1110 lines
680 KiB
Plaintext
1110 lines
680 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "view-in-github",
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"colab_type": "text"
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},
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"source": [
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"<a href=\"https://colab.research.google.com/github/udlbook/udlbook/blob/main/Blogs/BorealisNTK.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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]
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},
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{
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"cell_type": "markdown",
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"source": [
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"# Neural tangent kernel\n",
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"\n",
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"This blog contains code that accompanies the Borealis AI blog on the Neural Tangent Kernel."
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],
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"metadata": {
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"id": "Ao-2MW3o_SFN"
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}
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {
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"id": "_IQFHZEMZE8T"
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},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"from scipy.linalg import expm\n",
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"from matplotlib import cm\n",
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"from matplotlib.colors import ListedColormap"
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]
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},
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{
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"cell_type": "markdown",
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"source": [
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"Create some data and draw it."
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],
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"metadata": {
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"id": "1RYf0uIwA98m"
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}
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"id": "cJNZ2VIcYsD8"
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},
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"outputs": [],
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"source": [
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"# Input is one dimensional but has ones appended to incorporate biases\n",
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"X = np.array([[0.2, 0.4, 0.8],[1,1,1]])\n",
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"y = np.array([[-0.05],[-0.2],[0.3]])\n",
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"\n",
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"D_in = X.shape[0] # No of input dimensions (2)\n",
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"I = X.shape[1] # No of data points (3)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/",
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"height": 449
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},
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"id": "FpFlD4nUZDRt",
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"outputId": "b0cd7f72-4f63-4e19-ab3c-b6b274bbbad1"
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},
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"outputs": [
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{
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"output_type": "display_data",
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"data": {
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"text/plain": [
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"<Figure size 640x480 with 1 Axes>"
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],
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"image/png": "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\n"
|
|
},
|
|
"metadata": {}
|
|
}
|
|
],
|
|
"source": [
|
|
"fig, ax = plt.subplots()\n",
|
|
"ax.plot(X[0:1,:],y.T,'ro')\n",
|
|
"ax.set_xlim([0,1]); ax.set_ylim([-0.5,0.5])\n",
|
|
"ax.set_xlabel('x'); ax.set_ylabel('y')\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"source": [
|
|
"Support routines to run shallow network and compute derivative of neural network output with respect to network parameters."
|
|
],
|
|
"metadata": {
|
|
