Kolmogorov_Arnold_Newtwork.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/forbiddenvelocity/Kolmogorov-Arnold-Network/blob/main/Kolmogorov_Arnold_Newtwork.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "id": "ZPnC2ck5rJPP"
      },
      "outputs": [],
      "source": [
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.optim as optim\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 43,
      "metadata": {
        "id": "MCLvDF69rehP"
      },
      "outputs": [],
      "source": [
        "class OneDimSubnet(nn.Module):\n",
        "    def __init__(self, input_dim, hidden_dim):\n",
        "        super(OneDimSubnet, self).__init__()\n",
        "        self.fc1 = nn.Linear(1, hidden_dim)\n",
        "        self.fc2 = nn.Linear(hidden_dim, hidden_dim)\n",
        "        self.fc3 = nn.Linear(hidden_dim, hidden_dim)\n",
        "        self.fc4 = nn.Linear(hidden_dim, 1)\n",
        "        self.activation = nn.ReLU()\n",
        "        self.dropout = nn.Dropout(0.01)\n",
        "\n",
        "    def forward(self, x):\n",
        "        x = self.activation(self.fc1(x))\n",
        "        x = self.dropout(self.activation(self.fc2(x)))\n",
        "        x = self.dropout(self.activation(self.fc3(x)))\n",
        "        x = self.fc4(x)\n",
        "        return x"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {
        "id": "IXuVHc_0rqyB"
      },
      "outputs": [],
      "source": [
        "class KolmogorovArnoldNN(nn.Module):\n",
        "    def __init__(self, input_dim, hidden_dim, output_dim, num_subnets):\n",
        "        super(KolmogorovArnoldNN, self).__init__()\n",
        "        self.subnets = nn.ModuleList([OneDimSubnet(1, hidden_dim) for _ in range(num_subnets)])\n",
        "        self.final_layer = nn.Linear(num_subnets, output_dim)\n",
        "\n",
        "    def forward(self, x):\n",
        "        outputs = []\n",
        "        for i in range(x.size(1)):\n",
        "            subnet_output = self.subnets[i](x[:, i].unsqueeze(1))\n",
        "            outputs.append(subnet_output)\n",
        "        concatenated_outputs = torch.cat(outputs, dim=1)\n",
        "        final_output = self.final_layer(concatenated_outputs)\n",
        "        return final_output"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {
        "id": "qMNvZDbsry0N"
      },
      "outputs": [],
      "source": [
        "class StandardNN(nn.Module):\n",
        "    def __init__(self, input_dim, hidden_dim, output_dim):\n",
        "        super(StandardNN, self).__init__()\n",
        "        self.fc1 = nn.Linear(input_dim, hidden_dim)\n",
        "        self.fc2 = nn.Linear(hidden_dim, hidden_dim)\n",
        "        self.fc3 = nn.Linear(hidden_dim, output_dim)\n",
        "        self.activation = nn.ReLU()\n",
        "\n",
        "    def forward(self, x):\n",
        "        x = self.activation(self.fc1(x))\n",
        "        x = self.activation(self.fc2(x))\n",
        "        x = self.fc3(x)\n",
        "        return x"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 40,
      "metadata": {
        "id": "DBojRIShr-bD"
      },
      "outputs": [],
      "source": [
        "def train_model(model, criterion, optimizer, x, y, num_epochs):\n",
        "    loss_history = []\n",
        "    for epoch in range(num_epochs):\n",
        "        model.train()\n",
        "        optimizer.zero_grad()\n",
        "\n",
        "        outputs = model(x)\n",
        "        loss = criterion(outputs, y)\n",
        "\n",
        "        loss.backward()\n",
        "        optimizer.step()\n",
        "\n",
        "        loss_history.append(loss.item())\n",
        "\n",
        "        if (epoch + 1) % 100 == 0:\n",
        "            print(f'Epoch [{epoch + 1}/{num_epochs}], Loss: {loss.item():.4f}')\n",
        "\n",
        "    return loss_history\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 50,
      "metadata": {
        "id": "nuKM_1bwsKMu"
      },
      "outputs": [],
      "source": [
        "input_dim = 3\n",
        "hidden_dim = 5\n",
        "output_dim = 1\n",
        "num_epochs = 1000\n",
        "learning_rate = 0.005\n",
        "batch_size = 32\n",
        "num_subnets = input_dim  # Number of subnets should match the input dimension\n",
        "\n",
        "# Create dummy data\n",
        "x = torch.randn((1000, input_dim))\n",
        "y = torch.randn((1000, output_dim))\n",
        "\n",
        "# Initialize models, loss function and optimizers\n",
        "kann = KolmogorovArnoldNN(input_dim, hidden_dim, output_dim, num_subnets)\n",
        "standard_nn = StandardNN(input_dim, hidden_dim, output_dim)\n",
        "criterion = nn.MSELoss()\n",
        "optimizer_kann = optim.Adam(kann.parameters(), lr=learning_rate)\n",
        "optimizer_standard_nn = optim.Adam(standard_nn.parameters(), lr=learning_rate)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 51,
      "metadata": {
        "id": "VM3gvoW6uqyt",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "091411ef-41a2-4c9f-d191-144a40479c74"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch [100/1000], Loss: 0.9678\n",
            "Epoch [200/1000], Loss: 0.9643\n",
            "Epoch [300/1000], Loss: 0.9614\n",
            "Epoch [400/1000], Loss: 0.9571\n",
            "Epoch [500/1000], Loss: 0.9567\n",
            "Epoch [600/1000], Loss: 0.9584\n",
            "Epoch [700/1000], Loss: 0.9584\n",
            "Epoch [800/1000], Loss: 0.9522\n",
            "Epoch [900/1000], Loss: 0.9534\n",
            "Epoch [1000/1000], Loss: 0.9520\n",
            "Epoch [100/1000], Loss: 0.9734\n",
            "Epoch [200/1000], Loss: 0.9660\n",
            "Epoch [300/1000], Loss: 0.9595\n",
            "Epoch [400/1000], Loss: 0.9569\n",
            "Epoch [500/1000], Loss: 0.9534\n",
            "Epoch [600/1000], Loss: 0.9508\n",
            "Epoch [700/1000], Loss: 0.9491\n",
            "Epoch [800/1000], Loss: 0.9479\n",
            "Epoch [900/1000], Loss: 0.9463\n",
            "Epoch [1000/1000], Loss: 0.9454\n"
          ]
        }
      ],
      "source": [
        "loss_kann = train_model(kann, criterion, optimizer_kann, x, y, num_epochs)\n",
        "loss_standard_nn = train_model(standard_nn, criterion, optimizer_standard_nn, x, y, num_epochs)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 52,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 469
        },
        "id": "8fWnT018vLvr",
        "outputId": "e226138f-19c4-42ed-aeac-1c8351f6076c"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "plt.figure(figsize=(10, 5))\n",
        "plt.plot(loss_kann, label='Kolmogorov-Arnold NN')\n",
        "plt.plot(loss_standard_nn, label='Standard NN')\n",
        "plt.xlabel('Epoch')\n",
        "plt.ylabel('Loss')\n",
        "plt.title('Training Loss Comparison')\n",
        "plt.legend()\n",
        "plt.show()"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyM+X4TeLmQ4YxHdeoPZrnK5",
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}