</td>\n",
       "      <td>0.095355</td>\n",
       "      <td>0.013060</td>\n",
       "      <td>4.953301e-04</td>\n",
       "      <td>0.082081</td>\n",
       "      <td>0.009201</td>\n",
       "      <td>2.063908e-04</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>538.835754</td>\n",
       "      <td>21.680426</td>\n",
       "      <td>0.198053</td>\n",
       "      <td>0.039486</td>\n",
       "      <td>0.001619</td>\n",
       "      <td>0.038596</td>\n",
       "      <td>0.003683</td>\n",
       "      <td>0.000069</td>\n",
       "      <td>0.027622</td>\n",
       "      <td>0.002028</td>\n",
       "      <td>0.000024</td>\n",
       "      <td>0.018646</td>\n",
       "      <td>0.000869</td>\n",
       "      <td>0.000002</td>\n",
       "      <td>0.008453</td>\n",
       "      <td>0.000373</td>\n",
       "      <td>9.324909e-07</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>569.943970</td>\n",
       "      <td>14.177874</td>\n",
       "      <td>0.124071</td>\n",
       "      <td>0.018201</td>\n",
       "      <td>0.000619</td>\n",
       "      <td>0.091646</td>\n",
       "      <td>0.008896</td>\n",
       "      <td>0.000096</td>\n",
       "      <td>0.039875</td>\n",
       "      <td>0.002515</td>\n",
       "      <td>0.000014</td>\n",
       "      <td>0.008931</td>\n",
       "      <td>0.000650</td>\n",
       "      <td>0.000005</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>462.787750</td>\n",
       "      <td>167.859375</td>\n",
       "      <td>0.618895</td>\n",
       "      <td>0.366184</td>\n",
       "      <td>0.132532</td>\n",
       "      <td>0.274511</td>\n",
       "      <td>0.074367</td>\n",
       "      <td>0.006216</td>\n",
       "      <td>0.217250</td>\n",
       "      <td>0.049036</td>\n",
       "      <td>0.003042</td>\n",
       "      <td>0.185648</td>\n",
       "      <td>0.036743</td>\n",
       "      <td>0.001925</td>\n",
       "      <td>0.159761</td>\n",
       "      <td>0.027603</td>\n",
       "      <td>9.593506e-04</td>\n",
       "      <td>0.136480</td>\n",
       "      <td>0.022875</td>\n",
       "      <td>7.589663e-04</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>481.187836</td>\n",
       "      <td>21.275795</td>\n",
       "      <td>0.197569</td>\n",
       "      <td>0.041092</td>\n",
       "      <td>0.001955</td>\n",
       "      <td>0.117185</td>\n",
       "      <td>0.018937</td>\n",
       "      <td>0.000665</td>\n",
       "      <td>0.099367</td>\n",
       "      <td>0.012753</td>\n",
       "      <td>0.000281</td>\n",
       "      <td>0.085475</td>\n",
       "      <td>0.009725</td>\n",
       "      <td>0.000197</td>\n",
       "      <td>0.062330</td>\n",
       "      <td>0.005595</td>\n",
       "      <td>6.916394e-05</td>\n",
       "      <td>0.052907</td>\n",
       "      <td>0.004203</td>\n",
       "      <td>3.618403e-05</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>574.911987</td>\n",
       "      <td>42.508812</td>\n",
       "      <td>0.180569</td>\n",
       "      <td>0.037991</td>\n",
       "      <td>0.005424</td>\n",
       "      <td>0.108725</td>\n",
       "      <td>0.020727</td>\n",
       "      <td>0.004305</td>\n",
       "      <td>0.041011</td>\n",
       "      <td>0.003381</td>\n",
       "      <td>0.000071</td>\n",
       "      <td>0.028611</td>\n",
       "      <td>0.002046</td>\n",
       "      <td>0.000036</td>\n",
       "      <td>0.015887</td>\n",
       "      <td>0.001213</td>\n",
       "      <td>2.921311e-05</td>\n",
       "      <td>0.011662</td>\n",
       "      <td>0.000650</td>\n",
       "      <td>1.678485e-05</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>463.576508</td>\n",
       "      <td>53.591480</td>\n",
       "      <td>0.288984</td>\n",
       "      <td>0.092856</td>\n",
       "      <td>0.013347</td>\n",
       "      <td>0.224898</td>\n",
       "      <td>0.052918</td>\n",
       "      <td>0.003495</td>\n",
       "      <td>0.173352</td>\n",
       "      <td>0.032209</td>\n",
       "      <td>0.001432</td>\n",
       "      <td>0.133511</td>\n",
       "      <td>0.024035</td>\n",
       "      <td>0.001166</td>\n",
       "      <td>0.094518</td>\n",
       "      <td>0.015667</td>\n",
       "      <td>6.733207e-04</td>\n",
       "      <td>0.088208</td>\n",
       "      <td>0.012934</td>\n",
       "      <td>3.997425e-04</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>519.291260</td>\n",
       "      <td>17.618988</td>\n",
       "      <td>0.151518</td>\n",
       "      <td>0.026514</td>\n",
       "      <td>0.001151</td>\n",
       "      <td>0.085697</td>\n",
       "      <td>0.009568</td>\n",
       "      <td>0.000241</td>\n",
       "      <td>0.058985</td>\n",
       "      <td>0.004627</td>\n",
       "      <td>0.000063</td>\n",
       "      <td>0.039815</td>\n",
       "      <td>0.002514</td>\n",
       "      <td>0.000013</td>\n",
       "      <td>0.028490</td>\n",
       "      <td>0.001495</td>\n",
       "      <td>5.074164e-06</td>\n",
       "      <td>0.017248</td>\n",
       "      <td>0.000635</td>\n",
       "      <td>8.944363e-07</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>478.084625</td>\n",
       "      <td>124.346436</td>\n",
