Kolmogorov_Arnold_Networks.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/worthlessFella/deep_learning/blob/main/Kolmogorov_Arnold_Networks.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "134e7f9d",
      "metadata": {
        "id": "134e7f9d"
      },
      "source": [
        "# Hello, Kolmogorov-Arnold Networks (KAN)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "59cf5cd0",
      "metadata": {
        "id": "59cf5cd0"
      },
      "source": [
        "### Kolmogorov-Arnold representation theorem"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "f88e5321",
      "metadata": {
        "id": "f88e5321"
      },
      "source": [
        "Kolmogorov-Arnold representation theorem states that if $f$ is a multivariate continuous function\n",
        "on a bounded domain, then it can be written as a finite composition of continuous functions of a\n",
        "single variable and the binary operation of addition. More specifically, for a smooth $f : [0,1]^n \\to \\mathbb{R}$,\n",
        "\n",
        "\n",
        "$$f(x) = f(x_1,...,x_n)=\\sum_{q=1}^{2n+1}\\Phi_q(\\sum_{p=1}^n \\phi_{q,p}(x_p))$$\n",
        "\n",
        "where $\\phi_{q,p}:[0,1]\\to\\mathbb{R}$ and $\\Phi_q:\\mathbb{R}\\to\\mathbb{R}$. In a sense, they showed that the only true multivariate function is addition, since every other function can be written using univariate functions and sum. However, this 2-Layer width-$(2n+1)$ Kolmogorov-Arnold representation may not be smooth due to its limited expressive power. We augment its expressive power by generalizing it to arbitrary depths and widths."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "ebd8766a",
      "metadata": {
        "id": "ebd8766a"
      },
      "source": [
        "### Kolmogorov-Arnold Network (KAN)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "2cf3b1ee",
      "metadata": {
        "id": "2cf3b1ee"
      },
      "source": [
        "The Kolmogorov-Arnold representation can be written in matrix form\n",
        "\n",
        "$$f(x)={\\bf \\Phi}_{\\rm out}\\circ{\\bf \\Phi}_{\\rm in}\\circ {\\bf x}$$\n",
        "\n",
        "where\n",
        "\n",
        "$${\\bf \\Phi}_{\\rm in}= \\begin{pmatrix} \\phi_{1,1}(\\cdot) & \\cdots & \\phi_{1,n}(\\cdot) \\\\ \\vdots & & \\vdots \\\\ \\phi_{2n+1,1}(\\cdot) & \\cdots & \\phi_{2n+1,n}(\\cdot) \\end{pmatrix},\\quad {\\bf \\Phi}_{\\rm out}=\\begin{pmatrix} \\Phi_1(\\cdot) & \\cdots & \\Phi_{2n+1}(\\cdot)\\end{pmatrix}$$"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "f6521452",
      "metadata": {
        "id": "f6521452"
      },
      "source": [
        "We notice that both ${\\bf \\Phi}_{\\rm in}$ and ${\\bf \\Phi}_{\\rm out}$ are special cases of the following function matrix ${\\bf \\Phi}$ (with $n_{\\rm in}$ inputs, and $n_{\\rm out}$ outputs), we call a Kolmogorov-Arnold layer:\n",
        "\n",
        "$${\\bf \\Phi}= \\begin{pmatrix} \\phi_{1,1}(\\cdot) & \\cdots & \\phi_{1,n_{\\rm in}}(\\cdot) \\\\ \\vdots & & \\vdots \\\\ \\phi_{n_{\\rm out},1}(\\cdot) & \\cdots & \\phi_{n_{\\rm out},n_{\\rm in}}(\\cdot) \\end{pmatrix}$$\n",
        "\n",
        "${\\bf \\Phi}_{\\rm in}$ corresponds to $n_{\\rm in}=n, n_{\\rm out}=2n+1$, and ${\\bf \\Phi}_{\\rm out}$ corresponds to $n_{\\rm in}=2n+1, n_{\\rm out}=1$."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "1b410498",
      "metadata": {
        "id": "1b410498"
      },
      "source": [
        "After defining the layer, we can construct a Kolmogorov-Arnold network simply by stacking layers! Let's say we have $L$ layers, with the $l^{\\rm th}$ layer ${\\bf \\Phi}_l$ have shape $(n_{l+1}, n_{l})$. Then the whole network is\n",
        "\n",
        "$${\\rm KAN}({\\bf x})={\\bf \\Phi}_{L-1}\\circ\\cdots \\circ{\\bf \\Phi}_1\\circ{\\bf \\Phi}_0\\circ {\\bf x}$$"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "54bbde9a",
      "metadata": {
        "id": "54bbde9a"
      },
      "source": [
        "In constrast, a Multi-Layer Perceptron is interleaved by linear layers ${\\bf W}_l$ and nonlinearities $\\sigma$:\n",
        "\n",
        "$${\\rm MLP}({\\bf x})={\\bf W}_{L-1}\\circ\\sigma\\circ\\cdots\\circ {\\bf W}_1\\circ\\sigma\\circ {\\bf W}_0\\circ {\\bf x}$$"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "1c5f7795",
      "metadata": {
        "id": "1c5f7795"
      },
      "source": [
        "A KAN can be easily visualized. (1) A KAN is simply stack of KAN layers. (2) Each KAN layer can be visualized as a fully-connected layer, with a 1D function placed on each edge. Let's see an example below."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "adcb5f75",
      "metadata": {
        "id": "adcb5f75"
      },
      "source": [
        "### Get started with KANs"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "2571d531",