"id": "QpM2sQA2DN9t"
|
|
}
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 4,
|
|
"metadata": {
|
|
"id": "_D4tHA_cfc7Y"
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Define the Rectified Linear Unit (ReLU) function\n",
|
|
"def ReLU(preactivation):\n",
|
|
" activation = preactivation.clip(0.0)\n",
|
|
" return activation\n",
|
|
"\n",
|
|
"# Derivative of ReLU\n",
|
|
"def ReLUDeriv(z):\n",
|
|
" return (z>0).astype(int)\n",
|
|
"\n",
|
|
"# Shallow network function\n",
|
|
"def shallow_network(X, omega0, omega1, beta1):\n",
|
|
" preactivations = omega0 @ X\n",
|
|
" activations = ReLU(preactivations)\n",
|
|
" output = beta1 + omega1 @ activations / np.sqrt(omega1.size)\n",
|
|
" return output\n",
|
|
"\n",
|
|
"# Sum of squares loss\n",
|
|
"def loss(network_output, y):\n",
|
|
" return 0.5 * np.sum((network_output-y) * (network_output-y))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"source": [
|
|
"Initialize the parameters according to a normal distribution"
|
|
],
|
|
"metadata": {
|
|
"id": "F6yRB4wrEnR-"
|
|
}
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 5,
|
|
"metadata": {
|
|
"id": "zkYRfFGEOhpu"
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def initialize_parameters(D, seed=10, D_in = 2):\n",
|
|
" # Set the seed so we always get the same numbers\n",
|
|
" np.random.seed(seed)\n",
|
|
"\n",
|
|
" # Set weights in first layer according to random normal distribution\n",
|
|
" # But set last component (which computes biases) to zero\n",
|
|
" omega0 = np.random.normal(size=(D, D_in))\n",
|
|
" omega0[1,:] = 0\n",
|
|
" # Set weights in second layer according to random normal distribution\n",
|
|
" omega1 = np.random.normal(size=(1,D))\n",
|
|
" # Set bias to zero\n",
|
|
" beta1 = 0\n",
|
|
"\n",
|
|
" return omega0, omega1, beta1"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"source": [
|
|
"Routines to calculate the empirical and analytical NTK (i.e. the NTK with infinite hidden units) for the shallow network"
|
|
],
|
|
"metadata": {
|
|
"id": "mxW8E5kYIzlj"
|
|
}
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 6,
|
|
"metadata": {
|
|
"id": "fCNhfedhjLUA"
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Compute the empirical NTK for the shallow network\n",
|
|
"def compute_empirical_ntk(X1,X2, omega0, omega1, beta1):\n",
|
|
"\n",
|
|
" I1 = X1.shape[1]\n",
|
|
" I2 = X2.shape[1]\n",
|
|
" K = np.zeros((I1,I2))\n",
|
|
" preactivations1 = omega0 @ X1\n",
|
|
" preactivations2 = omega0 @ X2\n",
|
|
"\n",
|
|
" for i in range(I1):\n",
|
|
" for j in range(I2):\n",
|
|
" K[i,j] = np.mean(ReLU(preactivations1[:,i]) * ReLU(preactivations2[:,j])) + 1\n",
|
|
" K[i,j] = K[i,j] + X1[:,i] @ X2[:,j].T * np.mean(omega1 * omega1 * ReLUDeriv(preactivations1[:,i]) * ReLUDeriv(preactivations2[:,j]))\n",
|
|
" return K\n",
|
|
"\n",
|
|
"# Compute theoretical NTK for the shallow network\n",
|
|
"def compute_analytical_ntk(X1, X2):\n",
|
|
" I1 = X1.shape[1]\n",
|
|
" I2 = X2.shape[1]\n",
|
|
" K = np.zeros((I1,I2))\n",
|
|
"\n",
|
|
" for i in range(I1):\n",
|
|
" for j in range(I2):\n",
|
|
" x1 = X1[:,i]\n",
|
|
" x2 = X2[:,j]\n",
|
|
" norm1 = np.sqrt(x1.T@x1)\n",
|
|
" norm2 = np.sqrt(x2.T@x2)\n",
|
|
" if norm1==0 or norm2 ==0:\n",
|
|
" theta = 0\n",
|
|
" else:\n",
|
|
" theta = np.arccos(x1.T@x2/(norm1*norm2))\n",
|
|
" K[i,j] = x1.T@x2 * (np.pi-theta)/(2*np.pi)\n",
|
|
" K[i,j] = K[i,j] + norm1 * norm2 * ((np.pi-theta)*np.cos(theta)+np.sin(theta))/(2*np.pi) + 1\n",
|
|
" return K"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"source": [
|
|
"Compute empirical and analytical NTK for wide network with 10,000 hidden units and show they are almost the same"
|
|
],
|
|
"metadata": {
|
|
"id": "WnxLPbWxLfK2"
|
|
}
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 7,
|
|
"metadata": {
|
|
"colab": {
|
|
"base_uri": "https://localhost:8080/"
|
|
},
|
|
"id": "JKRtshxljG5y",
|
|
"outputId": "e441f49f-1911-40b8-a0b8-47673859b7b7"
|
|
},
|
|
"outputs": [
|
|
{
|
|
"output_type": "stream",
|
|
"name": "stdout",
|
|
"text": [
|
|
"Empirical NTK\n",
|
|
" [[2.03861529 2.05165862 2.08784793]\n",
|
|
" [2.05165862 2.1637655 2.26898074]\n",
|
|
" [2.08784793 2.26898074 2.64798733]]\n",
|
|
"\n",
|
|
"Analytical NTK\n",
|
|
" [[2.04 2.04888213 2.07923821]\n",
|
|
" [2.04888213 2.16 2.26003372]\n",
|
|
" [2.07923821 2.26003372 2.64 ]]\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Number of hidden units\n",
|
|
"D = 10000\n",
|
|
"# Random seed for initialized parameters\n",
|
|
"seed = 18\n",
|
|
"# Number of input dimension (2 as have appended a 1 to incorporate first layer biases)\n",
|
|
"D_in = 2\n",
|
|
"\n",
|
|
"# Initialize the parameters\n",
|
|
"omega0, omega1, beta1 = initialize_parameters(D, seed = seed, D_in=D_in)\n",
|
|