       "      <td>0.507225</td>\n",
       "      <td>0.254765</td>\n",
       "      <td>0.067330</td>\n",
       "      <td>0.182893</td>\n",
       "      <td>0.043455</td>\n",
       "      <td>0.006483</td>\n",
       "      <td>0.126383</td>\n",
       "      <td>0.019826</td>\n",
       "      <td>0.001121</td>\n",
       "      <td>0.089138</td>\n",
       "      <td>0.014123</td>\n",
       "      <td>0.000801</td>\n",
       "      <td>0.044779</td>\n",
       "      <td>0.005901</td>\n",
       "      <td>1.272047e-04</td>\n",
       "      <td>0.029706</td>\n",
       "      <td>0.003584</td>\n",
       "      <td>5.757449e-05</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dls.show_batch()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0afb6a68-3357-4c49-9d30-a5ef5bb4ba54",
   "metadata": {},
   "source": [
    "This looks good, so the last step is to create a `Learner` and find a good learning rate:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "b859ec68-4bbe-4cb8-b8dd-e9d7dc81d038",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "    /* Turns off some styling */\n",
       "    progress {\n",
       "        /* gets rid of default border in Firefox and Opera. */\n",
       "        border: none;\n",
       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "        background-size: auto;\n",
       "    }\n",
       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "        background: #F44336;\n",
       "    }\n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "SuggestedLRs(valley=0.002511886414140463)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "learn = tabular_learner(\n",
    "    dls, layers=[200, 200, 50, 50], metrics=[accuracy, RocAucBinary()]\n",
    ")\n",
    "\n",
    "learn.lr_find()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3de782df-1866-4c55-bcb9-d3552ad57162",
   "metadata": {},
   "source": [
    "This curve is similar to what we found before so let's pick a learning rate of $10^{-3}$ and train for 3 epochs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "8309f7af-de6c-4eaf-aa26-2b8e6e35c526",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "    /* Turns off some styling */\n",
       "    progress {\n",
       "        /* gets rid of default border in Firefox and Opera. */\n",
       "        border: none;\n",
       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "        background-size: auto;\n",
       "    }\n",
       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "        background: #F44336;\n",
       "    }\n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
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     "metadata": {},
     "output_type": "display_data"
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>accuracy</th>\n",
       "      <th>roc_auc_score</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
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       "      <td>0.966693</td>\n",
       "      <td>00:08</td>\n",
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       "    <tr>\n",
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       "      <td>00:08</td>\n",
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       "    <tr>\n",
       "      <td>2</td>\n",
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       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "learn.fit_one_cycle(n_epoch=3, lr_max=1e-3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f72bfce0-a29e-43fd-abd3-989e8b20e726",
   "metadata": {},
   "source": [
    "We can already see that training on the $N$-subjettiness features has produced a better model than our baseline, which achieved around 83% and $91%$ accuracy and AUC score respectively. Let's wrap up by computing these metrics on the test set with our `compute_metrics()` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "ccaf0e10-210a-4c5b-8cb6-686e8f475b87",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "    /* Turns off some styling */\n",
       "    progress {\n",
       "        /* gets rid of default border in Firefox and Opera. */\n",
       "        border: none;\n",
       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "        background-size: auto;\n",
       "    }\n",
       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "        background: #F44336;\n",
       "    }\n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.9037\n",
      "AUC: 0.9677\n",
      "Backround rejection at signal efficiency 0.3: 373.915\n"
     ]
    }
   ],
   "source": [
    "test_df = nsubjet_ds[\"test\"].to_pandas()\n",
    "fpr_nsubjet, tpr_nsubjet = compute_metrics(learn, test_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e95c83e-3135-4391-a898-2f0396bc5c1d",
   "metadata": {},
   "source": [
    "This is much better and now just a 1-2% the classifiers reported in the review paper! We can also compare both models by plotting the background rejection rate against the signal efficiency:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "db2039d0-7f9a-42a4-8656-6ddae4e27c72",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "plt.plot(tpr_baseline, 1 / (fpr_baseline + 1e-6), label=\"Baseline\")\n",
    "plt.plot(tpr_nsubjet, 1 / (fpr_nsubjet + 1e-6), label=\"6-body N-subjettiness\")\n",
