From 9da5422d9e13d6132944ea8bbbeca1ade29d2971 Mon Sep 17 00:00:00 2001 From: Mihir Kamat Date: Thu, 9 Oct 2025 19:38:01 -0400 Subject: [PATCH 01/10] Added gitignore --- .gitignore | 4 ++++ 1 file changed, 4 insertions(+) create mode 100644 .gitignore diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..6a57fc1 --- /dev/null +++ b/.gitignore @@ -0,0 +1,4 @@ +./Include +./Lib +./Scripts +./share \ No newline at end of file From e8d5e955dfdbffc1700a47da46f6e97aa9a82f51 Mon Sep 17 00:00:00 2001 From: Mihir Kamat Date: Thu, 9 Oct 2025 19:40:25 -0400 Subject: [PATCH 02/10] Added img folder to save plots --- img/.gitkeep | 0 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 img/.gitkeep diff --git a/img/.gitkeep b/img/.gitkeep new file mode 100644 index 0000000..e69de29 From fd3777c347c44c7c3c98eb3821a89b2ba9c261d4 Mon Sep 17 00:00:00 2001 From: Mihir Kamat Date: Thu, 9 Oct 2025 22:09:28 -0400 Subject: [PATCH 03/10] Modify original NTK script to handle 2d NTK calculation, as well as variable depth --- .gitignore | 8 +- NKT_simple_demo.ipynb | 318 ------------ img/width100.png | Bin 0 -> 22732 bytes img/width1000.png | Bin 0 -> 22059 bytes img/width1500.png | Bin 0 -> 23539 bytes img/width2000.png | Bin 0 -> 25791 bytes img/width500.png | Bin 0 -> 22143 bytes jax_NTK_library_experiments.ipynb | 769 ------------------------------ requirements.txt | 0 run.py | 180 +++++++ setup_venv.sh | 3 + testNTK.ipynb | 341 ------------- 12 files changed, 187 insertions(+), 1432 deletions(-) delete mode 100644 NKT_simple_demo.ipynb create mode 100644 img/width100.png create mode 100644 img/width1000.png create mode 100644 img/width1500.png create mode 100644 img/width2000.png create mode 100644 img/width500.png delete mode 100644 jax_NTK_library_experiments.ipynb create mode 100644 requirements.txt create mode 100644 run.py create mode 100644 setup_venv.sh delete mode 100644 testNTK.ipynb diff --git a/.gitignore b/.gitignore index 6a57fc1..b37762e 100644 --- a/.gitignore +++ b/.gitignore @@ -1,4 +1,4 @@ -./Include -./Lib -./Scripts -./share \ No newline at end of file +./Include/* +./Lib/* +./Scripts/* +./share/* \ No newline at end of file diff --git a/NKT_simple_demo.ipynb b/NKT_simple_demo.ipynb deleted file mode 100644 index 34385b9..0000000 --- a/NKT_simple_demo.ipynb +++ /dev/null @@ -1,318 +0,0 @@ -{ - "nbformat": 4, - "nbformat_minor": 0, - "metadata": { - "colab": { - "provenance": [], - "authorship_tag": "ABX9TyN119U+fLpKBTcJEfQ8q1iH", - "include_colab_link": true - }, - "kernelspec": { - "name": "python3", - "display_name": "Python 3" - }, - "language_info": { - "name": "python" - } - }, - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "id": "view-in-github", - "colab_type": "text" - }, - "source": [ - "\"Open" - ] - }, - { - "cell_type": "markdown", - "source": [ - "Import packages." - ], - "metadata": { - "id": "oXGr_oZIcA6a" - } - }, - { - "cell_type": "code", - "execution_count": 133, - "metadata": { - "id": "f16WQGsUlaxn" - }, - "outputs": [], - "source": [ - "import torch\n", - "import torch.nn as nn\n", - "import numpy as np\n", - "import random\n", - "import typing\n", - "import matplotlib.pyplot as plt\n", - "torch.use_deterministic_algorithms=True" - ] - }, - { - "cell_type": "markdown", - "source": [ - "Initialize model using torch. Need to handle set seed each time to manage randomness." - ], - "metadata": { - "id": "UUSLY2r3cG2_" - } - }, - { - "cell_type": "code", - "source": [ - "def init_model(n:int,seed:int,activation:nn.Module)->nn.Sequential:\n", - " torch.manual_seed(seed)\n", - " random.seed(seed)\n", - " net = nn.Sequential(\n", - " nn.Linear(2,n),\n", - " activation(),\n", - " nn.Linear(n,n),\n", - " activation(),\n", - " nn.Linear(n,n),\n", - " activation(),\n", - " nn.Linear(n,1)\n", - ")\n", - " return net" - ], - "metadata": { - "id": "nUZLQHfES9z5" - }, - "execution_count": 134, - "outputs": [] - }, - { - "cell_type": "markdown", - "source": [ - "Helpful functions. Get a list of model parameters or gradients associated with parameters. Also get 2x1 tensor input matching Jacot paper." - ], - "metadata": { - "id": "dxrLnFvNcTrw" - } - }, - { - "cell_type": "code", - "source": [ - "def get_grads(net):\n", - " theta = [param.grad.flatten() for name,param in net.named_parameters()]\n", - " theta = torch.concatenate(theta)\n", - " return theta\n", - "\n", - "def get_params(net):\n", - " theta = [param.flatten() for name,param in net.named_parameters()]\n", - " theta = torch.concatenate(theta)\n", - " return theta\n", - "\n", - "def input(gamma:float)->torch.Tensor:\n", - " gamma=torch.Tensor([gamma])\n", - " x=torch.tensor([torch.cos(gamma),torch.sin(gamma)])\n", - " return x" - ], - "metadata": { - "id": "_0z2gaMZUgSe" - }, - "execution_count": 135, - "outputs": [] - }, - { - "cell_type": "markdown", - "source": [ - "Function to get NKT. Here, I just used the gradients automatically calculated by torch. Torch calculates gradients of the loss function with respect to the parameters, so I used an identity mapping as the loss to get gradient of the output with respect to the parameters. The NKT is just the inner product of the gradients for each input." - ], - "metadata": { - "id": "RWe9KcvCdFNv" - } - }, - { - "cell_type": "code", - "source": [ - "def NKT(n:int,seed:int,act:nn.Module,x1:torch.Tensor,x2:torch.Tensor)->torch.Tensor:\n", - " loss_fn=nn.Identity()\n", - "\n", - " net=init_model(n,seed,act)\n", - " out=net.forward(x1)\n", - " loss = loss_fn(out)\n", - " loss.backward()\n", - " theta1=get_grads(net)\n", - "\n", - " net=init_model(n,seed,nn.ReLU)\n", - " out=net.forward(torch.Tensor(x2))\n", - " loss = loss_fn(out)\n", - " loss.backward()\n", - " theta2=get_grads(net)\n", - "\n", - " NKT=torch.inner(theta1,theta2)\n", - " return NKT\n", - "\n", - "def get_NKTs(n:int,seed:int,act:nn.Module,ref_x,gamma_spacing:float=0.01)->torch.Tensor:\n", - " gammas=torch.arange(-1,1,gamma_spacing)\n", - " NKTs=[NKT(n,seed,act,input(gamma),ref_x) for gamma in gammas]\n", - " return NKTs" - ], - "metadata": { - "id": "p2uboSG9Ukop" - }, - "execution_count": 146, - "outputs": [] - }, - { - "cell_type": "markdown", - "source": [ - "Experiment across 4 seeds with different depths." - ], - "metadata": { - "id": "zGfVfQkIdqZI" - } - }, - { - "cell_type": "code", - "source": [ - "seeds = [0,4,22,42]\n", - "n=100\n", - "act=nn.ReLU\n", - "x_ref=torch.Tensor([1,0])\n", - "gammas=torch.arange(-1,1,0.01)\n", - "\n", - "for seed in seeds:\n", - " NKTs=get_NKTs(n,seed,act,x_ref)\n", - " plt.plot(gammas,NKTs)\n", - "\n", - "plt.title(f\"NKTs across 4 seeds with depth {n}\")\n", - "plt.xlabel(\"gamma\")\n", - "plt.ylabel(\"NKT\")\n" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 489 - }, - "id": "dWip5243lpe2", - "outputId": "e11067a2-1e7f-46b3-a1ef-c806ff772d89" - }, - "execution_count": 147, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "Text(0, 0.5, 'NKT')" - ] - }, - "metadata": {}, - "execution_count": 147 - }, - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
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\n" - }, - "metadata": {} - } - ] - }, - { - "cell_type": "code", - "source": [ - "seeds = [0,4,22,42]\n", - "n=500\n", - "act=nn.ReLU\n", - "x_ref=torch.Tensor([1,0])\n", - "gammas=torch.arange(-1,1,0.01)\n", - "\n", - "for seed in seeds:\n", - " NKTs=get_NKTs(n,seed,act,x_ref)\n", - " plt.plot(gammas,NKTs)\n", - "\n", - "plt.title(f\"NKTs across 4 seeds with depth {n}\")\n", - "plt.xlabel(\"gamma\")\n", - "plt.ylabel(\"NKT\")\n" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 489 - }, - "id": "n0JIOlHWbZHI", - "outputId": "b0369878-5817-426b-c4db-1812a8f2b047" - }, - "execution_count": 148, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "Text(0, 0.5, 'NKT')" - ] - }, - "metadata": {}, - "execution_count": 148 - }, - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ] - }, - { - "cell_type": "code", - "source": [ - "seeds = [0,4,22,42]\n", - "n=1000\n", - "act=nn.ReLU\n", - "x_ref=torch.Tensor([1,0])\n", - "gammas=torch.arange(-1,1,0.01)\n", - "\n", - "for seed in seeds:\n", - " NKTs=get_NKTs(n,seed,act,x_ref)\n", - " plt.plot(gammas,NKTs)\n", - "\n", - "plt.title(f\"NKTs across 4 seeds with depth {n}\")\n", - "plt.xlabel(\"gamma\")\n", - "plt.ylabel(\"NKT\")\n" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 489 - }, - "id": "-TFokuWlbjPG", - "outputId": "e26bf254-6824-44b7-c452-36e1e8189696" - }, - "execution_count": 149, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "Text(0, 0.5, 'NKT')" - ] - }, - "metadata": {}, - "execution_count": 149 - }, - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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in /usr/local/lib/python3.12/dist-packages (from werkzeug>=1.0.1->tensorboard~=2.19.0->tensorflow>=2.15.0->neural-tangents) (3.0.3)\n", - "Requirement already satisfied: markdown-it-py>=2.2.0 in /usr/local/lib/python3.12/dist-packages (from rich->keras>=3.5.0->tensorflow>=2.15.0->neural-tangents) (4.0.0)\n", - "Requirement already satisfied: pygments<3.0.0,>=2.13.0 in /usr/local/lib/python3.12/dist-packages (from rich->keras>=3.5.0->tensorflow>=2.15.0->neural-tangents) (2.19.2)\n", - "Requirement