"\n",
|
|
"# Compute empirical and analytical NTKs\n",
|
|
"# When D is large, they should be similar\n",
|
|
"K = compute_empirical_ntk(X, X, omega0, omega1, beta1)\n",
|
|
"print(\"Empirical NTK\\n\", K)\n",
|
|
"K_analytical = compute_analytical_ntk(X,X)\n",
|
|
"print(\"\\nAnalytical NTK\\n\", K_analytical)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"source": [
|
|
"Compute Jacobian containing derivatives of network output with respect to network parameters for each input"
|
|
],
|
|
"metadata": {
|
|
"id": "FEUz7p4vL1hZ"
|
|
}
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"source": [
|
|
"# Get vector of derivatives of network output with respect to parameters\n",
|
|
"# omega0, omega1, beta1\n",
|
|
"# There are no offsets beta0 as they are incorporated by concatenating ones to each input\n",
|
|
"def derivative_vector(x,omega0, omega1, beta1):\n",
|
|
" preactivations = omega0 @ x\n",
|
|
" activations = ReLU(preactivations)\n",
|
|
" D = omega1.size\n",
|
|
"\n",
|
|
" dfdomega0 = ( np.ones((omega0.size,1)) @ ReLUDeriv(activations).T ) * np.concatenate((np.identity(D) * x[0,:],np.identity(D) * x[1,:]),axis=0) @ omega1.T / np.sqrt(D)\n",
|
|
" dfdbeta1 = np.ones((1,1))\n",
|
|
" dfdomega1 = activations / np.sqrt(D)\n",
|
|
"\n",
|
|
" return np.concatenate((dfdomega0, dfdbeta1, dfdomega1), axis=0)\n",
|
|
"\n",
|
|
"# Compute Jacobian of how network outputs change for each point given change in parameters\n",
|
|
"def get_jacobian(X, omega0, omega1, beta1):\n",
|
|
" n_param = omega0.size+omega1.size+1\n",
|
|
" n_data = X.shape[1]\n",
|
|
" jacobian = np.zeros((n_param, n_data))\n",
|
|
" for i in range (n_data):\n",
|
|
" jacobian[:,i:i+1] = derivative_vector(X[:,i:i+1], omega0, omega1, beta1)\n",
|
|
" return jacobian"
|
|
],
|
|
"metadata": {
|
|
"id": "eVAHtfx6L0fg"
|
|
},
|
|
"execution_count": 8,
|
|
"outputs": []
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"source": [
|
|
"Confirm that emprical NTK is just the product of the Jacobians"
|
|
],
|
|
"metadata": {
|
|
"id": "vlIfcHabNnhw"
|
|
}
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"source": [
|
|
"K = compute_empirical_ntk(X, X, omega0, omega1, beta1)\n",
|
|
"print(\"Empirical NTK\\n\", K)\n",
|
|
"K_from_jacobian = get_jacobian(X, omega0, omega1, beta1).T @ get_jacobian(X, omega0, omega1, beta1)\n",
|
|
"print(\"NTK from Jacobian\\n\", K_from_jacobian)"
|
|
],
|
|
"metadata": {
|
|
"colab": {
|
|
"base_uri": "https://localhost:8080/"
|
|
},
|
|
"id": "zml0O_LFNT5G",
|
|
"outputId": "bab5ab7a-68c2-4eaa-a6fc-90870a3cb016"
|
|
},
|
|
"execution_count": 9,
|
|
"outputs": [
|
|
{
|
|
"output_type": "stream",
|
|
"name": "stdout",
|
|
"text": [
|
|
"Empirical NTK\n",
|
|
" [[2.03861529 2.05165862 2.08784793]\n",
|
|
" [2.05165862 2.1637655 2.26898074]\n",
|
|
" [2.08784793 2.26898074 2.64798733]]\n",
|
|
"NTK from Jacobian\n",
|
|
" [[2.03861529 2.05165862 2.08784793]\n",
|
|
" [2.05165862 2.1637655 2.26898074]\n",
|
|
" [2.08784793 2.26898074 2.64798733]]\n"
|
|
]
|
|
}
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"source": [
|
|
"Compute prediction at training points, residuals, and parameters as a function of time during training process"
|
|
],
|
|
"metadata": {
|
|
"id": "R5FdFM9WW3kj"
|
|
}
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 10,
|
|
"metadata": {
|
|
"id": "92qsV0-XeYzZ"
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Define time steps and count them\n",
|
|
"t_all = np.arange(0,100,0.05)\n",
|
|
"nT = t_all.shape[0]\n",
|
|
"# Create array for predictions at training data points as a function of time\n",
|
|
"f_all = np.zeros((I,nT))\n",
|
|
"# Create array for residuals at training data points as a function of time\n",
|
|
"residuals_all = np.zeros((I,nT))\n",
|
|
"# Create array for 3D+1 parameters as a function of time\n",
|
|
"phi_t_all = np.zeros((3*D+1,nT))\n",
|
|
"\n",
|
|
"# Precompute the Moore Penrose inverse\n",
|
|
"moore_penrose_inverse = get_jacobian(X, omega0, omega1, beta1) @ (np.linalg.inv(K))\n",
|
|
"# Store the initial vectors in a vector\n",
|
|
"phi_0 = np.concatenate((omega0[:,0:1],omega0[:,1:2],np.ones((1,1))*beta1,omega1.T))\n",
|
|
"# Compute initial network outputs at training points\n",
|
|
"f_0 = shallow_network(X, omega0, omega1, beta1).T\n",
|
|
"\n",
|
|
"# For each time step\n",
|
|
"for t in range(len(t_all)):\n",
|
|
" # Compute prediction at data points\n",
|
|
" f_all[:,t:t+1] = y + expm(-K * t_all[t]) @ (f_0-y)\n",
|
|
" # Compute residuals at data points\n",
|
|
" residuals_all[:,t:t+1] = f_all[:,t:t+1]-y\n",
|
|
" # Compute parameter vector\n",
|
|
" phi_t_all[:,t:t+1] = phi_0 - moore_penrose_inverse @ (np.identity(3)-expm(-K * t_all[t])) @ (f_0-y)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"source": [
|
|