    "plt.xlabel(\"Signal befficiency $\\epsilon_{S}$\")\n",
    "plt.ylabel(\"Background rejection $1/\\epsilon_{B}$\")\n",
    "plt.xlim(0, 1)\n",
    "plt.yscale(\"log\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8c8bbf7-b28c-4d17-b202-c75c3b6d3b69",
   "metadata": {},
   "source": [
    "## Saving and sharing the model\n",
    "\n",
    "We've seen in this lecture how to load and prepare datasets for deep neural nets, and how to train the models with fastai. But what happens if you want to save your model for future use, or to simply reproduce the results from your paper in PRL 🙃? \n",
    "\n",
    "One way to do this is by use the `save()` method of the `Learner`, which will store your model in a format called [pickle](https://docs.python.org/3/library/pickle.html). This is great if you're doing quick experimentation, but at some point you might want to share the model with a colleague or the wider research community. \n",
    "\n",
    "In the same way we were able to download a dataset from the Hugging Face Hub, it is also possible to share fastai models on the platform! To do so, you'll first need to:\n",
    "\n",
    "* Create a Hugging Face account (it's free): https://huggingface.co/join\n",
    "* [Optional] Join the [Deep Learning for Particle Physicists](https://huggingface.co/dl4phys) organisation to share your models with the rest of the class.\n",
    "\n",
    "Once you're created an account, you can log into the Hub with the following helper function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "7298a36c-1412-4223-b981-2adc09d2de1b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a329d7846b1a476c9424c34ae6bc2864",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "VBox(children=(HTML(value='<center> <img\\nsrc=https://huggingface.co/front/assets/huggingface_logo-noborder.sv…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "notebook_login()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5c666d1-5e1a-4244-a0d4-a4e8261094f4",
   "metadata": {},
   "source": [
    "This will display a widget in which you can enter a Hugging Face token - you can find details on how to create tokens in the [Hub documentation](https://huggingface.co/docs/hub/security#user-access-tokens). Once you're logged in, pushing our model to the Hub is simple via the `push_to_hub_fastai()` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "90ecbf18-30f8-457d-a6ec-a777a07fb7f3",
   "metadata": {
    "tags": [
     "hide-output"
    ]
   },
   "outputs": [],
   "source": [
    "user_or_org = \"dl4phys\"  # This can also be your Hub username, e.g. lewtun\n",
    "model_id = \"lewtun-top-tagging-nsubs\"  # Change this to something different\n",
    "repo_id = f\"{user_or_org}/{model_id}\"\n",
    "\n",
    "push_to_hub_fastai(\n",
    "    learner=learn,\n",
    "    repo_id=repo_id,\n",
    "    commit_message=\"Add new Learner\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49c449c3-7205-4d0b-88e3-0b84467b177f",
   "metadata": {},
   "source": [
    "This will push the model's weights to the Hub, as well as a `pyproject.toml` file that defines the environment in which the `Learner` was created. Now that we've pushed our model to the Hub, we can now download it on any machine where fastai is installed! This is really handy when you need to quickly reproduce the results from your paper, e.g. here is how we use the `from_pretrained_fastai()` function to download the model and re-compute our scores on the test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "a815e915-777b-4725-8e7f-3402c8e34109",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "    /* Turns off some styling */\n",
       "    progress {\n",
       "        /* gets rid of default border in Firefox and Opera. */\n",
       "        border: none;\n",
       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "        background-size: auto;\n",
       "    }\n",
       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "        background: #F44336;\n",
       "    }\n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.9037\n",
      "AUC: 0.9677\n",
      "Backround rejection at signal efficiency 0.3: 373.915\n"
     ]
    }
   ],
   "source": [
    "learner = from_pretrained_fastai(repo_id)\n",
    "_, _ = compute_metrics(learner, test_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c46089c6-22a8-4279-845f-fc6cfb5d7ad2",
   "metadata": {},
   "source": [
    "## Exercises\n",
    "\n",
    "* Try changing the network architecture by adjusting the `layers` argument in `tabular_learner()` on the $N$-subjettiness features. What happens if you keep the number of nodes fixed and increase the number of layers? Similarly, what happens if you have just a single layer, but increase the number of nodes on that layer?\n",
    "* Push one of your new models to the `dl4phys` organisation on the Hugging Face Hub.\n",
    "* Train a model on the $N$-subjettiness features without including the jet mass and $p_T$. Does this have a positive or negative impact on performance?\n",
    "* Train a model using 2-body and 4-body $N$-subjettiness features to see if the performance is saturated with a smaller number of features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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