already satisfied: mdurl~=0.1 in /usr/local/lib/python3.12/dist-packages (from markdown-it-py>=2.2.0->rich->keras>=3.5.0->tensorflow>=2.15.0->neural-tangents) (0.1.2)\n" - ] - } - ], - "source": [ - "pip install jax jaxlib neural-tangents matplotlib" - ] - }, - { - "cell_type": "code", - "source": [ - "import jax\n", - "import jax.numpy as jnp\n", - "from neural_tangents import stax\n", - "\n", - "#Create perceptron with Relu\n", - "init_fn, apply_fn, kernel_fn = stax.serial(\n", - " stax.Dense(1024), stax.Relu(),\n", - " stax.Dense(1024), stax.Relu(),\n", - " stax.Dense(1)\n", - ")\n", - "\n", - "#Model after sin function,\n", - "#20 points between -5 and 5 (reshape into column vector)\n", - "x_train = jnp.linspace(-5, 5, 20).reshape(-1, 1)\n", - "y_train = jnp.sin(x_train)\n", - "\n", - "x_test = jnp.linspace(-6, 6, 100).reshape(-1, 1)\n", - "\n", - "#Create train data with NTK\n", - "kernel_train_train = kernel_fn(x_train, x_train, 'ntk')\n", - "kernel_test_train = kernel_fn(x_test, x_train, 'ntk')\n", - "\n", - "#Predict with train data\n", - "lambda_reg = 1e-3\n", - "K_inv = jnp.linalg.inv(kernel_train_train + lambda_reg * jnp.eye(len(x_train)))\n", - "y_pred = kernel_test_train @ K_inv @ y_train\n", - "\n", - "#Visualize contrast\n", - "import matplotlib.pyplot as plt\n", - "plt.figure()\n", - "plt.plot(x_train, y_train, 'ro', label='Train')\n", - "plt.plot(x_test, y_pred, 'b-', label='NTK Prediction')\n", - "plt.legend()\n", - "plt.show()" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 430 - }, - "id": "t1vl7aTW9tA-", - "outputId": "46853e64-a916-4d29-f872-38645fe50882" - }, - "execution_count": 54, - "outputs": [ - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ] - }, - { - "cell_type": "markdown", - "source": [ - "NKT prediction of a sine function or quadratic function performs very poorly without regularization." - ], - "metadata": { - "id": "yhLxqS0exi3I" - } - }, - { - "cell_type": "code", - "source": [ - "# try without regularization\n", - "#Create perceptron with Relu\n", - "init_fn, apply_fn, kernel_fn = stax.serial(\n", - " stax.Dense(128), stax.Relu(),\n", - " stax.Dense(128), stax.Relu(),\n", - " stax.Dense(1)\n", - ")\n", - "\n", - "#Model after sin function,\n", - "#20 points between -5 and 5 (reshape into column vector)\n", - "x_train = jnp.linspace(-5, 5, 20).reshape(-1, 1)\n", - "y_train = jnp.sin(x_train)\n", - "\n", - "x_test = jnp.linspace(-6, 6, 100).reshape(-1, 1)\n", - "\n", - "#Create train data with NTK\n", - "kernel_train_train = kernel_fn(x_train, x_train, 'ntk')\n", - "kernel_test_train = kernel_fn(x_test, x_train, 'ntk')\n", - "\n", - "#Predict with train data\n", - "lambda_reg = 0\n", - "K_inv = jnp.linalg.inv(kernel_train_train + lambda_reg * jnp.eye(len(x_train)))\n", - "y_pred = kernel_test_train @ K_inv @ y_train\n", - "\n", - "#Visualize contrast\n", - "import matplotlib.pyplot as plt\n", - "plt.figure()\n", - "plt.plot(x_train, y_train, 'ro', label='Train')\n", - "plt.plot(x_test, y_pred, 'b-', label='NTK Prediction')\n", - "plt.legend()\n", - "plt.show()" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 430 - }, - "id": "2V3VTrtUxPAk", - "outputId": "57de2559-b3e0-46a0-d6c9-8513d79a1367" - }, - "execution_count": 55, - "outputs": [ - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ] - }, - { - "cell_type": "code", - "source": [ - "# try without regularization\n", - "#Create perceptron with Relu\n", - "init_fn, apply_fn, kernel_fn = stax.serial(\n", - " stax.Dense(128), stax.Relu(),\n", - " stax.Dense(128), stax.Relu(),\n", - " stax.Dense(1)\n", - ")\n", - "\n", - "#Model after sin function,\n", - "#20 points between -5 and 5 (reshape into column vector)\n", - "x_train = jnp.linspace(-5, 5, 20).reshape(-1, 1)\n", - "y_train = jnp.square(x_train)\n", - "\n", - "x_test = jnp.linspace(-6, 6, 100).reshape(-1, 1)\n", - "\n", - "#Create train data with NTK\n", - "kernel_train_train = kernel_fn(x_train, x_train, 'ntk')\n", - "kernel_test_train = kernel_fn(x_test, x_train, 'ntk')\n", - "\n", - "#Predict with train data\n", - "lambda_reg = 0\n", - "K_inv = jnp.linalg.inv(kernel_train_train + lambda_reg * jnp.eye(len(x_train)))\n", - "y_pred = kernel_test_train @ K_inv @ y_train\n", - "\n", - "#Visualize contrast\n", - "import matplotlib.pyplot as plt\n", - "plt.figure()\n", - "plt.plot(x_train, y_train, 'ro', label='Train')\n", - "plt.plot(x_test, y_pred, 'b-', label='NTK Prediction')\n", - "plt.legend()\n", - "plt.show()" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 430 - }, - "id": "ZR7NocZYxuLK", - "outputId": "b1046e68-0a56-4a5c-c5a7-2df86e4ac20b" - }, - "execution_count": 56, - "outputs": [ - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ] - }, - { - "cell_type": "markdown", - "source": [ - "Try alternative activations (with regularization). Gelu and Gabor perform much better.\n", - "\n", - "---\n", - "\n" - ], - "metadata": { - "id": "deswUBfpzFVD" - } - }, - { - "cell_type": "code", - "source": [ - "# try with different activations\n", - "act=stax.Gelu()\n", - "\n", - "init_fn, apply_fn, kernel_fn = stax.serial(\n", - " stax.Dense(128), act,\n", - " stax.Dense(128), act,\n", - " stax.Dense(1)\n", - ")\n", - "\n", - "#Model after sin function,\n", - "#20 points between -5 and 5 (reshape into column vector)\n", - "x_train = jnp.linspace(-5, 5, 20).reshape(-1, 1)\n", - "y_train = jnp.sin(x_train)\n", - "\n", - "x_test = jnp.linspace(-6, 6, 100).reshape(-1, 1)\n", - "\n", - "#Create train data with NTK\n", - "kernel_train_train = kernel_fn(x_train, x_train, 'ntk')\n", - "kernel_test_train = kernel_fn(x_test, x_train, 'ntk')\n", - "\n", - "#Predict with train data\n", - "lambda_reg = 1e-3\n", - "K_inv = jnp.linalg.inv(kernel_train_train + lambda_reg * jnp.eye(len(x_train)))\n", - "y_pred = kernel_test_train @ K_inv @ y_train\n", - "\n", - "#Visualize contrast\n", - "import matplotlib.pyplot as plt\n", - "plt.figure()\n", - "plt.plot(x_train, y_train, 'ro', label='Train')\n", - "plt.plot(x_test, y_pred, 'b-', label='NTK Prediction')\n", - "plt.legend()\n", - "plt.show()" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 430 - }, - "id": "KKmAF7uNyWCu", - "outputId": "88f88f98-5219-49d4-fde0-fadd70f8a6fe" - }, - "execution_count": 57, - "outputs": [ - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ] - }, - { - "cell_type": "code", - "source": [ - "# try with different activations\n", - "act=stax.Gabor()\n", - "\n", - "init_fn, apply_fn, kernel_fn = stax.serial(\n", - " stax.Dense(128), act,\n", - " stax.Dense(128), act,\n", - " stax.Dense(1)\n", - ")\n", - "\n", - "#Model after sin function,\n", - "#20 points between -5 and 5 (reshape into column vector)\n", - "x_train = jnp.linspace(-5, 5, 20).reshape(-1, 1)\n", - "y_train = jnp.sin(x_train)\n", - "\n", - "x_test = jnp.linspace(-6, 6, 100).reshape(-1, 1)\n", - "\n", - "#Create train data with NTK\n", - "kernel_train_train = kernel_fn(x_train, x_train, 'ntk')\n", - "kernel_test_train = kernel_fn(x_test, x_train, 'ntk')\n", - "\n", - "#Predict with train data\n", - "lambda_reg = 1e-3\n", - "K_inv = jnp.linalg.inv(kernel_train_train + lambda_reg * jnp.eye(len(x_train)))\n", - "y_pred = kernel_test_train @ K_inv @ y_train\n", - "\n", - "#Visualize contrast\n", - "import matplotlib.pyplot as plt\n", - "plt.figure()\n", - "plt.plot(x_train, y_train, 'ro', label='Train')\n", - "plt.plot(x_test, y_pred, 'b-', label='NTK Prediction')\n", - "plt.legend()\n", - "plt.show()" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 430 - }, - "id": "nnJVkw9Bz7-Y", - "outputId": "bf329efc-9852-4519-f2a0-5a410b7ee1af" - }, - "execution_count": 58, - "outputs": [ - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ] - }, - { - "cell_type": "markdown", - "source": [ - "\n", - "Without regularization, Gabor performs poorly but does not blow up.\n", - "---\n", - "\n" - ], - "metadata": { - "id": "Or5pzZeN0qyr" - } - }, - { - "cell_type": "code", - "source": [ - "# try with different activations\n", - "act=stax.Gabor()\n", - "\n", - "init_fn, apply_fn, kernel_fn = stax.serial(\n", - " stax.Dense(128), act,\n", - " stax.Dense(128), act,\n", - " stax.Dense(1)\n", - ")\n", - "\n", - "#Model after sin function,\n", - "#20 points between -5 and 5 (reshape into column vector)\n", - "x_train = jnp.linspace(-5, 5, 20).reshape(-1, 1)\n", - "y_train = jnp.sin(x_train)\n", - "\n", - "x_test = jnp.linspace(-6, 6, 100).reshape(-1, 1)\n", - "\n", - "#Create train data with NTK\n", - "kernel_train_train = kernel_fn(x_train, x_train, 'ntk')\n", - "kernel_test_train = kernel_fn(x_test, x_train, 'ntk')\n", - "\n", - "#Predict with train data\n", - "lambda_reg = 0\n", - "K_inv = jnp.linalg.inv(kernel_train_train + lambda_reg * jnp.eye(len(x_train)))\n", - "y_pred = kernel_test_train @ K_inv @ y_train\n", - "\n", - "#Visualize contrast\n", - "import matplotlib.pyplot as plt\n", - "plt.figure()\n", - "plt.plot(x_train, y_train, 'ro', label='Train')\n", - "plt.plot(x_test, y_pred, 'b-', label='NTK Prediction')\n", - "plt.legend()\n", - "plt.show()" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 430 - }, - "id": "OZSrj6MP0kuc", - "outputId": "3c7785a0-4d8b-481a-bbb0-9d8a3ae05a92" - }, - "execution_count": 59, - "outputs": [ - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ] - }, - { - "cell_type": "markdown", - "source": [ - "Empirical NKTs. Using code from https://colab.research.google.com/github/google/neural-tangents/blob/main/notebooks/empirical_ntk_fcn.ipynb#scrollTo=lPh5LGz9JBK_.