597 lines
17 KiB
Plaintext
597 lines
17 KiB
Plaintext
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{
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"nbformat": 4,
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"nbformat_minor": 0,
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"metadata": {
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"colab": {
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"name": "Chain_rule.ipynb",
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"provenance": [],
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"collapsed_sections": [],
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"include_colab_link": true
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},
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.7.6"
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}
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},
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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/PacktPublishing/Hands-On-Computer-Vision-with-PyTorch/blob/master/Chapter01/Chain_rule.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": "code",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2020-09-24T13:23:27.984719Z",
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"start_time": "2020-09-24T13:23:27.929962Z"
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},
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"colab_type": "code",
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"id": "i5WpgCBbm_Jc",
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"colab": {}
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},
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"source": [
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"from copy import deepcopy\n",
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"import numpy as np\n",
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"def line():\n",
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" print('='*80)\n",
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"def feed_forward(inputs, outputs, weights): \n",
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" pre_hidden = np.dot(inputs,weights[0])+ weights[1]\n",
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" hidden = 1/(1+np.exp(-pre_hidden))\n",
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" out = np.dot(hidden, weights[2]) + weights[3]\n",
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" mean_squared_error = np.mean(np.square(out - outputs))\n",
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" return mean_squared_error"
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],
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "code",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2020-09-24T13:23:27.989715Z",
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"start_time": "2020-09-24T13:23:27.985804Z"
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},
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"colab_type": "code",
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"id": "YKQpTWlSnCwc",
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"colab": {}
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},
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"source": [
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"def update_weights(inputs, outputs, weights, lr):\n",
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" original_weights = deepcopy(weights)\n",
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" temp_weights = deepcopy(weights)\n",
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" updated_weights = deepcopy(weights)\n",
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" original_loss = feed_forward(inputs, outputs, original_weights)\n",
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" for i, layer in enumerate(original_weights):\n",
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" for index, weight in np.ndenumerate(layer):\n",
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" temp_weights = deepcopy(weights)\n",
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" temp_weights[i][index] += 0.0001\n",
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" _loss_plus = feed_forward(inputs, outputs, temp_weights)\n",
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" grad = (_loss_plus - original_loss)/(0.0001)\n",
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" updated_weights[i][index] -= grad*lr\n",
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" return updated_weights"
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],
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "code",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2020-09-24T13:23:28.000882Z",
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"start_time": "2020-09-24T13:23:27.991191Z"
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},
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"colab_type": "code",
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"id": "Vp9I03hRnh2G",
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"colab": {
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"base_uri": "https://localhost:8080/",
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"height": 170
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},
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"outputId": "6b284e11-c5a8-411e-ba4b-4fd81e466235"
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},
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"source": [
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"x = np.array([[1,1]]); y = np.array([[0]]) \n",
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"W = [\n",
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" np.array([[-0.0053, 0.3793],\n",
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" [-0.5820, -0.5204],\n",
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" [-0.2723, 0.1896]], dtype=np.float32).T, \n",
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" np.array([-0.0140, 0.5607, -0.0628], dtype=np.float32), \n",
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" np.array([[ 0.1528, -0.1745, -0.1135]], dtype=np.float32).T, \n",
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" np.array([-0.5516], dtype=np.float32)\n",
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"]\n",
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"line()\n",
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"print('Loss:'.upper())\n",
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"print(feed_forward(x,y,W))\n",
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"line()\n",
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"print('Weights:'.upper())\n",
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"[print(w) for w in W]\n",
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"line()\n",
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"print('Updated Weights:'.upper())\n",
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"for epx in range(1):\n",
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" updated_weights = update_weights(x,y,W,1)\n",
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"[print(w) for w in updated_weights];"
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],
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"execution_count": null,
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"outputs": [
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{
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"output_type": "stream",
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"text": [
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"================================================================================\n",
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"LOSS:\n",
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"0.33455008989960927\n",
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"================================================================================\n",
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"WEIGHTS:\n",
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"[[-0.0053 -0.582 -0.2723]\n",
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" [ 0.3793 -0.5204 0.1896]]\n",
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"[-0.014 0.5607 -0.0628]\n",
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"[[ 0.1528]\n",
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" [-0.1745]\n",
