test.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Evaluation of the numerical stability of an implementation of log(1-softmax) in Pytorch\n",
    "\n",
    "The studied function was proposed by *KFrank* in a [PyTorch forum discussion](https://discuss.pytorch.org/t/how-to-calculate-log-1-softmax-x-numerically-stably/169007/11?u=hichem)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mpmath import *\n",
    "import torch\n",
    "\n",
    "# Import The numerically stable log(1-softmax) function proposed by KFrank\n",
    "from log1msoftmax import log1m_softmax_kfrank\n",
    "\n",
    "# Set float precision in the mpmath package to be equal to 2000 bits\n",
    "mp.prec = 2000\n",
    "\n",
    "# Function to compute log(1-softmax) with 2000bits precision\n",
    "def log1msoftmax_pft(x : list):\n",
    "    m = max(x)\n",
    "    x = [i-m for i in x]\n",
    "    s = sum(exp(i) for i in x)\n",
    "    res = [log(1-exp(i)/s) for i in x]\n",
    "    return res\n",
    "\n",
    "\n",
    "# Function to compute softmax with 2000bits precision\n",
    "def softmax_pft(x : list):\n",
    "    m = max(x)\n",
    "    x = [i-m for i in x]\n",
    "    s = sum(exp(i) for i in x)\n",
    "    res = [exp(i)/s for i in x]\n",
    "    return res, s\n",
    "\n",
    "# Function to compute the Jacobian of log(1-softmax) with 2000bits precision\n",
    "def grad_log1msoftmax_pft(x : list):\n",
    "    m = max(x)\n",
    "    x = [i-m for i in x]\n",
    "    res = [[0]*len(x) for _ in range(len(x))]\n",
    "    sm_x, s = softmax_pft(x)\n",
    "    for i in range(len(x)):\n",
    "        for j in range(len(x)):\n",
    "            if i == j:\n",
    "                res[i][j] = -sm_x[i]\n",
    "                # res[i][j] = 0\n",
    "            else:\n",
    "                t = sm_x[j]*s/(s-exp(x[i]))\n",
    "                res[i][j] = sm_x[i]*t\n",
    "                # res[i][j] = 1\n",
    "    return res\n",
    "\n",
    "# This function computes the L1 distance between each element of l1 and l2 in parallel and returns the maximum distance found.\n",
    "def max_abs_dist(l1,l2):\n",
    "    assert len(l1) == len(l2)\n",
    "    max_error = 0\n",
    "    for x,y in zip(l1,l2):\n",
    "        d = abs(x - y)\n",
    "        if d > max_error:\n",
    "            max_error = d   \n",
    "    return max_error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numerical stability of log1m_softmax_kfrank : Methodology\n",
    "\n",
    "To confirm the stability and precision of the log1m_softmax_kfrank function (let’s call it KF), I compared its output and its gradient with the “real” values of the log(1-softmax).\n",
    "\n",
    "The “real” values of log(1-softmax) are computed using the mpmath package using a ridiculously high precision (2000 bits).\n",
    "\n",
    "The input I used is a randomly generated vector X of 100 elements on a normal distribution N(0,1) with a little modification : I set an element of X to be equal to C which varies from 0 to 100. As C grows, the sum of the exponents of X will be almost equal to exp(C) which creates the numerical instability.\n",
    "\n",
    "We proceed to compute the maximum absolute error between KF’s output and the “real” output of log(1-softmax), noted max(abs(KF(X) - real_values)) for each value of C."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_results(v : torch.Tensor, C, func=None):\n",
    "    perf_naive = []\n",
    "    perf_KFrank = []\n",
    "    perf_grad_KFrank = []\n",
    "    v = v.clone()\n",
    "    for prog, c in enumerate(C):\n",
    "        print(\"%s/%s\" % (prog, len(C)))\n",
    "        v[0] = c\n",
    "        b = v.clone()\n",
    "        perfect = log1msoftmax_pft(b.tolist())\n",
    "        naive = (1-b.softmax(-1)).log().tolist()\n",
    "\n",
    "        \n",
    "        max_grad_error = 0\n",
    "        pft_grad = grad_log1msoftmax_pft(b.tolist())\n",
    "        for i in range(len(v)):\n",
    "            b = v.clone().requires_grad_()\n",
    "            KFrank = log1m_softmax_kfrank(b)\n",
    "            KFrank[i].backward()\n",
    "            maxi = max_abs_dist(pft_grad[i],b.grad.tolist())\n",
    "            if maxi > max_grad_error:\n",
    "                max_grad_error = maxi\n",
    "\n",
    "        perf_naive.append(max_abs_dist(perfect, naive))\n",
    "        perf_KFrank.append(max_abs_dist(perfect, KFrank.tolist()))\n",
    "        perf_grad_KFrank.append(max_grad_error)\n",
    "    return perf_naive, perf_KFrank, perf_grad_KFrank\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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   ],
   "source": [
    "a = torch.randn(100)\n",
    "C = np.linspace(0,200,400)\n",
    "perf_naive, perf_KFrank, perf_grad_KFrank = get_results(a,C)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next image is a plot of the maximum absolute error between KF’s output and the “real” output of log(1-softmax), noted max(abs(KF(X) - real_values)), with respect to C. I also plotted the naive implementation torch.log(1-torch.softmax(X)) for reference. As we can see, KF stays stable and accurate while the “naive” approach diverges to infinity after C ≈ 25. The maximum absolute error of KF, reported in this test, is approximately 6.56e-6."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Maximum MAE (ours) = 6.561922861487168616e-6\n",
      "Maximum MAE (KFrank) = 6.561922861487168616e-6\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.plot(C, perf_naive, label='naive')\n",
    "plt.plot(C, perf_KFrank, label='KF')\n",
    "plt.legend()\n",
    "plt.xlabel('C')\n",
    "plt.ylabel('max(|output - real_values|)')\n",
    "plt.title('Normal vector')\n",
    "\n",
    "print(\"Maximum MAE (KFrank) = %s\" % nstr(max(perf_KFrank), 20))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Same observation when comparing the Jacobian of KF with the \"real\" Jacobian of the log(1-softmax) function. The maximum absolute error of KF, reported in this test, is approximately 6.79e-6."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Maximum MAE on gradient (KFrank) = 6.794929504e-6\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(C, perf_grad_KFrank, label='KF')\n",
    "plt.legend()\n",
    "plt.xlabel('C')\n",
    "plt.ylabel('max(|jacobian - real_jacobian|)')\n",
    "plt.title('Normal vector')\n",
    "\n",
    "print(\"Maximum MAE on gradient (KFrank) = %s\" % nstr(max(perf_grad_KFrank), 10))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "wfd_eval",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.14"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}