"Draw predictions at data points over time"
|
|
],
|
|
"metadata": {
|
|
"id": "hIyny7ZKZFfK"
|
|
}
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 11,
|
|
"metadata": {
|
|
"id": "wfF_oTS5Z4Wi",
|
|
"colab": {
|
|
"base_uri": "https://localhost:8080/",
|
|
"height": 449
|
|
},
|
|
"outputId": "c311f0e2-f876-4c7c-933f-e24f68453e97"
|
|
},
|
|
"outputs": [
|
|
{
|
|
"output_type": "display_data",
|
|
"data": {
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
],
|
|
"image/png": 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\n"
|
|
},
|
|
"metadata": {}
|
|
}
|
|
],
|
|
"source": [
|
|
"fig, ax = plt.subplots()\n",
|
|
"ax.plot(t_all,np.squeeze(f_all[0,:]),'r-', label='Training point 1')\n",
|
|
"ax.plot(t_all,np.squeeze(f_all[1,:]),'g-', label='Training point 2')\n",
|
|
"ax.plot(t_all,np.squeeze(f_all[2,:]),'b-', label='Training point 3')\n",
|
|
"ax.set_xlim([0,10]); ax.set_ylim([-0.5,0.5])\n",
|
|
"ax.set_xlabel('t'); ax.set_ylabel('prediction at training data points')\n",
|
|
"ax.legend()\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"source": [
|
|
"Plot residuals as a function of time"
|
|
],
|
|
"metadata": {
|
|
"id": "wSMoLi5nZKYv"
|
|
}
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"source": [
|
|
"fig, ax = plt.subplots()\n",
|
|
"ax.plot(t_all,np.squeeze(residuals_all[0,:]),'r-', label='Training point 1')\n",
|
|
"ax.plot(t_all,np.squeeze(residuals_all[1,:]),'g-', label='Training point 2')\n",
|
|
"ax.plot(t_all,np.squeeze(residuals_all[2,:]),'b-', label='Training point 3')\n",
|
|
"ax.set_xlim([0,10]); ax.set_ylim([-0.5,0.5])\n",
|
|
"ax.set_xlabel('t'); ax.set_ylabel('residual at training data points')\n",
|
|
"ax.legend()\n",
|
|
"plt.show()"
|
|
],
|
|
"metadata": {
|
|
"colab": {
|
|
"base_uri": "https://localhost:8080/",
|
|
"height": 449
|
|
},
|
|
"id": "8QYKlzzUZLKP",
|
|
"outputId": "26959ce0-26c7-43fe-c7f7-7e271a337eae"
|
|
},
|
|
"execution_count": 12,
|
|
"outputs": [
|
|
{
|
|
"output_type": "display_data",
|
|
"data": {
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
],
|
|
"image/png": 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\n"
|
|
},
|
|
"metadata": {}
|
|
}
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"source": [
|
|
"Plot loss as a function of time"
|
|
],
|
|
"metadata": {
|
|
"id": "o2V9v-TlZQrZ"
|
|
}
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"source": [
|
|
"fig, ax = plt.subplots()\n",
|
|
"square_error = np.sum(residuals_all * residuals_all, axis=0)\n",
|
|
"ax.plot(t_all, square_error,'k-')\n",
|
|
"ax.set_xlim([0,10]); ax.set_ylim([-0.0,1.0])\n",
|
|
"ax.set_xlabel('t'); ax.set_ylabel('Loss')\n",
|
|
"plt.show()"
|
|
],
|
|
"metadata": {
|
|
"colab": {
|
|
"base_uri": "https://localhost:8080/",
|
|
"height": 455
|
|
},
|
|
"id": "89H_zWQHZQZt",
|
|
"outputId": "4002e625-3763-40f9-d186-fc4fc07c6c7d"
|
|
},
|
|
"execution_count": 13,
|
|
"outputs": [
|
|
{
|
|
"output_type": "display_data",
|
|
"data": {
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
],
|
|
"image/png": 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\n"
|
|
},
|
|
"metadata": {}
|
|
}
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"source": [
|
|
"Plot parameters as a function of time (almost constant with large width)"
|
|
],
|
|
"metadata": {
|
|
"id": "eboxCz0dZW0s"
|
|
}
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"source": [
|
|
"fig, ax = plt.subplots()\n",
|
|
"ax.plot(t_all, np.squeeze(phi_t_all[20,:]),'c-', label='Layer 1 weight')\n",
|
|
"ax.plot(t_all, np.squeeze(phi_t_all[15250,:]),'m-', label = 'Layer 1 bias')\n",
|
|
"ax.plot(t_all, np.squeeze(phi_t_all[20305,:]),'k-', label = 'Layer 2 weight')\n",
|
|
"ax.plot(t_all, np.squeeze(phi_t_all[30000,:]),'y-', label = 'Layer 2 bias')\n",
|
|
"ax.set_xlim([0,5]); ax.set_ylim([-2.5,2.5])\n",
|
|
"ax.set_xlabel('t'); ax.set_ylabel('phi')\n",
|
|
"ax.legend()\n",
|
|
"plt.show()"
|
|
],
|
|
"metadata": {
|
|
"colab": {
|
|
"base_uri": "https://localhost:8080/",
|
|
"height": 449
|
|
},
|
|
"id": "q6yxIev6ZWob",
|
|
"outputId": "546bef23-955a-4115-f38b-5200f16dba88"
|
|
},
|
|
"execution_count": 14,
|
|
"outputs": [
|
|
{
|
|
"output_type": "display_data",
|
|
"data": {
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
],
|
|
"image/png": 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\n"
|
|
},
|
|
"metadata": {}
|
|
}
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"source": [
|
|
"Helper routines to run network using parameter vector directly"
|
|
],
|
|
"metadata": {
|
|
"id": "PvAKER77a8Hj"
|
|
}
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 15,
|
|
"metadata": {
|
|
"id": "WQUPORoBVEbv"
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def vector_to_params(params):\n",
|
|
" D = int((params.size-1)/3)\n",