      "metadata": {
        "id": "2571d531"
      },
      "source": [
        "Initialize KAN"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install pykan"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zzT2ylS6UXi3",
        "outputId": "7351e25c-ba13-409c-b0bb-057e26b7486f"
      },
      "id": "zzT2ylS6UXi3",
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Collecting pykan\n",
            "  Downloading pykan-0.0.5-py3-none-any.whl (33 kB)\n",
            "Installing collected packages: pykan\n",
            "Successfully installed pykan-0.0.5\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import torch\n",
        "from kan import *"
      ],
      "metadata": {
        "id": "IlZVfcy6UhNs"
      },
      "id": "IlZVfcy6UhNs",
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "id": "2075ef56",
      "metadata": {
        "id": "2075ef56"
      },
      "outputs": [],
      "source": [
        "\n",
        "# create a KAN: 2D inputs, 1D output, and 5 hidden neurons. cubic spline (k=3), 5 grid intervals (grid=5).\n",
        "model = KAN(width=[2,5,1], grid=5, k=3, seed=0)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "3d72e076",
      "metadata": {
        "id": "3d72e076"
      },
      "source": [
        "Create dataset"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "id": "46717e8b",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "46717e8b",
        "outputId": "129a871b-b6af-4cb5-ab55-a73b01df8c6e"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(torch.Size([1000, 2]), torch.Size([1000, 1]))"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ],
      "source": [
        "# create dataset f(x,y) = exp(sin(pi*x)+y^2)\n",
        "f = lambda x: torch.exp(torch.sin(torch.pi*x[:,[0]]) + x[:,[1]]**2)\n",
        "dataset = create_dataset(f, n_var=2)\n",
        "dataset['train_input'].shape, dataset['train_label'].shape"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "8c6add1d",
      "metadata": {
        "id": "8c6add1d"
      },
      "source": [
        "Plot KAN at initialization"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "id": "ac76f858",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 345
        },
        "id": "ac76f858",
        "outputId": "300591a9-caec-441d-c5a3-33f3250afd53"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x400 with 16 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# plot KAN at initialization\n",
        "model(dataset['train_input']);\n",
        "model.plot(beta=100)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "ddf67e30",
      "metadata": {
        "id": "ddf67e30"
      },
      "source": [
        "Train KAN with sparsity regularization"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "id": "97111d75",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "97111d75",
        "outputId": "be6d8fe7-2286-4d94-ea1b-0367b0bd62bb"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "train loss: 1.18e-01 | test loss: 1.20e-01 | reg: 1.74e+01 : 100%|██| 20/20 [00:17<00:00,  1.11it/s]\n"
          ]
        }
      ],
      "source": [
        "# train the model\n",
        "model.train(dataset, opt=\"LBFGS\", steps=20, lamb=0.01, lamb_entropy=10.);"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "2f30c3ab",
      "metadata": {
        "id": "2f30c3ab"
      },
      "source": [
        "Plot trained KAN"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "id": "3f95fcdd",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 345
        },
        "id": "3f95fcdd",
        "outputId": "33c71997-f768-4026-ff46-8c93e6216eb3"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x400 with 16 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "model.plot()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "61d537b7",
      "metadata": {
        "id": "61d537b7"
      },
      "source": [
        "Prune KAN and replot (keep the original shape)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "id": "1269a698",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 345
        },
        "id": "1269a698",
        "outputId": "6033a81b-08e3-4d5a-901c-47bb9e252caa"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x400 with 16 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "model.prune()\n",
        "model.plot(mask=True)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "576856cf",
      "metadata": {
        "id": "576856cf"
      },
      "source": [
        "Prune KAN and replot (get a smaller shape)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "id": "7fe6fb12",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 345
        },
        "id": "7fe6fb12",