\n", - "\n", - "Here, I use batch size = 1 and plot the distribution of the eigenvalue magnitude of the NKTs. Smaller widths tend to have a less concentrated eigenvalue distribution." - ], - "metadata": { - "id": "Y9_T1WjU1gGt" - } - }, - { - "cell_type": "code", - "source": [ - "from jax import jit\n", - "from jax import numpy as jnp\n", - "from jax import random\n", - "\n", - "import neural_tangents as nt\n", - "from neural_tangents import stax" - ], - "metadata": { - "id": "IuZTCAjC0yZJ" - }, - "execution_count": 60, - "outputs": [] - }, - { - "cell_type": "code", - "source": [ - "def get_ntk_fns(O: int, width:int):\n", - " # Define an FCN.\n", - " init_fn, apply_fn, _ = stax.serial(\n", - " stax.Dense(width),\n", - " stax.Relu(),\n", - " stax.Dense(width),\n", - " stax.Relu(),\n", - " stax.Dense(width),\n", - " stax.Relu(),\n", - " stax.Dense(O)\n", - " )\n", - "\n", - " kwargs = dict(\n", - " f=apply_fn,\n", - " trace_axes=(),\n", - " vmap_axes=0\n", - " )\n", - "\n", - " # Different NTK implementations\n", - " jacobian_contraction = jit(nt.empirical_ntk_fn(\n", - " **kwargs, implementation=nt.NtkImplementation.JACOBIAN_CONTRACTION))\n", - " ntvp = jit(nt.empirical_ntk_fn(\n", - " **kwargs, implementation=nt.NtkImplementation.NTK_VECTOR_PRODUCTS))\n", - " str_derivatives = jit(nt.empirical_ntk_fn(\n", - " **kwargs, implementation=nt.NtkImplementation.STRUCTURED_DERIVATIVES))\n", - " auto = jit(nt.empirical_ntk_fn(\n", - " **kwargs, implementation=nt.NtkImplementation.AUTO))\n", - "\n", - " # Parameters \\theta\n", - " _, params = init_fn(random.PRNGKey(0), x1.shape)\n", - " return params, (jacobian_contraction, ntvp, str_derivatives, auto)" - ], - "metadata": { - "id": "52fbuTLL1kcA" - }, - "execution_count": 61, - "outputs": [] - }, - { - "cell_type": "code", - "source": [ - "width=2048 # matching sample notebook code\n", - "O = 32 # Consdier 1x1 output\n", - "N = 1 # consider case of just one input (batch size=1)\n", - "\n", - "# Input images x\n", - "input_shape = (3072,)\n", - "k1, k2 = random.split(random.PRNGKey(1), 2)\n", - "x1 = random.normal(k1, (N, *input_shape))\n", - "x2 = random.normal(k2, (N, *input_shape))\n", - "\n", - "params, (ntk_fn_jacobian_contraction, ntk_fn_ntvp, ntk_fn_str_derivatives, ntk_fn_auto) = get_ntk_fns(O=O, width=width)\n", - "\n", - "# NTK-vector products\n", - "k = ntk_fn_ntvp(x1, x2, params).squeeze()\n", - "(lambdas,_) = jnp.linalg.eig(k)\n", - "plt.figure\n", - "plt.hist(jnp.abs(lambdas))\n", - "plt.title(f\"NTK Eigenvalue Distribution, Width={width}\")\n" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 469 - }, - "id": "_KFzz7cs2R_y", - "outputId": "568b2ac3-281b-4b41-d1a8-89dad12cd4ec" - }, - "execution_count": 62, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "Text(0.5, 1.0, 'NTK Eigenvalue Distribution, Width=2048')" - ] - }, - "metadata": {}, - "execution_count": 62 - }, - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ] - }, - { - "cell_type": "code", - "source": [ - "width=1024 # matching sample notebook code\n", - "O = 32 # Consdier 1x1 output\n", - "N = 1 # consider case of just one input (batch size=1)\n", - "\n", - "# Input images x\n", - "input_shape = (3072,)\n", - "k1, k2 = random.split(random.PRNGKey(1), 2)\n", - "x1 = random.normal(k1, (N, *input_shape))\n", - "x2 = random.normal(k2, (N, *input_shape))\n", - "\n", - "params, (ntk_fn_jacobian_contraction, ntk_fn_ntvp, ntk_fn_str_derivatives, ntk_fn_auto) = get_ntk_fns(O=O, width=width)\n", - "\n", - "# NTK-vector products\n", - "k = ntk_fn_ntvp(x1, x2, params).squeeze()\n", - "(lambdas,_) = jnp.linalg.eig(k)\n", - "plt.figure\n", - "plt.hist(jnp.abs(lambdas))\n", - "plt.title(f\"NTK Eigenvalue Distribution, Width={width}\")\n" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 469 - }, - "id": "YzkSA9Z--qhE", - "outputId": "4a706046-9ac0-4eca-c99c-30d175422071" - }, - "execution_count": 63, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "Text(0.5, 1.0, 'NTK Eigenvalue Distribution, Width=1024')" - ] - }, - "metadata": {}, - "execution_count": 63 - }, - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ] - }, - { - "cell_type": "code", - "source": [ - "width=256 # matching sample notebook code\n", - "O = 32 # Consdier 1x1 output\n", - "N = 1 # consider case of just one input (batch size=1)\n", - "\n", - "# Input images x\n", - "input_shape = (3072,)\n", - "k1, k2 = random.split(random.PRNGKey(1), 2)\n", - "x1 = random.normal(k1, (N, *input_shape))\n", - "x2 = random.normal(k2, (N, *input_shape))\n", - "\n", - "params, (ntk_fn_jacobian_contraction, ntk_fn_ntvp, ntk_fn_str_derivatives, ntk_fn_auto) = get_ntk_fns(O=O, width=width)\n", - "\n", - "# NTK-vector products\n", - "k = ntk_fn_ntvp(x1, x2, params).squeeze()\n", - "(lambdas,_) = jnp.linalg.eig(k)\n", - "plt.figure\n", - "plt.hist(jnp.abs(lambdas))\n", - "plt.title(f\"NTK Eigenvalue Distribution, Width={width}\")\n" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 469 - }, - "id": "0PXykugi_KzY", - "outputId": "3f15714e-4e67-4f2d-a8ad-a6eefa0aac55" - }, - "execution_count": 64, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "Text(0.5, 1.0, 'NTK Eigenvalue Distribution, Width=256')" - ] - }, - "metadata": {}, - "execution_count": 64 - }, - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ] - }, - { - "cell_type": "code", - "source": [ - "width=16 # matching sample notebook code\n", - "O = 32 # Consdier 1x1 output\n", - "N = 1 # consider case of just one input (batch size=1)\n", - "\n", - "# Input images x\n", - "input_shape = (3072,)\n", - "k1, k2 = random.split(random.PRNGKey(1), 2)\n", - "x1 = random.normal(k1, (N, *input_shape))\n", - "x2 = random.normal(k2, (N, *input_shape))\n", - "\n", - "params, (ntk_fn_jacobian_contraction, ntk_fn_ntvp, ntk_fn_str_derivatives, ntk_fn_auto) = get_ntk_fns(O=O, width=width)\n", - "\n", - "# NTK-vector products\n", - "k = ntk_fn_ntvp(x1, x2, params).squeeze()\n", - "(lambdas,_) = jnp.linalg.eig(k)\n", - "plt.figure\n", - "plt.hist(jnp.abs(lambdas))\n", - "plt.title(f\"NTK Eigenvalue Distribution, Width={width}\")\n" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 469 - }, - "id": "rWqjIubA_A5X", - "outputId": "e42f180e-7762-4701-fa93-40ced4aff5a4" - }, - "execution_count": 65, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "Text(0.5, 1.0, 'NTK Eigenvalue Distribution, Width=16')" - ] - }, - "metadata": {}, - "execution_count": 65 - }, - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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xRm3atMl1W+mVwoc3Fea5pqWl6fz581fcl6+vb5HmZ+TMZbt8PkpoaKikooc+eAfh4zo3YcIEvfnmm3ruuee8ts+HH35Yv/32myZMmKD77rtPixcvLrbPR6hdu7Yk5XnXwOVtMTExWrNmjdq0aePV2+7i4uI0efJkvfPOOwoLC1N6eroGDhzo1mfZsmWKj493O4X8+++/F+rDrKpWrZpnvyNHjrjdSRQTE6Ovv/5anTp1yvcP7tV444035HA4dMcddxTYr1KlSoqLi1NcXJwuXLigvn376plnntG4cePk5+fn9dr279/vdrbkwIEDys7Odk1Uzflf9+Wv4eVnJqT8g0peateureTk5Fzt+/btc20vTqGhoa6AUalSJTVs2NBtYnbr1q21efNm/fjjjypfvnyBZxBz6t2/f3+u9ryeozfG8LHHHsvzTrHLtW/fvkif+BsbG6u5c+fm+kDFY8eOScp/IjHs4LLLdS4mJkb33Xef/v3vf3v1U0THjx+vUaNGaenSpXrwwQe9tt/LRUREqHHjxlqwYIHrsoAkbdiwQd98841b3wEDBigrK0tTpkzJtZ/MzMwif6plgwYN1KRJEy1ZskRLlixRjRo11K5dO7c+5cuXz/U/3OnTpxfqf98xMTHatm2bLly44Gpbvnx5rg9KGjBggP7zn/9o7ty5ufZx/vz5Il0Gy5GUlKRVq1YpLi4uz1PzOX799Ve3dV9fXzVs2FDGGF28eFHSH+FEyh0GimrGjBlu6zkfnte9e3dJUmBgoEJCQrRx40a3fjNnzsy1L09qu/POO/X5559r69atrrazZ89qzpw5ioqK8mjeSlG1bdtWu3bt0qpVq1zzPXK0bt1aW7du1WeffaamTZsWeLlM+uP5bNu2TZ9//rmr7ZdffsnzTGGlSpWuevyKe85H79695XQ6NW/ePLezizkfonelEI3ixZkPaPz48XrjjTeUnJysRo0aeW2/L7zwgk6ePKlXXnlFwcHBhTq7smzZsjw/4fSOO+7I99NUn332WfXu3Vtt2rTR0KFDdfLkSb388stq3LixWyBp3769HnzwQSUmJmrXrl3q0qWLKlSooP3792vp0qX65z//qf79+xfpucbFxWnixIny8/PTsGHDcp3pueuuu/TGG28oKChIDRs21NatW7VmzRpVq1btivu+//77tWzZMnXr1k0DBgzQwYMH9eabb+a6jXnw4MF6++239dBDD2ndunVq06aNsrKytG/fPr399tv65JNP1KxZswKPlZmZqTfffFPSH2dmjhw5og8//FC7d+9Wx44dNWfOnAIf36VLF4WHh6tNmzYKCwvTd999p5dfflk9evRw/fHLuYY/fvx4DRw4UBUqVFDPnj1df/g9lZKSol69eqlbt27aunWr3nzzTQ0aNEg333yzq8/999+vpKQk3X///WrWrJk2btyY58eMe1Lb2LFj9dZbb6l79+569NFHFRwcrNdff10pKSl65513inS2b/369erYsaMmTZqU52eaXK5t27aaN2+evvjii1wTb1u3bq20tDSlpaW5JuEWZMyYMXrjjTfUrVs3PfbYY65bbWvXrq3du3e79Y2NjdWsWbM0depU1a1bV6GhoW5znAqjYcOGRQpou3fv1ocffijpj7NcaWlpmjp1qqQ/5mD17NlTkhQeHq7x48dr4sSJ6tatm/r06aOvv/5ac+fO1T333KPmzZt7fGx4UYneawOrLr3V9nI5t71dza22ed2mmZmZafr06WMkmcTExHxrK+hWW11y62l+t00uXrzY1K9f3zidTtO4cWPz4Ycfmn79+pn69evnOtacOXNMbGys8ff3NwEBAaZJkyZmzJgx5tixY64+tWvXNj169Mj12MtvLc2xf/9+V62bNm3Ktf3kyZNm6NChJiQkxFSuXNl07drV7Nu3L9ftjnndamuMMS+88IKpWbOmcTqdpk2bNubLL7/Ms5YLFy6Y5557zjRq1Mg4nU5TtWpVExsbayZPnmzS0tJy1XWpy299rFixoomKijL9+vUzy5Ytc906WtDr8e9//9u0a9fOVKtWzTidThMTE2OeeOKJXMeeMmWKqVmzpilXrpzbbZySTEJCQp71Xf7+y3nP7N271/Tv398EBASYqlWrmhEjRpjz58+7PfbcuXNm2LBhJigoyAQEBJgBAwaYn3/+Oc/3dH615XXL88GDB03//v1NlSpVjJ+fn2nRooVZvny5W5+cMV26dKlbe17v5Y8++shIMrNnz87zNbhccnKya7wuv709OzvbVKlSxUgyS5YsyfXYvJ7P7t27Tfv27Y2fn5+pWbOmmTJlinn11Vdz3WqbmppqevToYQICAtxuh83vd0x+7+uiyDlGXsvlzyc7O9tMnz7d3HTTTaZChQomMjLSTJgwwVy4cOGq68DVcRhTxNlOwDXulltuUfXq1bV69eqSLgUolDFjxuitt97SgQMHSu3HnwOFwZwPlHoXL15UZmamW9v69ev19ddfW/u6d8Ab1q1bp6eeeorggTKPMx8o9Q4fPqzOnTvrvvvuU0REhPbt26fZs2crKChI3377baHmVQAA7GHCKUq9qlWrKjY2Vq+88op++eUXVapUST169FBSUhLBAwCuQZz5AAAAVjHnAwAAWEX4AAAAVl1zcz6ys7N17NgxBQQEFMtHRAMAAO8zxuj06dOKiIi44ofsXXPh49ixY1f9BVgAAKBkHD16VLVq1SqwzzUXPnI+gvno0aMKDAws4WoAAEBhpKenKzIy8orfIyRdg+Ej51JLYGAg4QMAgFKmMFMmmHAKAACsInwAAACrCB8AAMAqwgcAALCK8AEAAKwifAAAAKsIHwAAwCrCBwAAsIrwAQAArCJ8AAAAqzwKH4mJiWrevLkCAgIUGhqqPn36KDk52a1Phw4d5HA43JaHHnrIq0UDAIDSy6PwsWHDBiUkJGjbtm1avXq1Ll68qC5duujs2bNu/R544AH99NNPruX555/3atEAAKD08uiL5VauXOm2Pn/+fIWGhmrHjh1q166dq71ixYoKDw/3ToUAAKBMuao5H2lpaZKk4OBgt/aFCxcqJCREjRs31rhx43Tu3Ll895GRkaH09HS3BQAAlF0enfm4VHZ2th5//HG1adNGjRs3drUPGjRItWvXVkREhHbv3q0nn3xSycnJevfdd/PcT2JioiZPnlzUMjwWNfZja8fylsNJPUq6BAAAvMZhjDFFeeDDDz+s//3f/9WmTZtUq1atfPt9+umn6tSpkw4cOKCYmJhc2zMyMpSRkeFaT09PV2RkpNLS0hQYGFiU0gpE+AAAwPvS09MVFBRUqL/fRTrzMWLECC1fvlwbN24sMHhIUsuWLSUp3/DhdDrldDqLUgYAACiFPAofxhiNHDlS7733ntavX686depc8TG7du2SJNWoUaNIBQIAgLLFo/CRkJCgRYsW6YMPPlBAQIBSU1MlSUFBQfL399fBgwe1aNEi3XnnnapWrZp2796tUaNGqV27dmratGmxPAEAAFC6eBQ+Zs2aJemPDxK71Lx58zRkyBD5+vpqzZo1mjZtms6ePavIyEj169dPEyZM8FrBAACgdPP4sktBIiMjtWHDhqsqCAAAlG18twsAALCK8AEAAKwifAAAAKsIHwAAwCrCBwAAsIrwAQAArCJ8AAAAqwgfAADAKsIHAACwivABAACsInwAAACrCB8AAMAqwgcAALCK8AEAAKwifAAAAKsIHwAAwCrCBwAAsIrwAQAArCJ8AAAAqwgfAADAKsIHAACwivABAACsInwAAACrCB8AAMAqwgcAALCK8AEAAKwifAAAAKsIHwAAwCrCBwAAsIrwAQAArCJ8AAAAqwgfAADAKsIHAACwivABAACsInwAAACrCB8AAMAqwgcAALCK8AEAAKwifAAAAKsIHwAAwCrCBwAAsIrwAQAArCJ8AAAAqwgfAADAKsIHAACwivABAACsInwAAACrCB8AAMAqwgcAALCK8AEAAKwifAAAAKsIHwAAwCrCBwAAsIrwAQAArCJ8AAAAqwgfAADAKsIHAACwivABAACsInwAAACrCB8AAMAqj8JHYmKimjdvroCAAIWGhqpPnz5KTk526/P7778rISFB1apVU+XKldWvXz8dP37cq0UDAIDSy6PwsWHDBiUkJGjbtm1avXq1Ll68qC5duujs2bOuPqNGjdJHH32kpUuXasOGDTp27Jj69u3r9cIBAEDp5ONJ55UrV7qtz58/X6GhodqxY4fatWuntLQ0vfrqq1q0aJFuv/12SdK8efPUoEEDbdu2Tbfeeqv3KgcAAKXSVc35SEtLkyQFBwdLknbs2KGLFy+qc+fOrj7169fXDTfcoK1bt+a5j4yMDKWnp7stAACg7Cpy+MjOztbjjz+uNm3aqHHjxpKk1NRU+fr6qkqVKm59w8LClJqamud+EhMTFRQU5FoiIyOLWhIAACgFihw+EhIS9O2332rx4sVXVcC4ceOUlpbmWo4ePXpV+wMAANc2j+Z85BgxYoSWL1+ujRs3qlatWq728PBwXbhwQadOnXI7+3H8+HGFh4fnuS+n0ymn01mUMgAAQCnk0ZkPY4xGjBih9957T59++qnq1Knjtj02NlYVKlTQ2rVrXW3Jycn64Ycf1KpVK+9UDAAASjWPznwkJCRo0aJF+uCDDxQQEOCaxxEUFCR/f38FBQVp2LBhGj16tIKDgxUYGKiRI0eqVatW3OkCAAAkeRg+Zs2aJUnq0KGDW/u8efM0ZMgQSdJLL72kcuXKqV+/fsrIyFDXrl01c+ZMrxQLAABKP4/ChzHmin38/Pw0Y8YMzZgxo8hFAQCAsovvdgEAAFYRPgAAgFWEDwAAYBXhAwAAWEX4AAAAVhE+AACAVYQPAABgFeEDAABYRfgAAABWET4AAIBVhA8AAGAV4QMAAFhF+AAAAFYRPgAAgFWEDwAAYBXhAwAAWEX4AAAAVhE+AACAVYQPAABgFeEDAABYRfgAAABWET4AAIBVhA8AAGAV4QMAAFhF+AAAAFYRPgAAgFWEDwAAYBXhAwAAWEX4AAAAVhE+AACAVYQPAABgFeEDAABYRfgAAABWET4AAIBVhA8AAGAV4QMAAFhF+AAAAFYRPgAAgFWEDwAAYBXhAwAAWEX4AAAAVhE+AACAVYQPAABgFeEDAABYRfgAAABWET4AAIBVhA8AAGAV4QMAAFhF+AAAAFYRPgAAgFWEDwAAYBXhAwAAWEX4AAAAVhE+AACAVYQPAABgFeEDAABYRfgAAABWET4AAIBVhA8AAGCVx+Fj48aN6tmzpyIiIuRwOPT++++7bR8yZIgcDofb0q1bN2/VCwAASjmPw8fZs2d18803a8aMGfn26datm3766SfX8tZbb11VkQAAoOzw8fQB3bt3V/fu3Qvs43Q6FR4eXuSiAABA2VUscz7Wr1+v0NBQ1atXTw8//LB+/fXXfPtmZGQoPT3dbQEAAGWX18NHt27dtGDBAq1du1bPPfecNmzYoO7duysrKyvP/omJiQoKCnItkZGR3i4JAABcQzy+7HIlAwcOdP27SZMmatq0qWJiYrR+/Xp16tQpV/9x48Zp9OjRrvX09HQCCAAAZVix32obHR2tkJAQHThwIM/tTqdTgYGBbgsAACi7ij18/Pjjj/r1119Vo0aN4j4UAAAoBTy+7HLmzBm3sxgpKSnatWuXgoODFRwcrMmTJ6tfv34KDw/XwYMHNWbMGNWtW1ddu3b1auEAAKB08jh8fPnll+rYsaNrPWe+Rnx8vGbNmqXdu3fr9ddf16lTpxQREaEuXbpoypQpcjqd3qsaAACUWh6Hjw4dOsgYk+/2Tz755KoKAgAAZRvf7QIAAKwifAAAAKsIHwAAwCrCBwAAsIrwAQAArCJ8AAAAqwgfAADAKsIHAACwivABAACsInwAAACrCB8AAMAqwgcAALCK8AEAAKwifAAAAKsIHwAAwCrCBwAAsIrwAQAArCJ8AAAAqwgfAADAKsIHAACwivABAACsInwAAACrCB8AAMAqwgcAALCK8AEAAKwifAAAAKsIHwAAwCrCBwAAsIrwAQAArCJ8AAAAqwgfAADAKsIHAACwivABAACsInwAAACrCB8AAMAqwgcAALCK8AEAAKwifAAAAKsIHwAAwCrCBwAAsIrwAQAArCJ8AAAAqwgfAADAKsIHAACwivABAACsInwAAACrCB8AAMAqwgcAALCK8AEAAKwifAAAAKsIHwAAwCrCBwAAsIrwAQAArCJ8AAAAqwgfAADAKsIHAACwivABAACsInwAAACrCB8AAMAqwgcAALDK4/CxceNG9ezZUxEREXI4HHr//ffdthtjNHHiRNWoUUP+/v7q3Lmz9u/f7616AQBAKedx+Dh79qxuvvlmzZgxI8/tzz//vP71r39p9uzZ2r59uypVqqSuXbvq999/v+piAQBA6efj6QO6d++u7t2757nNGKNp06ZpwoQJ6t27tyRpwYIFCgsL0/vvv6+BAwfmekxGRoYyMjJc6+np6Z6WBAAAShGvzvlISUlRamqqOnfu7GoLCgpSy5YttXXr1jwfk5iYqKCgINcSGRnpzZIAAMA1xqvhIzU1VZIUFhbm1h4WFubadrlx48YpLS3NtRw9etSbJQEAgGuMx5ddvM3pdMrpdJZ0GQAAwBKvnvkIDw+XJB0/ftyt/fjx465tAADg+ubV8FGnTh2Fh4dr7dq1rrb09HRt375drVq18uahAABAKeXxZZczZ87owIEDrvWUlBTt2rVLwcHBuuGGG/T4449r6tSpuvHGG1WnTh099dRTioiIUJ8+fbxZNwAAKKU8Dh9ffvmlOnbs6FofPXq0JCk+Pl7z58/XmDFjdPbsWQ0fPlynTp1S27ZttXLlSvn5+XmvagAAUGo5jDGmpIu4VHp6uoKCgpSWlqbAwECv7z9q7Mde32dxO5zUo6RLAACgQJ78/ea7XQAAgFWEDwAAYBXhAwAAWEX4AAAAVhE+AACAVYQPAABgFeEDAABYRfgAAABWET4AAIBVhA8AAGAV4QMAAFhF+AAAAFYRPgAAgFWEDwAAYBXhAwAAWEX4AAAAVhE+AACAVYQPAABgFeEDAABYRfgAAABWET4AAIBVhA8AAGAV4QMAAFhF+AAAAFYRPgAAgFWEDwAAYBXhAwAAWEX4AAAAVhE+AACAVYQPAABgFeEDAABYRfgAAABWET4AAIBVhA8AAGAV4QMAAFhF+AAAAFYRPgAAgFWEDwAAYBXhAwAAWEX4AAAAVhE+AACAVYQPAABgFeEDAABYRfgAAABWET4AAIBVhA8AAGAV4QMAAFhF+AAAAFYRPgAAgFWEDwAAYBXhAwAAWEX4AAAAVhE+AACAVYQPAABgFeEDAABYRfgAAABWET4AAIBVhA8AAGAV4QMAAFjl9fDx9NNPy+FwuC3169f39mEAAEAp5VMcO23UqJHWrFnzfwfxKZbDAACAUqhYUoGPj4/Cw8OLY9cAAKCUK5Y5H/v371dERISio6N177336ocffsi3b0ZGhtLT090WAABQdnk9fLRs2VLz58/XypUrNWvWLKWkpOi2227T6dOn8+yfmJiooKAg1xIZGentkgAAwDXEYYwxxXmAU6dOqXbt2nrxxRc1bNiwXNszMjKUkZHhWk9PT1dkZKTS0tIUGBjo9Xqixn7s9X0Wt8NJPUq6BAAACpSenq6goKBC/f0u9pmgVapU0U033aQDBw7kud3pdMrpdBZ3GQAA4BpR7J/zcebMGR08eFA1atQo7kMBAIBSwOvh429/+5s2bNigw4cPa8uWLbr77rtVvnx53XPPPd4+FAAAKIW8ftnlxx9/1D333KNff/1V1atXV9u2bbVt2zZVr17d24cCAAClkNfDx+LFi729SwAAUIbw3S4AAMAqwgcAALCK8AEAAKwifAAAAKsIHwAAwCrCBwAAsIrwAQAArCJ8AAAAqwgfAADAKsIHAACwivABAACsInwAAACrCB8AAMAqwgcAALCK8AEAAKwifAAAAKsIHwAAwCrCBwAAsIrwAQAArCJ8AAAAqwgfAADAKsIHAACwivABAACsInwAAACrCB8AAMAqwgcAALCK8AEAAKwifAAAAKsIHwAAwCrCBwAAsIrwAQAArCJ8AAAAqwgfAADAKsIHAACwivABAACs8inpAoBrRdTYj0u6BI8dTupR0iUAgMc48wEAAKwifAAAAKsIHwAAwCrCBwAAsIrwAQAArCJ8AAAAqwgfAADAKsIHAACwivABAACsInwAAACrCB8AAMAqwgcAALCK8AEAAKziW21LgdL4batAfng/28O3HttRGt/TJf3e4MwHAACwivABAACsInwAAACrCB8AAMAqwgcAALCK8AEAAKwifAAAAKsIHwAAwCrCBwAAsKrYwseMGTMUFRUlPz8/tWzZUp9//nlxHQoAAJQixRI+lixZotGjR2vSpEn66quvdPPNN6tr1676+eefi+NwAACgFCmW8PHiiy/qgQce0NChQ9WwYUPNnj1bFStW1GuvvVYchwMAAKWI179Y7sKFC9qxY4fGjRvnaitXrpw6d+6srVu35uqfkZGhjIwM13paWpokKT093dulSZKyM84Vy36BklBcPyfFiZ9Be0rj+6M0Ko3v6eJ4b+Ts0xhzxb5eDx8nTpxQVlaWwsLC3NrDwsK0b9++XP0TExM1efLkXO2RkZHeLg0oc4KmlXQFuJbx/kB+ivO9cfr0aQUFBRXYx+vhw1Pjxo3T6NGjXevZ2dn67bffVK1aNTkcjhKs7NqWnp6uyMhIHT16VIGBgSVdDsSYXIsYk2sPY3Lt8daYGGN0+vRpRUREXLGv18NHSEiIypcvr+PHj7u1Hz9+XOHh4bn6O51OOZ1Ot7YqVap4u6wyKzAwkB/gawxjcu1hTK49jMm1xxtjcqUzHjm8PuHU19dXsbGxWrt2rastOztba9euVatWrbx9OAAAUMoUy2WX0aNHKz4+Xs2aNVOLFi00bdo0nT17VkOHDi2OwwEAgFKkWMJHXFycfvnlF02cOFGpqam65ZZbtHLlylyTUFF0TqdTkyZNynXJCiWHMbn2MCbXHsbk2lMSY+IwhbknBgAAwEv4bhcAAGAV4QMAAFhF+AAAAFYRPgAAgFWEDwAAYBXh4xo2Y8YMRUVFyc/PTy1bttTnn3+eb9+5c+fqtttuU9WqVVW1alV17ty5wP4oGk/G5FKLFy+Ww+FQnz59irfA65CnY3Lq1CklJCSoRo0acjqduummm7RixQpL1V4fPB2TadOmqV69evL391dkZKRGjRql33//3VK1ZdvGjRvVs2dPRUREyOFw6P3337/iY9avX68//elPcjqdqlu3rubPn+/9wgyuSYsXLza+vr7mtddeM3v27DEPPPCAqVKlijl+/Hie/QcNGmRmzJhhdu7cab777jszZMgQExQUZH788UfLlZddno5JjpSUFFOzZk1z2223md69e9sp9jrh6ZhkZGSYZs2amTvvvNNs2rTJpKSkmPXr15tdu3ZZrrzs8nRMFi5caJxOp1m4cKFJSUkxn3zyialRo4YZNWqU5crLphUrVpjx48ebd99910gy7733XoH9Dx06ZCpWrGhGjx5t9u7da6ZPn27Kly9vVq5c6dW6CB/XqBYtWpiEhATXelZWlomIiDCJiYmFenxmZqYJCAgwr7/+enGVeN0pyphkZmaa1q1bm1deecXEx8cTPrzM0zGZNWuWiY6ONhcuXLBV4nXH0zFJSEgwt99+u1vb6NGjTZs2bYq1zutRYcLHmDFjTKNGjdza4uLiTNeuXb1aC5ddrkEXLlzQjh071LlzZ1dbuXLl1LlzZ23durVQ+zh37pwuXryo4ODg4irzulLUMfnHP/6h0NBQDRs2zEaZ15WijMmHH36oVq1aKSEhQWFhYWrcuLGeffZZZWVl2Sq7TCvKmLRu3Vo7duxwXZo5dOiQVqxYoTvvvNNKzXC3detWt/GTpK5duxb6b09hFcvHq+PqnDhxQllZWbk+jj4sLEz79u0r1D6efPJJRURE5HoToWiKMiabNm3Sq6++ql27dlmo8PpTlDE5dOiQPv30U917771asWKFDhw4oEceeUQXL17UpEmTbJRdphVlTAYNGqQTJ06obdu2MsYoMzNTDz30kP7+97/bKBmXSU1NzXP80tPTdf78efn7+3vlOJz5KIOSkpK0ePFivffee/Lz8yvpcq5Lp0+f1uDBgzV37lyFhISUdDn4/7KzsxUaGqo5c+YoNjZWcXFxGj9+vGbPnl3SpV231q9fr2effVYzZ87UV199pXfffVcff/yxpkyZUtKloRhx5uMaFBISovLly+v48eNu7cePH1d4eHiBj/2f//kfJSUlac2aNWratGlxlnld8XRMDh48qMOHD6tnz56utuzsbEmSj4+PkpOTFRMTU7xFl3FF+TmpUaOGKlSooPLly7vaGjRooNTUVF24cEG+vr7FWnNZV5QxeeqppzR48GDdf//9kqQmTZro7NmzGj58uMaPH69y5fg/sk3h4eF5jl9gYKDXznpInPm4Jvn6+io2NlZr1651tWVnZ2vt2rVq1apVvo97/vnnNWXKFK1cuVLNmjWzUep1w9MxqV+/vr755hvt2rXLtfTq1UsdO3bUrl27FBkZabP8MqkoPydt2rTRgQMHXEFQkr7//nvVqFGD4OEFRRmTc+fO5QoYOeHQ8L2n1rVq1cpt/CRp9erVBf7tKRKvTl+F1yxevNg4nU4zf/58s3fvXjN8+HBTpUoVk5qaaowxZvDgwWbs2LGu/klJScbX19csW7bM/PTTT67l9OnTJfUUyhxPx+Ry3O3ifZ6OyQ8//GACAgLMiBEjTHJyslm+fLkJDQ01U6dOLamnUOZ4OiaTJk0yAQEB5q233jKHDh0yq1atMjExMWbAgAEl9RTKlNOnT5udO3eanTt3GknmxRdfNDt37jRHjhwxxhgzduxYM3jwYFf/nFttn3jiCfPdd9+ZGTNmcKvt9Wb69OnmhhtuML6+vqZFixZm27Ztrm3t27c38fHxrvXatWsbSbmWSZMm2S+8DPNkTC5H+Cgeno7Jli1bTMuWLY3T6TTR0dHmmWeeMZmZmZarLts8GZOLFy+ap59+2sTExBg/Pz8TGRlpHnnkEXPy5En7hZdB69aty/NvQ84YxMfHm/bt2+d6zC233GJ8fX1NdHS0mTdvntfrchjDeS0AAGAPcz4AAIBVhA8AAGAV4QMAAFhF+AAAAFYRPgAAgFWEDwAAYBXhAwAAWEX4AAAAVhE+AACAVYQPAABgFeEDAABY9f8AHyQgGtldq7UAAAAASUVORK5CYII=\n" - }, - "metadata": {} - } - ] - } - ] -} \ No newline at end of file diff --git a/requirements.txt b/requirements.txt new file mode 100644 index 0000000..e69de29 diff --git a/run.py b/run.py new file mode 100644 index 0000000..cb93214 --- /dev/null +++ b/run.py @@ -0,0 +1,180 @@ +import torch +import torch.nn as nn +import numpy as np +import random +import matplotlib.pyplot as plt +import math + +# Simple Mean Loss function + +class MeanLoss(nn.Module): + def __init__(self): + super(MeanLoss, self).