|
|
" omega0 = np.ones((D,2))\n",
|
|
" omega0[:,0:1] = params[0:D,0:1]\n",
|
|
" omega0[:,1:2] = params[D:D*2,0:1]\n",
|
|
" beta1 = params[D*2:D*2+1,0:1]\n",
|
|
" omega1 = params[D*2+1:D*3+1,0:1].T\n",
|
|
" return omega0, omega1, beta1\n",
|
|
"\n",
|
|
"def shallow_network_param_vector(X, phi):\n",
|
|
" omega0, omega1, beta1 = vector_to_params(phi)\n",
|
|
" return shallow_network(X,omega0,omega1,beta1)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 16,
|
|
"metadata": {
|
|
"id": "cv9ZrUoRkuhI",
|
|
"colab": {
|
|
"base_uri": "https://localhost:8080/",
|
|
"height": 449
|
|
},
|
|
"outputId": "a33a32f1-47be-49d4-c61e-bf3183953a45"
|
|
},
|
|
"outputs": [
|
|
{
|
|
"output_type": "display_data",
|
|
"data": {
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
],
|
|
"image/png": 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\n"
|
|
},
|
|
"metadata": {}
|
|
}
|
|
],
|
|
"source": [
|
|
"# Define an array of points where will make new predictions\n",
|
|
"x_vals = np.arange(0,1,0.001)[None,:]\n",
|
|
"x_vals = np.concatenate((x_vals, np.ones_like(x_vals)))\n",
|
|
"\n",
|
|
"# Compute parameters at 6 different time points\n",
|
|
"phi_1 = phi_0 - moore_penrose_inverse @ (np.identity(3)-expm(-K * 0.1)) @ (f_0-y)\n",
|
|
"phi_2 = phi_0 - moore_penrose_inverse @ (np.identity(3)-expm(-K * 0.5)) @ (f_0-y)\n",
|
|
"phi_3 = phi_0 - moore_penrose_inverse @ (np.identity(3)-expm(-K * 1.5)) @ (f_0-y)\n",
|
|
"phi_4 = phi_0 - moore_penrose_inverse @ (np.identity(3)-expm(-K * 5.0)) @ (f_0-y)\n",
|
|
"phi_5 = phi_0 - moore_penrose_inverse @ (np.identity(3)-expm(-K * 25.0)) @ (f_0-y)\n",
|
|
"phi_6 = phi_0 - moore_penrose_inverse @ (np.identity(3)-expm(-K * 5000.0)) @ (f_0-y)\n",
|
|
"\n",
|
|
"# Draw the function evolution over time\n",
|
|
"fig, ax = plt.subplots()\n",
|
|
"ax.plot(X[0:1,:],y.T,'ro')\n",
|
|
"ax.plot(x_vals[0:1,:].T, shallow_network_param_vector(x_vals, phi_0).T,'r-',label='t=0')\n",
|
|
"ax.plot(x_vals[0:1,:].T, shallow_network_param_vector(x_vals, phi_1).T,'b-',label='t=0.1')\n",
|
|
"ax.plot(x_vals[0:1,:].T, shallow_network_param_vector(x_vals, phi_2).T,'g-',label='t=0.5')\n",
|
|
"ax.plot(x_vals[0:1,:].T, shallow_network_param_vector(x_vals, phi_3).T,'c-',label='t=1.5')\n",
|
|
"ax.plot(x_vals[0:1,:].T, shallow_network_param_vector(x_vals, phi_4).T,'y-',label='t=5.0')\n",
|
|
"ax.plot(x_vals[0:1,:].T, shallow_network_param_vector(x_vals, phi_5).T,'m-',label='t=25.0')\n",
|
|
"ax.plot(x_vals[0:1,:].T, shallow_network_param_vector(x_vals, phi_6).T,'k-',label='t=5000.0')\n",
|
|
"ax.set_xlim([0,1]); ax.set_ylim([-0.5,0.5])\n",
|
|
"ax.set_xlabel('x'); ax.set_ylabel('Predicted output')\n",
|
|
"ax.legend()\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"source": [
|
|
"The previous way of making predictions used the full non-linear model. Here, we make predictions using the empirical kernel"
|
|
],
|
|
"metadata": {
|
|
"id": "SEn7WsKUfHi_"
|
|
}
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 17,
|
|
"metadata": {
|
|
"id": "nBSpVJA7hDnF"
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
" # Make predictions directly using kernel method (linear approximation)\n",
|
|
"def kernel_predict_empirical(X,x,y,t, f_0, omega0, omega1, beta1):\n",
|
|
" K = compute_empirical_ntk(X,X, omega0, omega1, beta1)\n",
|
|
" predict = compute_empirical_ntk(x,X, omega0, omega1, beta1) @ np.linalg.inv(K) @ (np.identity(3)-expm(-K * t)) @ (f_0-y)\n",
|
|
" return predict"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 18,
|
|
"metadata": {
|
|
"colab": {
|
|
"base_uri": "https://localhost:8080/",
|
|
"height": 449
|
|
},
|
|
"id": "8ZQFrsr1hKnr",
|
|
"outputId": "a0bdb8e6-514d-4426-b43a-f8a6f3761733"
|
|
},
|
|
"outputs": [
|
|
{
|
|
"output_type": "display_data",
|
|
"data": {
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
],
|
|
"image/png": 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\n"
|
|
},
|
|
"metadata": {}
|
|
}
|
|
],
|
|
"source": [
|
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"# Get predictions at time 0\n",
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"f_0_x = shallow_network_param_vector(x_vals, phi_0).T\n",
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"# Get predictions at six different time points\n",
|
|
"f_0_test = f_0_x - kernel_predict_empirical(X, x_vals, y, 0.0, f_0, omega0, omega1, beta1)\n",
|
|
"f_1_test = f_0_x - kernel_predict_empirical(X, x_vals, y, 0.1, f_0, omega0, omega1, beta1)\n",
|
|
"f_2_test = f_0_x - kernel_predict_empirical(X, x_vals, y, 0.5, f_0, omega0, omega1, beta1)\n",
|
|
"f_3_test = f_0_x - kernel_predict_empirical(X, x_vals, y, 1.5, f_0, omega0, omega1, beta1)\n",
|
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"f_4_test = f_0_x - kernel_predict_empirical(X, x_vals, y, 5.0, f_0, omega0, omega1, beta1)\n",