        "outputId": "cfe8a4a5-14cc-4ba6-b483-4af6f78313a9"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x400 with 10 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "model = model.prune()\n",
        "model(dataset['train_input'])\n",
        "model.plot()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "bd08ad99",
      "metadata": {
        "id": "bd08ad99"
      },
      "source": [
        "Continue training and replot"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "id": "18a2db11",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "18a2db11",
        "outputId": "af09e8cf-d3a0-4b4f-f595-692be200f178"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "train loss: 4.03e-03 | test loss: 4.13e-03 | reg: 1.43e+01 : 100%|██| 50/50 [00:19<00:00,  2.61it/s]\n"
          ]
        }
      ],
      "source": [
        "model.train(dataset, opt=\"LBFGS\", steps=50);"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "id": "af27aba7",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 345
        },
        "id": "af27aba7",
        "outputId": "40bb3cea-8b92-4041-c459-9970f14b9396"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x400 with 10 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "model.plot()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "cf35d505",
      "metadata": {
        "id": "cf35d505"
      },
      "source": [
        "Automatically or manually set activation functions to be symbolic"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "id": "b3c0642b",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "b3c0642b",
        "outputId": "09a62348-8f37-40af-cd35-79ba2236929d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "fixing (0,0,0) with sin, r2=0.9985771775245667\n",
            "fixing (0,0,1) with sin, r2=0.9999732375144958\n",
            "fixing (0,0,2) with sin, r2=0.9987999200820923\n",
            "fixing (0,1,0) with sin, r2=0.7753256559371948\n",
            "fixing (0,1,1) with sin, r2=0.9886652231216431\n",
            "fixing (0,1,2) with x^2, r2=0.9991509318351746\n",
            "fixing (1,0,0) with x^4, r2=0.9967542290687561\n",
            "fixing (1,1,0) with exp, r2=0.9999944567680359\n",
            "fixing (1,2,0) with log, r2=0.9297364354133606\n"
          ]
        }
      ],
      "source": [
        "mode = \"auto\" # \"manual\"\n",
        "\n",
        "if mode == \"manual\":\n",
        "    # manual mode\n",
        "    model.fix_symbolic(0,0,0,'sin');\n",
        "    model.fix_symbolic(0,1,0,'x^2');\n",
        "    model.fix_symbolic(1,0,0,'exp');\n",
        "elif mode == \"auto\":\n",
        "    # automatic mode\n",
        "    lib = ['x','x^2','x^3','x^4','exp','log','sqrt','tanh','sin','abs']\n",
        "    model.auto_symbolic(lib=lib)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "821ba616",
      "metadata": {
        "id": "821ba616"
      },
      "source": [
        "Continue training to almost machine precision"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "id": "c0800415",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "c0800415",
        "outputId": "6bf6a962-4b0a-44fe-8c90-24ae677b8e3a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "train loss: 4.47e-03 | test loss: 4.44e-03 | reg: 3.14e+01 : 100%|██| 50/50 [00:19<00:00,  2.61it/s]\n"
          ]
        }
      ],
      "source": [
        "model.train(dataset, opt=\"LBFGS\", steps=50);"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "e39da499",
      "metadata": {
        "id": "e39da499"
      },
      "source": [
        "Obtain the symbolic formula"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "id": "bf44f7e0",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        },
        "id": "bf44f7e0",
        "outputId": "777ac6d4-1b42-4246-eb87-fd2427ded317"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.26*(0.34*sin(3.16*x_1 - 0.e-2) + 1)**4 + 4.21*exp(1.0*sin(3.14*x_1) + 1.85*sin(1.25*x_2 - 1.57)) + 0.05*log(-0.05*(-x_2 - 0.9)**2 - 0.02*sin(2.63*x_1 + 9.35) + 7.79) - 0.01"
            ],
            "text/latex": "$\\displaystyle 0.26 \\left(0.34 \\sin{\\left(3.16 x_{1} - 0.01 \\right)} + 1\\right)^{4} + 4.21 e^{1.0 \\sin{\\left(3.14 x_{1} \\right)} + 1.85 \\sin{\\left(1.25 x_{2} - 1.57 \\right)}} + 0.05 \\log{\\left(- 0.05 \\left(- x_{2} - 0.9\\right)^{2} - 0.02 \\sin{\\left(2.63 x_{1} + 9.35 \\right)} + 7.79 \\right)} - 0.01$"
          },
          "metadata": {},
          "execution_count": 14
        }
      ],
      "source": [
        "model.symbolic_formula()[0][0]"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3 (ipykernel)",
      "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": "3.9.7"
    },
    "colab": {
      "provenance": [],
      "include_colab_link": true
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}