__init__() + + def forward(self, input_tensor): + loss_out = torch.mean(input_tensor) + return loss_out + + def loss_with_costgrad(self, net_out): + L = net_out.shape[0] + loss_out = self.forward(net_out) + dloss_out = torch.tensor([ + 1.0 / L for _ in range(L) + ]) + return loss_out, dloss_out + + +torch.use_deterministic_algorithms=True + +def input(gamma:float)->torch.Tensor: + gamma=torch.Tensor([gamma]) + x=torch.tensor([torch.cos(gamma),torch.sin(gamma)]) + return x + +def flatten(ls): + return [item for sublist in ls for item in sublist] + +def create_model(width, depth, seed, activation:nn.Module): + torch.manual_seed(seed) + random.seed(seed) + # Append input layer with array of hidden layer and output layer + mdl = nn.Sequential( + *([nn.Linear(2, width), activation()] \ + + flatten([[nn.Linear(width, width), activation()] for k in range(depth - 2)]) \ + + [nn.Linear(width, 2)]) + ) + + return mdl + +def reset_grads(model): + for name, param in model.named_parameters(): + if "weight" in name: + param.grad = None + +def get_cost_grads(model): + dCost = [] + for name, param in model.named_parameters(): + if "weight" in name: + dCost.append(param.grad.flatten()) + + dCost = torch.concatenate(dCost) + return dCost + + +def undo_first_in_chainrule(grad, dCdF): + dFunc = torch.stack([ + grad / torch.Tensor([dCdF[i]]) for i in range(dCdF.shape[0]) + ]) + + return dFunc + +def get_NTK(model, ref_input, input): + loss_function = MeanLoss() + + out1 = model.forward(ref_input) + loss, g_loss = loss_function.loss_with_costgrad(out1) # return loss and gradient of loss wrt function output + + loss.backward() + cost_grads_1 = get_cost_grads(model) # dC/dtheta + N1 = undo_first_in_chainrule(cost_grads_1, g_loss) # undoing first chainrule to get vector of dFunctionOutput/dTheta (actual NTK element) + + out2 = model.forward(input) + loss2, g_loss2 = loss_function.loss_with_costgrad(out2) + + loss2.backward() + cost_grads_2 = get_cost_grads(model) + N2 = undo_first_in_chainrule(cost_grads_2, g_loss2) + + # Made adjustment for 2d NTK + NTK = torch.matmul(N1, torch.t(N2)) + reset_grads(model) + return NTK + + +def doNTK(model, gamma_spacing:float=0.01)->torch.Tensor: + gammas = torch.arange(-1, 1, gamma_spacing) + + NTK_arr = [ + get_NTK(model, input(0.0), input(gamma)) for gamma in gammas + ] + + return gammas, NTK_arr + + + +mod = create_model(100, 4, 32, nn.ReLU) +X, Y = doNTK(mod, 0.01) +bY = [Y[n][0, 0].item() for n in range(len(Y))] + +plt.plot(X,bY) +plt.savefig("img/width100.png") +print("Saved with width 100.") +plt.clf() + +mod = create_model(500, 4, 32, nn.ReLU) +X, Y = doNTK(mod, 0.01) +bY = [Y[n][0, 0].item() for n in range(len(Y))] + +plt.plot(X,bY) +plt.savefig("img/width500.png") +print("Saved with width 500.") +plt.clf() + + +mod = create_model(1000, 4, 32, nn.ReLU) +X, Y = doNTK(mod, 0.01) +bY = [Y[n][0, 0].item() for n in range(len(Y))] + +plt.plot(X,bY) +plt.savefig("img/width1000.png") +print("Saved with width 1000.") +plt.clf() + + +mod = create_model(1500, 4, 32, nn.ReLU) +X, Y = doNTK(mod, 0.01) +bY = [Y[n][0, 0].item() for n in range(len(Y))] + +plt.plot(X,bY) +plt.savefig("img/width1500.png") +print("Saved with width 1500.") +plt.clf() + + +mod = create_model(2000, 4, 32, nn.ReLU) +X, Y = doNTK(mod, 0.01) +bY = [Y[n][0, 0].item() for n in range(len(Y))] + +plt.plot(X,bY) +plt.savefig("img/width2000.png") +print("Saved with width 2000.") +plt.clf() + + +# res = mod.forward(input(gamma)) + +# n = res.shape[0] + +# loss = loss_func(res) + +# loss.backward() + +# # now we calculate array of dC/dtheta + +# dCost = [] +# for name, param in mod.named_parameters(): +# if "weight" in name: +# dCost.append(param.grad.flatten()) + +# dCost = torch.concatenate(dCost) + +# print(dCost) + +# # then because dC/dtheta is a result of chain rule, we can finally divide dC/dtheta with dC/dOutput to get dOutput/dtheta, which is the NTK +# # dMean is [1 / n, 1 / n, 1 / n...] + +# dMean = torch.Tensor([1.0 / n for k in range(n)]) + +# dFunc = torch.stack([ +# dCost / torch.Tensor([dMean[i]]) for i in range(dMean.shape[0]) +# ]) diff --git a/setup_venv.sh b/setup_venv.sh new file mode 100644 index 0000000..f38f3b3 --- /dev/null +++ b/setup_venv.sh @@ -0,0 +1,3 @@ +python -m venv . +source bin/activate +pip3 install numpy matplotlib \ No newline at end of file diff --git a/testNTK.ipynb b/testNTK.ipynb deleted file mode 100644 index 114d84b..0000000 --- a/testNTK.ipynb +++ /dev/null @@ -1,341 +0,0 @@ -{ - "nbformat": 4, - "nbformat_minor": 0, - "metadata": { - "colab": { - "provenance": [], - "include_colab_link": true - }, - "kernelspec": { - "name": "python3", - "display_name": "Python 3" - }, - "language_info": { - "name": "python" - } - }, - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "id": "view-in-github", - "colab_type": "text" - }, - "source": [ - "\"Open" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "LdHAb7OL9qHr", - "outputId": "2b8cfa2f-f130-4d07-f649-4eda671b77d1" - }, - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "Requirement already satisfied: jax in /usr/local/lib/python3.12/dist-packages (0.5.3)\n", - "Requirement already satisfied: jaxlib in /usr/local/lib/python3.12/dist-packages (0.5.3)\n", - "Collecting neural-tangents\n", - " Downloading neural_tangents-0.6.5-py2.py3-none-any.whl.metadata (26 kB)\n", - "Requirement already satisfied: matplotlib in /usr/local/lib/python3.12/dist-packages (3.10.0)\n", - "Requirement already satisfied: ml_dtypes>=0.4.0 in /usr/local/lib/python3.12/dist-packages (from jax) (0.5.3)\n", - "Requirement already satisfied: numpy>=1.25 in /usr/local/lib/python3.12/dist-packages (from jax) (2.0.2)\n", - "Requirement already satisfied: opt_einsum in /usr/local/lib/python3.12/dist-packages (from jax) (3.4.0)\n", - "Requirement already satisfied: scipy>=1.11.1 in /usr/local/lib/python3.12/dist-packages (from jax) (1.16.2)\n", - "Requirement already satisfied: frozendict>=2.3.8 in /usr/local/lib/python3.12/dist-packages (from neural-tangents) (2.4.6)\n", - "Requirement already satisfied: tensorflow>=2.15.0 in /usr/local/lib/python3.12/dist-packages (from neural-tangents) (2.19.0)\n", - "Collecting tf2jax>=0.3.5 (from neural-tangents)\n", - " Downloading tf2jax-0.3.8-py3-none-any.whl.metadata (15 kB)\n", - "Requirement already satisfied: contourpy>=1.0.1 in 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"kernel_train_train = kernel_fn(x_train, x_train, 'ntk')\n", - "kernel_test_train = kernel_fn(x_test, x_train, 'ntk')\n", - "\n", - "#Predict with train data\n", - "lambda_reg = 1e-3\n", - "K_inv = jnp.linalg.inv(kernel_train_train + lambda_reg * jnp.eye(len(x_train)))\n", - "y_pred = kernel_test_train @ K_inv @ y_train\n", - "\n", - "#Visualize contrast\n", - "import matplotlib.pyplot as plt\n", - "plt.figure()\n", - "plt.plot(x_train, y_train, 'ro', label='Train')\n", - "plt.plot(x_test, y_pred, 'b-', label='NTK Prediction')\n", - "plt.legend()\n", - "plt.show()" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 430 - }, - "id": "t1vl7aTW9tA-", - "outputId": "6b5afbfb-4d60-4bb7-925e-f357108f3533" - }, - "execution_count": null, - "outputs": [ - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
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\n" - }, - "metadata": {} - } - ] - }, - { - "cell_type": "code", - "source": [ - "from jax import grad\n", - "\n", - "#Set random RTK for a pytree\n", - "key = jax.random.PRNGKey(0)\n", - "params = init_fn(key, (-1, 1))[1]\n", - "\n", - "#MSE formula\n", - "def loss_fn(params, x, y):\n", - " preds = apply_fn(params, x)\n", - " return jnp.mean((preds - y) ** 2)\n", - "\n", - "#pytree of gradients\n", - "grad_fn = grad(loss_fn)\n", - "\n", - "#approximate with gd\n", - "for step in range(5000):\n", - " grads = grad_fn(params, x_train, y_train)\n", - " params = jax.tree_util.tree_map(lambda p, g: p - 0.01 * g, params, grads)\n", - "\n", - "y_pred_finite = apply_fn(params, x_test)\n", - "\n", - "#Display\n", - "plt.plot(x_test, y_pred, label='NTK')\n", - "plt.plot(x_test, y_pred_finite, label='Finite Network')\n", - "plt.legend()\n", - "plt.show()" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 430 - }, - "id": "uTovztmm-Gdp", - "outputId": "9b110583-fb36-4442-ac09-c239639e8794" - }, - "execution_count": null, - "outputs": [ - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ] - }, - { - "cell_type": "code", - "source": [ - "#Create perceptron with Relu\n", - "init_fn, apply_fn, kernel_fn = stax.serial(\n", - " stax.Dense(1024), stax.Relu(),\n", - " stax.Dense(1024), stax.Relu(),\n", - " stax.Dense(32)\n", - ")\n", - "\n", - "#Model after sin function,\n", - "#20 points between -5 and 5 (reshape into column