|
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"f_5_test = f_0_x - kernel_predict_empirical(X, x_vals, y, 25.0, f_0, omega0, omega1, beta1)\n",
|
|
"f_6_test = f_0_x - kernel_predict_empirical(X, x_vals, y, 500.0, f_0, omega0, omega1, beta1)\n",
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"\n",
|
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"fig, ax = plt.subplots()\n",
|
|
"ax.plot(X[0:1,:],y.T,'ro')\n",
|
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"ax.plot(x_vals[0:1,:].T, f_0_test,'r-',label='t=0')\n",
|
|
"ax.plot(x_vals[0:1,:].T, f_1_test,'b-',label='t=0.1')\n",
|
|
"ax.plot(x_vals[0:1,:].T, f_2_test,'g-',label='t=0.5')\n",
|
|
"ax.plot(x_vals[0:1,:].T, f_3_test,'c-',label='t=1.5')\n",
|
|
"ax.plot(x_vals[0:1,:].T, f_4_test,'y-',label='t=5.0')\n",
|
|
"ax.plot(x_vals[0:1,:].T, f_5_test,'m-',label='t=25.0')\n",
|
|
"ax.plot(x_vals[0:1,:].T, f_6_test,'k-',label='t=500.0')\n",
|
|
"ax.set_xlim([0,1]); ax.set_ylim([-0.5,0.5])\n",
|
|
"ax.set_xlabel('x'); ax.set_ylabel('Predicted output')\n",
|
|
"ax.legend()\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"source": [
|
|
"Now let's do the same thing with the analytical kernel (i.e. with an infinitely wide network)"
|
|
],
|
|
"metadata": {
|
|
"id": "8syQAEh0gnvB"
|
|
}
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 19,
|
|
"metadata": {
|
|
"id": "uW3FL0rP3m9f"
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def kernel_predict_analytical(X,x,y,t, f_0):\n",
|
|
" K = compute_analytical_ntk(X,X)\n",
|
|
" predict = compute_analytical_ntk(x,X) @ np.linalg.inv(K) @ (np.identity(3)-expm(-K * t)) @ (f_0-y)\n",
|
|
" return predict"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 20,
|
|
"metadata": {
|
|
"colab": {
|
|
"base_uri": "https://localhost:8080/",
|
|
"height": 449
|
|
},
|
|
"id": "5aUwSdSn3ivu",
|
|
"outputId": "9e9f1ac2-d37c-4253-d21e-f1fa8d92cc90"
|
|
},
|
|
"outputs": [
|
|
{
|
|
"output_type": "display_data",
|
|
"data": {
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
],
|
|
"image/png": 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\n"
|
|
},
|
|
"metadata": {}
|
|
}
|
|
],
|
|
"source": [
|
|
"# Get predictions at time 0\n",
|
|
"f_0_x = shallow_network_param_vector(x_vals, phi_0).T\n",
|
|
"# Get predictions at six different time points\n",
|
|
"f_0_test = f_0_x - kernel_predict_analytical(X, x_vals, y, 0.0, f_0)\n",
|
|
"f_1_test = f_0_x - kernel_predict_analytical(X, x_vals, y, 0.1, f_0)\n",
|
|
"f_2_test = f_0_x - kernel_predict_analytical(X, x_vals, y, 0.5, f_0)\n",
|
|
"f_3_test = f_0_x - kernel_predict_analytical(X, x_vals, y, 1.5, f_0)\n",
|
|
"f_4_test = f_0_x - kernel_predict_analytical(X, x_vals, y, 5.0, f_0)\n",
|
|
"f_5_test = f_0_x - kernel_predict_analytical(X, x_vals, y, 25.0, f_0)\n",
|
|
"f_6_test = f_0_x - kernel_predict_analytical(X, x_vals, y, 500.0, f_0)\n",
|
|
"\n",
|
|
"fig, ax = plt.subplots()\n",
|
|
"ax.plot(X[0:1,:],y.T,'ro')\n",
|
|
"ax.plot(x_vals[0:1,:].T, f_0_test,'r-',label='t=0')\n",
|
|
"ax.plot(x_vals[0:1,:].T, f_1_test,'b-',label='t=0.1')\n",
|
|
"ax.plot(x_vals[0:1,:].T, f_2_test,'g-',label='t=0.5')\n",
|
|
"ax.plot(x_vals[0:1,:].T, f_3_test,'c-',label='t=1.5')\n",
|
|
"ax.plot(x_vals[0:1,:].T, f_4_test,'y-',label='t=5.0')\n",
|
|
"ax.plot(x_vals[0:1,:].T, f_5_test,'m-',label='t=25.0')\n",
|
|
"ax.plot(x_vals[0:1,:].T, f_6_test,'k-',label='t=500.0')\n",
|
|
"ax.set_xlim([0,1]); ax.set_ylim([-0.5,0.5])\n",
|
|
"ax.set_xlabel('x'); ax.set_ylabel('Predicted output')\n",
|
|
"ax.legend()\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"source": [
|
|
"Compute the mean prediction and uncertainty at a given time"
|
|
],
|
|
"metadata": {
|
|
"id": "r6D-N-7ph6uZ"
|
|
}
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 21,
|
|
"metadata": {
|
|
"id": "R7zkbyAleeiy"
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Compute initial covariance\n",
|
|
"def compute_cov_init(X1, X2, sigma_sq_p=2.0):\n",
|
|
" I1 = X1.shape[1]\n",
|
|
" I2 = X2.shape[1]\n",
|
|
" K = np.zeros((I1,I2))\n",
|
|
"\n",
|
|
" for i in range(I1):\n",
|
|
" for j in range(I2):\n",
|
|
" x1 = X1[:,i]\n",
|
|
" x2 = X2[:,j]\n",
|
|
" norm1 = np.sqrt(x1.T@x1)\n",
|
|
" norm2 = np.sqrt(x2.T@x2)\n",
|
|
" if norm1 < 1e-10 or norm2 < 1e-10:\n",
|
|
" theta = 0\n",
|
|
" else:\n",
|
|
" if np.array_equal(x1,x2):\n",
|
|
" theta = 0\n",
|
|
" else:\n",
|
|
" theta = np.arccos(x1.T@x2/(norm1*norm2))\n",
|
|
" K[i,j] = sigma_sq_p * norm1 * norm2 * ((np.pi-theta)*np.cos(theta)+np.sin(theta))/(2*np.pi) + 1\n",
|
|
" return K\n",
|
|
"\n",
|
|
"# Equations 14 and 15 from Lee et al. (2019)\n",
|
|
"def kernel_predict_uncertainty(X,x,y,t, sigma_sq_n=0.001):\n",
|
|
" NTKXX = compute_analytical_ntk(X, X)\n",
|
|