vector)\n", - "x_train = jnp.linspace(-5, 5, 20).reshape(-1, 1)\n", - "y_train = jnp.sin(x_train)\n", - "\n", - "x_test = jnp.linspace(-6, 6, 100).reshape(-1, 1)\n", - "\n", - "#Create train data with NTK\n", - "kernel_train_train = kernel_fn(x_train, x_train, 'ntk')\n", - "kernel_test_train = kernel_fn(x_test, x_train, 'ntk')\n", - "\n", - "#Predict with train data\n", - "lambda_reg = 1e-3\n", - "K_inv = jnp.linalg.inv(kernel_train_train + lambda_reg * jnp.eye(len(x_train)))\n", - "y_pred = kernel_test_train @ K_inv @ y_train\n", - "\n", - "#Visualize contrast\n", - "import matplotlib.pyplot as plt\n", - "plt.figure()\n", - "plt.plot(x_train, y_train, 'ro', label='Train')\n", - "plt.plot(x_test, y_pred, 'b-', label='NTK Prediction')\n", - "plt.legend()\n", - "plt.show()" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 430 - }, - "id": "N_ozCT3zDMNs", - "outputId": "1bbd8101-e210-4d3a-9510-1de0c0dd724b" - }, - "execution_count": null, - "outputs": [ - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ] - }, - { - "cell_type": "code", - "source": [ - "#Create perceptron with Relu\n", - "init_fn, apply_fn, kernel_fn = stax.serial(\n", - " stax.Dense(128), stax.Relu(),\n", - " stax.Dense(128), stax.Relu(),\n", - " stax.Dense(1)\n", - ")\n", - "\n", - "#Model after sin function,\n", - "#20 points between -5 and 5 (reshape into column vector)\n", - "x_train = jnp.linspace(-5, 5, 20).reshape(-1, 1)\n", - "y_train = jnp.sin(x_train)\n", - "\n", - "x_test = jnp.linspace(-6, 6, 100).reshape(-1, 1)\n", - "\n", - "#Create train data with NTK\n", - "kernel_train_train = kernel_fn(x_train, x_train, 'ntk')\n", - "kernel_test_train = kernel_fn(x_test, x_train, 'ntk')\n", - "\n", - "#Predict with train data\n", - "lambda_reg = 1e-3\n", - "K_inv = jnp.linalg.inv(kernel_train_train + lambda_reg * jnp.eye(len(x_train)))\n", - "y_pred = kernel_test_train @ K_inv @ y_train\n", - "\n", - "#Visualize contrast\n", - "import matplotlib.pyplot as plt\n", - "plt.figure()\n", - "plt.plot(x_train, y_train, 'ro', label='Train')\n", - "plt.plot(x_test, y_pred, 'b-', label='NTK Prediction')\n", - "plt.legend()\n", - "plt.show()" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 430 - }, - "id": "PWAtDbyBDkK8", - "outputId": "34a2721a-7a28-4703-a2a8-58960947e798" - }, - "execution_count": null, - "outputs": [ - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ] - } - ] -} \ No newline at end of file From 168a1723241c5c17ff57e73577cae0d1ebf6ae07 Mon Sep 17 00:00:00 2001 From: Mihir Kamat Date: Thu, 9 Oct 2025 22:14:48 -0400 Subject: [PATCH 04/10] Update .gitignore --- .gitignore | 7 ++++++- 1 file changed, 6 insertions(+), 1 deletion(-) diff --git a/.gitignore b/.gitignore index b37762e..d8dfac2 100644 --- a/.gitignore +++ b/.gitignore @@ -1,4 +1,9 @@ ./Include/* ./Lib/* ./Scripts/* -./share/* \ No newline at end of file +./share/* + +Include/* +Lib/* +Scripts/* +share/* \ No newline at end of file From ca951b8644002a6fd7e52981ebb6746a06c1b85c Mon Sep 17 00:00:00 2001 From: Mihir Kamat Date: Thu, 9 Oct 2025 22:34:19 -0400 Subject: [PATCH 05/10] Modified for dynamic adjustment of gpu/cpu modes --- run.py | 43 ++++++++++++++++++++++++------------------- 1 file changed, 24 insertions(+), 19 deletions(-) diff --git a/run.py b/run.py index cb93214..cca017a 100644 --- a/run.py +++ b/run.py @@ -61,14 +61,14 @@ def get_cost_grads(model): return dCost -def undo_first_in_chainrule(grad, dCdF): +def undo_first_in_chainrule(grad, dCdF, dev): dFunc = torch.stack([ - grad / torch.Tensor([dCdF[i]]) for i in range(dCdF.shape[0]) + grad / torch.Tensor([dCdF[i]]).to(dev) for i in range(dCdF.shape[0]) ]) - return dFunc + return dFunc.to(dev) -def get_NTK(model, ref_input, input): +def get_NTK(model, ref_input, input, device): loss_function = MeanLoss() out1 = model.forward(ref_input) @@ -76,14 +76,14 @@ def get_NTK(model, ref_input, input): loss.backward() cost_grads_1 = get_cost_grads(model) # dC/dtheta - N1 = undo_first_in_chainrule(cost_grads_1, g_loss) # undoing first chainrule to get vector of dFunctionOutput/dTheta (actual NTK element) + N1 = undo_first_in_chainrule(cost_grads_1, g_loss, device) # undoing first chainrule to get vector of dFunctionOutput/dTheta (actual NTK element) out2 = model.forward(input) loss2, g_loss2 = loss_function.loss_with_costgrad(out2) loss2.backward() cost_grads_2 = get_cost_grads(model) - N2 = undo_first_in_chainrule(cost_grads_2, g_loss2) + N2 = undo_first_in_chainrule(cost_grads_2, g_loss2, device) # Made adjustment for 2d NTK NTK = torch.matmul(N1, torch.t(N2)) @@ -91,19 +91,24 @@ def get_NTK(model, ref_input, input): return NTK -def doNTK(model, gamma_spacing:float=0.01)->torch.Tensor: +def doNTK(model, device, gamma_spacing:float=0.01)->torch.Tensor: gammas = torch.arange(-1, 1, gamma_spacing) NTK_arr = [ - get_NTK(model, input(0.0), input(gamma)) for gamma in gammas + get_NTK(model, input(0.0).to(device), input(gamma).to(device), device) for gamma in gammas ] return gammas, NTK_arr +if torch.cuda.is_available(): + device = torch.device("cuda") + print("Using GPU:", torch.cuda.get_device_name(0)) +else: + device = torch.device("cpu") + print("Using CPU") - -mod = create_model(100, 4, 32, nn.ReLU) -X, Y = doNTK(mod, 0.01) +mod = create_model(100, 4, 32, nn.ReLU).to(device) +X, Y = doNTK(mod, device, 0.01) bY = [Y[n][0, 0].item() for n in range(len(Y))] plt.plot(X,bY) @@ -111,8 +116,8 @@ def doNTK(model, gamma_spacing:float=0.01)->torch.Tensor: print("Saved with width 100.") plt.clf() -mod = create_model(500, 4, 32, nn.ReLU) -X, Y = doNTK(mod, 0.01) +mod = create_model(500, 4, 32, nn.ReLU).to(device) +X, Y = doNTK(mod, device, 0.01) bY = [Y[n][0, 0].item() for n in range(len(Y))] plt.plot(X,bY) @@ -121,8 +126,8 @@ def doNTK(model, gamma_spacing:float=0.01)->torch.Tensor: plt.clf() -mod = create_model(1000, 4, 32, nn.ReLU) -X, Y = doNTK(mod, 0.01) +mod = create_model(1000, 4, 32, nn.ReLU).to(device) +X, Y = doNTK(mod, device, 0.01) bY = [Y[n][0, 0].item() for n in range(len(Y))] plt.plot(X,bY) @@ -131,8 +136,8 @@ def doNTK(model, gamma_spacing:float=0.01)->torch.Tensor: plt.clf() -mod = create_model(1500, 4, 32, nn.ReLU) -X, Y = doNTK(mod, 0.01) +mod = create_model(1500, 4, 32, nn.ReLU).to(device) +X, Y = doNTK(mod, device, 0.01) bY = [Y[n][0, 0].item() for n in range(len(Y))] plt.plot(X,bY) @@ -141,8 +146,8 @@ def doNTK(model, gamma_spacing:float=0.01)->torch.Tensor: plt.clf() -mod = create_model(2000, 4, 32, nn.ReLU) -X, Y = doNTK(mod, 0.01) +mod = create_model(2000, 4, 32, nn.ReLU).to(device) +X, Y = doNTK(mod, device, 0.01) bY = [Y[n][0, 0].item() for n in range(len(Y))] plt.plot(X,bY) From 4108535d5d444f3c940f7282ccf3d76ba1644f7f Mon Sep 17 00:00:00 2001 From: Mihir Kamat Date: Thu, 9 Oct 2025 22:57:04 -0400 Subject: [PATCH 06/10] Added 3d plots -- X, Y are inputs and Z is NTK value --- img/width100.png | Bin 22732 -> 21383 bytes img/width1000.png | Bin 22059 -> 20977 bytes img/width1000_surface.png | Bin 0 -> 82673 bytes img/width100_surface.png | Bin 0 -> 73562 bytes img/width1500.png | Bin 23539 -> 22348 bytes img/width1500_surface.png | Bin 0 -> 88596 bytes img/width2000.png | Bin 25791 -> 0 bytes img/width500.png | Bin 22143 -> 20932 bytes img/width500_surface.png | Bin 0 -> 74494 bytes 9 files changed, 0 insertions(+), 0 deletions(-) create mode 100644 img/width1000_surface.png create 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torch.tensor([1.0, 0.0]).to(device), torch.tensor([_X, _Y]).to(device), device)[0, 0].item() for _X in X] for _Y in Y ] return gX, gY, np.array(gZ) @@ -130,118 +132,30 @@ def doNTK_surface(model, loss_function, device, numpts)->torch.Tensor: device = torch.device("cpu") print("Using CPU") +########################################### ADJUST HERE +ACTIVATION = nn.ReLU +WIDTHS = [100, 500, 1000, 1500] +DEPTH = 4 +SEED = 32 +LOSS = mean_loss +SURFACE_POINTS = 50 +########################################### + +for W in WIDTHS: + mod = create_model(W, DEPTH, SEED, ACTIVATION).to(device) + X, Y, Z = doNTK_surface(mod, LOSS, device, SURFACE_POINTS) + fig = plt.figure() + ax = fig.add_subplot(111, projection='3d') + surf = ax.plot_surface(X, Y, Z, cmap='viridis') + s = "img/width_"+str(W)+"_Act_"+ACTIVATION.