" NTKxX = compute_analytical_ntk(x, X)\n",
|
|
"\n",
|
|
" f_0_xx_cov = compute_cov_init(x,x)\n",
|
|
" f_0_XX_cov = compute_cov_init(X,X)\n",
|
|
" f_0_Xx_cov = compute_cov_init(X,x)\n",
|
|
" Z = NTKxX @ np.linalg.inv(NTKXX) @ (np.identity(3)-expm(-K * t))\n",
|
|
"\n",
|
|
" mean =Z @ y\n",
|
|
" cov = f_0_xx_cov + Z @ f_0_XX_cov @ Z.T -2 * Z @ f_0_Xx_cov\n",
|
|
" return mean, np.sqrt(np.diag(cov+np.identity(cov.shape[0])*sigma_sq_n))[:,None]"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"source": [
|
|
"Draw function with uncertainty at a number of different time points"
|
|
],
|
|
"metadata": {
|
|
"id": "zz9AtywWid-4"
|
|
}
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 22,
|
|
"metadata": {
|
|
"id": "BMHCOgNScoI1",
|
|
"colab": {
|
|
"base_uri": "https://localhost:8080/",
|
|
"height": 1000
|
|
},
|
|
"outputId": "7e951f0d-9c3f-4c31-9445-24922c64e83f"
|
|
},
|
|
"outputs": [
|
|
{
|
|
"output_type": "stream",
|
|
"name": "stdout",
|
|
"text": [
|
|
"Time, t=0.000\n"
|
|
]
|
|
},
|
|
{
|
|
"output_type": "display_data",
|
|
"data": {
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
],
|
|
"image/png": "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\n"
|
|
},
|
|
"metadata": {}
|
|
},
|
|
{
|
|
"output_type": "stream",
|
|
"name": "stdout",
|
|
"text": [
|
|
"Time, t=0.100\n"
|
|
]
|
|
},
|
|
{
|
|
"output_type": "display_data",
|
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"data": {
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"text/plain": [
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"<Figure size 640x480 with 1 Axes>"
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],
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"image/png": 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\n"
|
|
},
|
|
"metadata": {}
|
|
},
|
|
{
|
|
"output_type": "stream",
|
|
"name": "stdout",
|
|
"text": [
|
|
"Time, t=0.500\n"
|
|
]
|
|
},
|
|
{
|
|
"output_type": "display_data",
|
|
"data": {
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
],
|
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"image/png": 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\n"
|
|
},
|
|
"metadata": {}
|
|
},
|
|
{
|
|
"output_type": "stream",
|
|
"name": "stdout",
|
|
"text": [
|
|
"Time, t=1.500\n"
|
|
]
|
|
},
|
|
{
|
|
"output_type": "display_data",
|
|
"data": {
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
],
|
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"image/png": 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\n"
|
|
},
|
|
"metadata": {}
|
|
},
|
|
{
|
|
"output_type": "stream",
|
|
"name": "stdout",
|
|
"text": [
|
|
"Time, t=5.000\n"
|
|
]
|
|
},
|
|
{
|
|
"output_type": "display_data",
|
|
"data": {
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
],
|
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"image/png": 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\n"
|
|
},
|
|
"metadata": {}
|
|
},
|
|
{
|
|
"output_type": "stream",
|
|
"name": "stdout",
|
|
"text": [
|
|
"Time, t=25.000\n"
|
|
]
|
|
},
|
|
{
|
|
"output_type": "display_data",
|
|
"data": {
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
],
|
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"image/png": 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\n"
|
|
},
|
|
"metadata": {}
|
|
},
|
|
{
|
|
"output_type": "stream",
|
|
"name": "stdout",
|
|
"text": [
|
|
"Time, t=500.000\n"
|
|
]
|
|
},
|
|
{
|
|
"output_type": "display_data",
|
|
"data": {
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
],
|
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"image/png": 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\n"
|
|
},
|
|
"metadata": {}
|
|
}
|
|
],
|
|
"source": [
|
|
"def draw_func_uncertain(X, y, x ,predict_mean, predict_std, t):\n",
|
|
" fig, ax = plt.subplots()\n",
|
|
" ax.plot(X[0:1,:],y.T,'ro')\n",
|
|
" ax.plot(x[0:1,:].T, predict_mean,'r-')\n",
|
|
" lower = predict_mean-predict_std\n",
|
|
" upper = predict_mean+predict_std\n",
|
|
" ax.fill_between(np.squeeze(x[0:1,:].T), np.squeeze(lower), np.squeeze(upper), color='lightgray')\n",
|
|
" ax.set_xlim([0,1]); ax.set_ylim([-0.5,0.5])\n",
|
|
" ax.set_xlabel('x'); ax.set_ylabel('y')\n",
|
|
" plt.show()\n",
|
|
"\n",
|
|
"for t in (0.0, 0.1, 0.5,1.5,5.0,25.0,500.0):\n",
|
|
" print('Time, t=%3.3f'%(t))\n",
|
|
" f_mean, f_std = kernel_predict_uncertainty(X, x_vals, y, t)\n",
|
|
" draw_func_uncertain(X, y, x_vals, f_mean, f_std, t)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"source": [
|
|
"Draw the kernel"
|
|
],
|
|
"metadata": {
|
|
"id": "P6eg1Co5lIcZ"
|
|
}
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"source": [
|
|
"def draw_kernel(X1):\n",
|
|
" # Define pretty colormap\n",
|
|
" my_colormap_vals_hex =('2a0902', '2b0a03', '2c0b04', '2d0c05', '2e0c06', '2f0d07', '300d08', '310e09', '320f0a', '330f0b', '34100b', '35110c', '36110d', '37120e', '38120f', '39130f', '3a1410', '3b1411', '3c1511', '3d1612', '3e1613', '3f1713', '401714', '411814', '421915', '431915', '451a16', '461b16', '471b17', '481c17', '491d18', '4a1d18', '4b1e19', '4c1f19', '4d1f1a', '4e201b', '50211b', '51211c', '52221c', '53231d', '54231d', '55241e', '56251e', '57261f', '58261f', '592720', '5b2821', '5c2821', '5d2922', '5e2a22', '5f2b23', '602b23', '612c24', '622d25', '632e25', '652e26', '662f26', '673027', '683027', '693128', '6a3229', '6b3329', '6c342a', '6d342a', '6f352b', '70362c', '71372c', '72372d', '73382e', '74392e', '753a2f', '763a2f', '773b30', '783c31', '7a3d31', '7b3e32', '7c3e33', '7d3f33', '7e4034', '7f4134', '804235', '814236', '824336', '834437', '854538', '864638', '874739', '88473a', '89483a', '8a493b', '8b4a3c', '8c4b3c', '8d4c3d', '8e4c3e', '8f4d3f', '904e3f', '924f40', '935041', '945141', '955242', '965343', '975343', '985444', '995545', '9a5646', '9b5746', '9c5847', '9d5948', '9e5a49', '9f5a49', 'a05b4a', 'a15c4b', 'a35d4b', 'a45e4c', 'a55f4d', 'a6604e', 'a7614e', 'a8624f', 'a96350', 'aa6451', 'ab6552', 'ac6552', 'ad6653', 'ae6754', 'af6855', 'b06955', 'b16a56', 'b26b57', 'b36c58', 'b46d59', 'b56e59', 'b66f5a', 'b7705b', 'b8715c', 'b9725d', 'ba735d', 'bb745e', 'bc755f', 'bd7660', 'be7761', 'bf7862', 'c07962', 'c17a63', 'c27b64', 'c27c65', 'c37d66', 'c47e67', 'c57f68', 'c68068', 'c78169', 'c8826a', 'c9836b', 'ca846c', 'cb856d', 'cc866e', 'cd876f', 'ce886f', 'ce8970', 'cf8a71', 'd08b72', 'd18c73', 'd28d74', 'd38e75', 'd48f76', 'd59077', 'd59178', 'd69279', 'd7937a', 'd8957b', 'd9967b', 'da977c', 'da987d', 'db997e', 'dc9a7f', 'dd9b80', 'de9c81', 'de9d82', 'df9e83', 'e09f84', 'e1a185', 'e2a286', 'e2a387', 'e3a488', 'e4a589', 'e5a68a', 'e5a78b', 'e6a88c', 'e7aa8d', 'e7ab8e', 'e8ac8f', 'e9ad90', 'eaae91', 'eaaf92', 'ebb093', 'ecb295', 'ecb396', 'edb497', 'eeb598', 'eeb699', 'efb79a', 'efb99b', 'f0ba9c', 'f1bb9d', 'f1bc9e', 'f2bd9f', 'f2bfa1', 'f3c0a2', 'f3c1a3', 'f4c2a4', 'f5c3a5', 'f5c5a6', 'f6c6a7', 'f6c7a8', 'f7c8aa', 'f7c9ab', 'f8cbac', 'f8ccad', 'f8cdae', 'f9ceb0', 'f9d0b1', 'fad1b2', 'fad2b3', 'fbd3b4', 'fbd5b6', 'fbd6b7', 'fcd7b8', 'fcd8b9', 'fcdaba', 'fddbbc', 'fddcbd', 'fddebe', 'fddfbf', 'fee0c1', 'fee1c2', 'fee3c3', 'fee4c5', 'ffe5c6', 'ffe7c7', 'ffe8c9', 'ffe9ca', 'ffebcb', 'ffeccd', 'ffedce', 'ffefcf', 'fff0d1', 'fff2d2', 'fff3d3', 'fff4d5', 'fff6d6', 'fff7d8', 'fff8d9', 'fffada', 'fffbdc', 'fffcdd', 'fffedf', 'ffffe0')\n",
|
|
" my_colormap_vals_dec = np.array([int(element,base=16) for element in my_colormap_vals_hex])\n",
|
|
" r = np.floor(my_colormap_vals_dec/(256*256))\n",
|
|
" g = np.floor((my_colormap_vals_dec - r *256 *256)/256)\n",
|
|
" b = np.floor(my_colormap_vals_dec - r * 256 *256 - g * 256)\n",
|
|
" my_colormap = ListedColormap(np.vstack((r,g,b)).transpose()/255.0)\n",
|
|
"\n",
|
|
" # Make grid of intercept/slope values to plot\n",
|
|
" x_mesh, y_mesh = np.meshgrid(np.arange(-4,4,0.05), np.arange(-4,4,0.05))\n",
|
|
" kernel_mesh = np.zeros_like(x_mesh)\n",
|
|
"\n",
|
|
" for idx, x in np.ndenumerate(x_mesh):\n",
|
|
" X2 = np.ones((2,1))\n",
|
|
" X2[0,0] = x+0.0001\n",
|
|
" X2[1,0] = y_mesh[idx]+0.0001\n",
|
|
" kernel_mesh[idx] = compute_analytical_ntk(X1, X2)[0,0]\n",
|
|
"\n",
|
|
" fig,ax = plt.subplots()\n",
|
|
" fig.set_size_inches(8,8)\n",
|
|
" ax.contour(x_mesh,y_mesh,kernel_mesh,20,colors=['#80808080'])\n",
|
|
" ax.contourf(x_mesh,y_mesh,kernel_mesh,256,cmap=my_colormap)\n",
|
|
" ax.set_ylim([-4,4])\n",
|
|
" ax.set_xlabel('$x^*[0]$')\n",
|
|
" ax.set_ylabel('$x^*[1]$')\n",
|
|
"\n",
|
|
" plt.show()\n",
|
|
"\n",
|
|
"# Draw kernel for X1 = 1.0\n",
|
|
"X1 = np.ones((2,1))\n",
|
|
"X1[0,0] = 1.000000\n",
|
|
"draw_kernel(X1)"
|
|
],
|
|
"metadata": {
|
|
"id": "FcJHyAsl9t47",
|
|
"colab": {
|
|
"base_uri": "https://localhost:8080/",
|
|
"height": 707
|
|
},
|
|
"outputId": "9857d813-9a12-456e-fba1-1e56a33485a5"
|
|
},
|
|
"execution_count": 27,
|
|
"outputs": [
|
|
{
|
|
"output_type": "display_data",
|
|
"data": {
|
|
"text/plain": [
|
|
"<Figure size 800x800 with 1 Axes>"
|
|
],
|
|
"image/png": 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\n"
|
|
},
|
|
"metadata": {}
|
|
}
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"source": [],
|
|
"metadata": {
|
|
"id": "IbsfhoWQmSlr"
|
|
},
|
|
"execution_count": null,
|
|
"outputs": []
|
|
}
|
|
],
|
|
"metadata": {
|
|
"colab": {
|
|
"provenance": [],
|
|
"authorship_tag": "ABX9TyMCXVjR6HT+aA9YlWJYI8AH",
|
|
"include_colab_link": true
|
|
},
|
|
"kernelspec": {
|
|
"display_name": "Python 3",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"name": "python"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 0
|
|
}
|