__name__ + plt.savefig(s+"_surface.png") + plt.clf() + + gap = 2.0 / SURFACE_POINTS + X, Y = doNTK(mod, LOSS, device, gap) + bY = [Y[n][0, 0].item() for n in range(len(Y))] + plt.plot(X, bY) + plt.savefig(s+".png") + print("Saved with width "+str(W)) + plt.clf() - -mod = create_model(100, 4, 32, nn.ReLU).to(device) - -X, Y, Z = doNTK_surface(mod, mean_loss, device, 50) -fig = plt.figure() -ax = fig.add_subplot(111, projection='3d') -surf = ax.plot_surface(X, Y, Z, cmap='viridis') -plt.savefig("img/width100_surface.png") -plt.clf() - -X, Y = doNTK(mod, mean_loss, device, 0.01) -bY = [Y[n][0, 0].item() for n in range(len(Y))] -plt.plot(X, bY) -plt.savefig("img/width100.png") -print("Saved with width 100.") -plt.clf() - - - -mod = create_model(500, 4, 32, nn.ReLU).to(device) - -X, Y, Z = doNTK_surface(mod, mean_loss, device, 50) -fig = plt.figure() -ax = fig.add_subplot(111, projection='3d') -surf = ax.plot_surface(X, Y, Z, cmap='viridis') -plt.savefig("img/width500_surface.png") -plt.clf() - -X, Y = doNTK(mod, mean_loss, device, 0.01) -bY = [Y[n][0, 0].item() for n in range(len(Y))] -plt.plot(X,bY) -plt.savefig("img/width500.png") -print("Saved with width 500.") -plt.clf() - - -mod = create_model(1000, 4, 32, nn.ReLU).to(device) - -X, Y, Z = doNTK_surface(mod, mean_loss, device, 50) -fig = plt.figure() -ax = fig.add_subplot(111, projection='3d') -surf = ax.plot_surface(X, Y, Z, cmap='viridis') -plt.savefig("img/width1000_surface.png") -plt.clf() - -X, Y = doNTK(mod, mean_loss, device, 0.01) -bY = [Y[n][0, 0].item() for n in range(len(Y))] -plt.plot(X,bY) -plt.savefig("img/width1000.png") -print("Saved with width 1000.") -plt.clf() - - -mod = create_model(1500, 4, 32, nn.ReLU).to(device) - -X, Y, Z = doNTK_surface(mod, mean_loss, device, 50) -fig = plt.figure() -ax = fig.add_subplot(111, projection='3d') -surf = ax.plot_surface(X, Y, Z, cmap='viridis') -plt.savefig("img/width1500_surface.png") -plt.clf() - -X, Y = doNTK(mod, mean_loss, device, 0.01) -bY = [Y[n][0, 0].item() for n in range(len(Y))] -plt.plot(X,bY) -plt.savefig("img/width1500.png") -print("Saved with width 1500.") -plt.clf() - - -# mod = create_model(2000, 4, 32, nn.ReLU).to(device) - -# X, Y, Z = doNTK_surface(mod, mean_loss, device, 50) -# fig = plt.figure() -# ax = fig.add_subplot(111, projection='3d') -# surf = ax.plot_surface(X, Y, Z, cmap='viridis') -# plt.savefig("img/width2000_surface.png") -# plt.clf() - -# X, Y = doNTK(mod, device, 0.01) -# bY = [Y[n][0, 0].item() for n in range(len(Y))] -# plt.plot(X,bY) -# plt.savefig("img/width2000.png") -# print("Saved with width 2000.") -# plt.clf() - - -# # res = mod.forward(input(gamma)) - -# # n = res.shape[0] - -# # loss = loss_func(res) - -# # loss.backward() - -# # # now we calculate array of dC/dtheta - -# # dCost = [] -# # for name, param in mod.named_parameters(): -# # if "weight" in name: -# # dCost.append(param.grad.flatten()) - -# # dCost = torch.concatenate(dCost) - -# # print(dCost) - -# # # then because dC/dtheta is a result of chain rule, we can finally divide dC/dtheta with dC/dOutput to get dOutput/dtheta, which is the NTK -# # # dMean is [1 / n, 1 / n, 1 / n...] - -# # dMean = torch.Tensor([1.0 / n for k in range(n)]) - -# # dFunc = torch.stack([ -# # dCost / torch.Tensor([dMean[i]]) for i in range(dMean.shape[0]) -# # ]) From 576e690b231ce6deb45523570b595aa67e4fd931 Mon Sep 17 00:00:00 2001 From: Mihir Kamat Date: Fri, 10 Oct 2025 14:21:20 -0400 Subject: [PATCH 10/10] Alphabetical order for img --- ...th_100_Act_ReLU.png => a.width_100_Act_ReLU.png} | Bin ...surface.png => a.width_100_Act_ReLU_surface.png} | Bin ...th_500_Act_ReLU.png => b.width_500_Act_ReLU.png} | Bin ...surface.png => b.width_500_Act_ReLU_surface.png} | Bin ..._1000_Act_ReLU.png => c.width_1000_Act_ReLU.png} | Bin ...urface.png => c.width_1000_Act_ReLU_surface.png} | Bin ..._1500_Act_ReLU.png => d.width_1500_Act_ReLU.png} | Bin ...urface.png => d.width_1500_Act_ReLU_surface.png} | Bin 8 files changed, 0 insertions(+), 0 deletions(-) rename img/{width_100_Act_ReLU.png => a.width_100_Act_ReLU.png} (100%) rename img/{width_100_Act_ReLU_surface.png => a.width_100_Act_ReLU_surface.png} (100%) rename img/{width_500_Act_ReLU.png => b.width_500_Act_ReLU.png} (100%) rename img/{width_500_Act_ReLU_surface.png => b.width_500_Act_ReLU_surface.png} (100%) rename img/{width_1000_Act_ReLU.png => c.width_1000_Act_ReLU.png} (100%) rename img/{width_1000_Act_ReLU_surface.png => c.width_1000_Act_ReLU_surface.png} (100%) rename img/{width_1500_Act_ReLU.png => d.width_1500_Act_ReLU.png} (100%) rename img/{width_1500_Act_ReLU_surface.png => d.width_1500_Act_ReLU_surface.png} (100%) diff --git a/img/width_100_Act_ReLU.png b/img/a.width_100_Act_ReLU.png similarity index 100% rename from img/width_100_Act_ReLU.png rename to img/a.width_100_Act_ReLU.png diff --git a/img/width_100_Act_ReLU_surface.png b/img/a.width_100_Act_ReLU_surface.png similarity index 100% rename from img/width_100_Act_ReLU_surface.png rename to img/a.width_100_Act_ReLU_surface.png diff --git a/img/width_500_Act_ReLU.png b/img/b.width_500_Act_ReLU.png similarity index 100% rename from img/width_500_Act_ReLU.png rename to img/b.width_500_Act_ReLU.png diff --git a/img/width_500_Act_ReLU_surface.png b/img/b.width_500_Act_ReLU_surface.png similarity index 100% rename from img/width_500_Act_ReLU_surface.png rename to img/b.width_500_Act_ReLU_surface.png diff --git a/img/width_1000_Act_ReLU.png b/img/c.width_1000_Act_ReLU.png similarity index 100% rename from img/width_1000_Act_ReLU.png rename to img/c.width_1000_Act_ReLU.png diff --git a/img/width_1000_Act_ReLU_surface.png b/img/c.width_1000_Act_ReLU_surface.png similarity index 100% rename from img/width_1000_Act_ReLU_surface.png rename to img/c.width_1000_Act_ReLU_surface.png diff --git a/img/width_1500_Act_ReLU.png b/img/d.width_1500_Act_ReLU.png similarity index 100% rename from img/width_1500_Act_ReLU.png rename to img/d.width_1500_Act_ReLU.png diff --git a/img/width_1500_Act_ReLU_surface.png b/img/d.width_1500_Act_ReLU_surface.png similarity index 100% rename from img/width_1500_Act_ReLU_surface.png rename to img/d.width_1500_Act_ReLU_surface.png

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zgCZheZ7P~@m-uWKi%KuXnx7Tj|8Pak0$_9oviW!R3hvWk$b0XB3>C*DS?AXCEd&Ld zhNd=vk0bQAS6=?aQ9nKVm7YT6(#R|0D)9zZx``+*aVh8F^EZRGXZ$lio(4t)6%0ZS z2&E-;=Kt|@(A)pl`~By409gOqK9`4)ZHKJp#_V6O9Onx93;bNargQbBiWTv{0DQbk AX#fBK literal 0 HcmV?d00001 From 5524ae261780370ce2c795c3b513e3942a53d81d Mon Sep 17 00:00:00 2001 From: Mihir Kamat Date: Thu, 9 Oct 2025 22:58:12 -0400 Subject: [PATCH 07/10] Plot 3d surface of XY inputs vs NTK --- run.py | 108 +++++++++++++++++++++++++++++++++++++++++---------------- 1 file changed, 79 insertions(+), 29 deletions(-) diff --git a/run.py b/run.py index cca017a..ed7f6a8 100644 --- a/run.py +++ b/run.py @@ -100,6 +100,17 @@ def doNTK(model, device, gamma_spacing:float=0.01)->torch.Tensor: return gammas, NTK_arr +def doNTK_surface(model, device, numpts)->torch.Tensor: + X = np.linspace(-1, 1, numpts, dtype=np.float32) + Y = np.linspace(-1, 1, numpts, dtype=np.float32) + gX, gY = np.meshgrid(X, Y) + + gZ = [ + [get_NTK(model, torch.tensor([_X, _Y]).to(device), torch.tensor([1.0, 0.0]).to(device), device)[0, 0].item() for _X in X] for _Y in Y + ] + + return gX, gY, np.array(gZ) + if torch.cuda.is_available(): device = torch.device("cuda") print("Using GPU:", torch.cuda.get_device_name(0)) @@ -107,19 +118,37 @@ def doNTK(model, device, gamma_spacing:float=0.01)->torch.Tensor: device = torch.device("cpu") print("Using CPU") + + mod = create_model(100, 4, 32, nn.ReLU).to(device) + +X, Y, Z = doNTK_surface(mod, device, 50) +fig = plt.figure() +ax = fig.add_subplot(111, projection='3d') +surf = ax.plot_surface(X, Y, Z, cmap='viridis') +plt.savefig("img/width100_surface.png") +plt.clf() + X, Y = doNTK(mod, device, 0.01) bY = [Y[n][0, 0].item() for n in range(len(Y))] - -plt.plot(X,bY) +plt.plot(X, bY) plt.savefig("img/width100.png") print("Saved with width 100.") plt.clf() + + mod = create_model(500, 4, 32, nn.ReLU).to(device) + +X, Y, Z = doNTK_surface(mod, device, 50) +fig = plt.figure() +ax = fig.add_subplot(111, projection='3d') +surf = ax.plot_surface(X, Y, Z, cmap='viridis') +plt.savefig("img/width500_surface.png") +plt.clf() + X, Y = doNTK(mod, device, 0.01) bY = [Y[n][0, 0].item() for n in range(len(Y))] - plt.plot(X,bY) plt.savefig("img/width500.png") print("Saved with width 500.") @@ -127,9 +156,16 @@ def doNTK(model, device, gamma_spacing:float=0.01)->torch.Tensor: mod = create_model(1000, 4, 32, nn.ReLU).to(device) + +X, Y, Z = doNTK_surface(mod, device, 50) +fig = plt.figure() +ax = fig.add_subplot(111, projection='3d') +surf = ax.plot_surface(X, Y, Z, cmap='viridis') +plt.savefig("img/width1000_surface.png") +plt.clf() + X, Y = doNTK(mod, device, 0.01) bY = [Y[n][0, 0].item() for n in range(len(Y))] - plt.plot(X,bY) plt.savefig("img/width1000.png") print("Saved with width 1000.") @@ -137,49 +173,63 @@ def doNTK(model, device, gamma_spacing:float=0.01)->torch.Tensor: mod = create_model(1500, 4, 32, nn.ReLU).to(device) + +X, Y, Z = doNTK_surface(mod, device, 50) +fig = plt.figure() +ax = fig.add_subplot(111, projection='3d') +surf = ax.plot_surface(X, Y, Z, cmap='viridis') +plt.savefig("img/width1500_surface.png") +plt.clf() + X, Y = doNTK(mod, device, 0.01) bY = [Y[n][0, 0].item() for n in range(len(Y))] - plt.plot(X,bY) plt.savefig("img/width1500.png") print("Saved with width 1500.") plt.clf() -mod = create_model(2000, 4, 32, nn.ReLU).to(device) -X, Y = doNTK(mod, device, 0.01) -bY = [Y[n][0, 0].item() for n in range(len(Y))] +# mod = create_model(2000, 4, 32, nn.ReLU).to(device) -plt.plot(X,bY) -plt.savefig("img/width2000.png") -print("Saved with width 2000.") -plt.clf() +# X, Y, Z = doNTK_surface(mod, device, 50) +# fig = plt.figure() +# ax = fig.add_subplot(111, projection='3d') +# surf = ax.plot_surface(X, Y, Z, cmap='viridis') +# plt.savefig("img/width2000_surface.png") +# plt.clf() + +# X, Y = doNTK(mod, device, 0.01) +# bY = [Y[n][0, 0].item() for n in range(len(Y))] +# plt.plot(X,bY) +# plt.savefig("img/width2000.png") +# print("Saved with width 2000.") +# plt.clf() -# res = mod.forward(input(gamma)) +# # res = mod.forward(input(gamma)) -# n = res.shape[0] +# # n = res.shape[0] -# loss = loss_func(res) +# # loss = loss_func(res) -# loss.backward() +# # loss.backward() -# # now we calculate array of dC/dtheta +# # # now we calculate array of dC/dtheta -# dCost = [] -# for name, param in mod.named_parameters(): -# if "weight" in name: -# dCost.append(param.grad.flatten()) +# # dCost = [] +# # for name, param in mod.named_parameters(): +# # if "weight" in name: +# # dCost.append(param.grad.flatten()) -# dCost = torch.concatenate(dCost) +# # dCost = torch.concatenate(dCost) -# print(dCost) +# # print(dCost) -# # then because dC/dtheta is a result of chain rule, we can finally divide dC/dtheta with dC/dOutput to get dOutput/dtheta, which is the NTK -# # dMean is [1 / n, 1 / n, 1 / n...] +# # # then because dC/dtheta is a result of chain rule, we can finally divide dC/dtheta with dC/dOutput to get dOutput/dtheta, which is the NTK +# # # dMean is [1 / n, 1 / n, 1 / n...] -# dMean = torch.Tensor([1.0 / n for k in range(n)]) +# # dMean = torch.Tensor([1.0 / n for k in range(n)]) -# dFunc = torch.stack([ -# dCost / torch.Tensor([dMean[i]]) for i in range(dMean.shape[0]) -# ]) +# # dFunc = torch.stack([ +# # dCost / torch.Tensor([dMean[i]]) for i in range(dMean.shape[0]) +# # ]) From 391d632cc459071f731ff74d66899dc3c0a4ed29 Mon Sep 17 00:00:00 2001 From: Mihir Kamat Date: Thu, 9 Oct 2025 23:48:35 -0400 Subject: [PATCH 08/10] Made generic loss wrapper so that script can handle any loss function --- run.py | 84 +++++++++++++++++++++++++++++++++------------------------- 1 file changed, 48 insertions(+), 36 deletions(-) diff --git a/run.py b/run.py index ed7f6a8..75e2434 100644 --- a/run.py +++ b/run.py @@ -5,26 +5,8 @@ import matplotlib.pyplot as plt import math -# Simple Mean Loss function - -class MeanLoss(nn.Module): - def __init__(self): - super(MeanLoss, self).__init__() - - def forward(self, input_tensor): - loss_out = torch.mean(input_tensor) - return loss_out - - def loss_with_costgrad(self, net_out): - L = net_out.shape[0] - loss_out = self.forward(net_out) - dloss_out = torch.tensor([ - 1.0 / L for _ in range(L) - ]) - return loss_out, dloss_out - +# Util funcs -torch.use_deterministic_algorithms=True def input(gamma:float)->torch.Tensor: gamma=torch.Tensor([gamma]) @@ -34,6 +16,34 @@ def input(gamma:float)->torch.Tensor: def flatten(ls): return [item for sublist in ls for item in sublist] + +# Simple Mean Loss function + +def mean_loss(inp): + return torch.mean(inp) + +# Loss Wrapper function, returns the loss and the gradient of loss wrt net output + +class LossWrapper(nn.Module): + def __init__(self, loss_function): + super(LossWrapper, self).__init__() + self.loss_function = loss_function + + def loss_with_costgrad(self, net_out): + L = net_out.shape[0] + ret_loss = self.loss_function(net_out) + + nout = net_out.clone().detach() + nout.requires_grad_(True) + loss_out = self.loss_function(nout) + nout.retain_grad() + loss_out.backward() + + return ret_loss, nout.grad + + +torch.use_deterministic_algorithms=True + def create_model(width, depth, seed, activation:nn.Module): torch.manual_seed(seed) random.seed(seed) @@ -68,18 +78,20 @@ def undo_first_in_chainrule(grad, dCdF, dev): return dFunc.to(dev) -def get_NTK(model, ref_input, input, device): - loss_function = MeanLoss() +def get_NTK(model, loss_function, ref_input, input, device): + + lfn = LossWrapper(loss_function) out1 = model.forward(ref_input) - loss, g_loss = loss_function.loss_with_costgrad(out1) # return loss and gradient of loss wrt function output + # lfn.loss_with_costgrad(out1) + loss, g_loss = lfn.loss_with_costgrad(out1) # return loss and gradient of loss wrt function output loss.backward() cost_grads_1 = get_cost_grads(model) # dC/dtheta N1 = undo_first_in_chainrule(cost_grads_1, g_loss, device) # undoing first chainrule to get vector of dFunctionOutput/dTheta (actual NTK element) out2 = model.forward(input) - loss2, g_loss2 = loss_function.loss_with_costgrad(out2) + loss2, g_loss2 = lfn.loss_with_costgrad(out2) loss2.backward() cost_grads_2 = get_cost_grads(model) @@ -91,22 +103,22 @@ def get_NTK(model, ref_input, input, device): return NTK -def doNTK(model, device, gamma_spacing:float=0.01)->torch.Tensor: +def doNTK(model, loss_function, device, gamma_spacing:float=0.01)->torch.Tensor: gammas = torch.arange(-1, 1, gamma_spacing) NTK_arr = [ - get_NTK(model, input(0.0).to(device), input(gamma).to(device), device) for gamma in gammas + get_NTK(model, loss_function, input(0.0).to(device), input(gamma).to(device), device) for gamma in gammas ] return gammas, NTK_arr -def doNTK_surface(model, device, numpts)->torch.Tensor: +def doNTK_surface(model, loss_function, device, numpts)->torch.Tensor: X = np.linspace(-1, 1, numpts, dtype=np.float32) Y = np.linspace(-1, 1, numpts, dtype=np.float32) gX, gY = np.meshgrid(X, Y) gZ = [ - [get_NTK(model, torch.tensor([_X, _Y]).to(device), torch.tensor([1.0, 0.0]).to(device), device)[0, 0].item() for _X in X] for _Y in Y + [get_NTK(model, loss_function, torch.tensor([_X, _Y]).to(device), torch.tensor([1.0, 0.0]).to(device), device)[0, 0].item() for _X in X] for _Y in Y ] return gX, gY, np.array(gZ) @@ -122,14 +134,14 @@ def doNTK_surface(model, device, numpts)->torch.Tensor: mod = create_model(100, 4, 32, nn.ReLU).to(device) -X, Y, Z = doNTK_surface(mod, device, 50) +X, Y, Z = doNTK_surface(mod, mean_loss, device, 50) fig = plt.figure() ax = fig.add_subplot(111, projection='3d') surf = ax.plot_surface(X, Y, Z, cmap='viridis') plt.savefig("img/width100_surface.png") plt.clf() -X, Y = doNTK(mod, device, 0.01) +X, Y = doNTK(mod, mean_loss, device, 0.01) bY = [Y[n][0, 0].item() for n in range(len(Y))] plt.plot(X, bY) plt.savefig("img/width100.png") @@ -140,14 +152,14 @@ def doNTK_surface(model, device, numpts)->torch.Tensor: mod = create_model(500, 4, 32, nn.ReLU).to(device) -X, Y, Z = doNTK_surface(mod, device, 50) +X, Y, Z = doNTK_surface(mod, mean_loss, device, 50) fig = plt.figure() ax = fig.add_subplot(111, projection='3d') surf = ax.plot_surface(X, Y, Z, cmap='viridis') plt.savefig("img/width500_surface.png") plt.clf() -X, Y = doNTK(mod, device, 0.01) +X, Y = doNTK(mod, mean_loss, device, 0.01) bY = [Y[n][0, 0].item() for n in range(len(Y))] plt.plot(X,bY) plt.savefig("img/width500.png") @@ -157,14 +169,14 @@ def doNTK_surface(model, device, numpts)->torch.Tensor: mod = create_model(1000, 4, 32, nn.ReLU).to(device) -X, Y, Z = doNTK_surface(mod, device, 50) +X, Y, Z = doNTK_surface(mod, mean_loss, device, 50) fig = plt.figure() ax = fig.add_subplot(111, projection='3d') surf = ax.plot_surface(X, Y, Z, cmap='viridis') plt.savefig("img/width1000_surface.png") plt.clf() -X, Y = doNTK(mod, device, 0.01) +X, Y = doNTK(mod, mean_loss, device, 0.01) bY = [Y[n][0, 0].item() for n in range(len(Y))] plt.plot(X,bY) plt.savefig("img/width1000.png") @@ -174,14 +186,14 @@ def doNTK_surface(model, device, numpts)->torch.Tensor: mod = create_model(1500, 4, 32, nn.ReLU).to(device) -X, Y, Z = doNTK_surface(mod, device, 50) +X, Y, Z = doNTK_surface(mod, mean_loss, device, 50) fig = plt.figure() ax = fig.add_subplot(111, projection='3d') surf = ax.plot_surface(X, Y, Z, cmap='viridis') plt.savefig("img/width1500_surface.png") plt.clf() -X, Y = doNTK(mod, device, 0.01) +X, Y = doNTK(mod, mean_loss, device, 0.01) bY = [Y[n][0, 0].item() for n in range(len(Y))] plt.plot(X,bY) plt.savefig("img/width1500.png") @@ -191,7 +203,7 @@ def doNTK_surface(model, device, numpts)->torch.Tensor: # mod = create_model(2000, 4, 32, nn.ReLU).to(device) -# X, Y, Z = doNTK_surface(mod, device, 50) +# X, Y, Z = doNTK_surface(mod, mean_loss, device, 50) # fig = plt.figure() # ax = fig.add_subplot(111, projection='3d') # surf = ax.plot_surface(X, Y, Z, cmap='viridis') From 1ebdc0a953be9684eabe1bff176f8f6d207bae3c Mon Sep 17 00:00:00 2001 From: Mihir Kamat Date: Fri, 10 Oct 2025 14:16:16 -0400 Subject: [PATCH 09/10] Clean up the code --- img/width100.png | Bin 21383 -> 0 bytes img/width1000.png | Bin 20977 -> 0 bytes img/width1000_surface.png | Bin 82673 -> 0 bytes img/width100_surface.png | Bin 73562 -> 0 bytes img/width1500.png | Bin 22348 -> 0 bytes img/width1500_surface.png | Bin 88596 -> 0 bytes img/width500.png | Bin 20932 -> 0 bytes img/width500_surface.png | Bin 74494 -> 0 bytes img/width_1000_Act_ReLU.png | Bin 0 -> 20798 bytes img/width_1000_Act_ReLU_surface.png | Bin 0 -> 65245 bytes img/width_100_Act_ReLU.png | Bin 0 -> 20901 bytes img/width_100_Act_ReLU_surface.png | Bin 0 -> 67793 bytes img/width_1500_Act_ReLU.png | Bin 0 -> 21976 bytes img/width_1500_Act_ReLU_surface.png | Bin 0 -> 70277 bytes img/width_500_Act_ReLU.png | Bin 0 -> 20776 bytes img/width_500_Act_ReLU_surface.png | Bin 0 -> 65757 bytes run.py | 144 ++++++---------------------- 17 files changed, 29 insertions(+), 115 deletions(-) delete mode 100644 img/width100.png delete mode 100644 img/width1000.png delete mode 100644 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