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" [-0.1135]]\n",
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"[-0.5516]\n",
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"================================================================================\n",
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"UPDATED WEIGHTS:\n",
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"[[ 0.03748801 -0.62894595 -0.30494714]\n",
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" [ 0.42208242 -0.5673459 0.156948 ]]\n",
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"[ 0.02878801 0.51375407 -0.09545201]\n",
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"[[0.8341824 ]\n",
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" [0.25095794]\n",
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" [0.4228859 ]]\n",
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"[0.60529804]\n"
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],
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"name": "stdout"
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}
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"colab_type": "text",
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"id": "3llIoQD7xMJf"
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},
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"source": [
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"### Chain Rule\n",
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"Calculate the updated weight value using Chain rule"
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2020-09-24T13:23:28.004119Z",
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"start_time": "2020-09-24T13:23:28.001851Z"
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},
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"colab_type": "code",
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"id": "fSSV-hAcufCd",
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"colab": {}
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},
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"source": [
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"pre_hidden = np.dot(x,W[0])+ W[1]\n",
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"hidden = 1/(1+np.exp(-pre_hidden))\n",
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"predicted_value = np.dot(hidden, W[2]) + W[3]"
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],
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "code",
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"metadata": {
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||
|
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"ExecuteTime": {
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||
|
|
"end_time": "2020-09-24T13:23:28.008250Z",
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||
|
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"start_time": "2020-09-24T13:23:28.004921Z"
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},
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"colab_type": "code",
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"id": "juDL0c_fwp0c",
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"colab": {
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||
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"base_uri": "https://localhost:8080/",
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||
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"height": 34
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||
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},
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||
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"outputId": "2cbf40fa-41ad-4b42-bc94-56b2496f2dfe"
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||
|
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},
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||
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"source": [
|
||
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"tmp = W[0][0][0] - (-2*(0-(predicted_value[0][0]))*(W[2][0][0])*hidden[0,0]*(1-hidden[0,0])*x[0][0])\n",
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"print(tmp, updated_weights[0][0][0])"
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],
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"execution_count": null,
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||
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"outputs": [
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||
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{
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||
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"output_type": "stream",
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||
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"text": [
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||
|
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"0.03748860333147175 0.037488014\n"
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],
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||
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"name": "stdout"
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||
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}
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]
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},
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{
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"cell_type": "code",
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|
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"metadata": {
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||
|
|
"ExecuteTime": {
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||
|
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"end_time": "2020-09-24T13:23:28.012629Z",
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||
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"start_time": "2020-09-24T13:23:28.009257Z"
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},
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"colab_type": "code",
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"id": "bIzE0_CD4ePv",
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"colab": {
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||
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"base_uri": "https://localhost:8080/",
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||
|
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"height": 34
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|
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},
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||
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"outputId": "8f64a525-9fc3-4e69-efa6-29538785a885"
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},
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"source": [
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"tmp = W[0][0][1] - (-2*(0-(predicted_value[0][0]))*(W[2][1][0])*hidden[0,1]*(1-hidden[0,1])*x[0][0])\n",
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"print(tmp, updated_weights[0][0][1])"
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],
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"execution_count": null,
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"outputs": [
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||
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{
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||
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"output_type": "stream",
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||
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"text": [
|
||
|
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"-0.6289373468565382 -0.62894595\n"
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||
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|
],
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||
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"name": "stdout"
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||
|
|
}
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||
|
|
]
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||
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},
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||
|
|
{
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||
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|
"cell_type": "code",
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||
|
|
"metadata": {
|
||
|
|
"ExecuteTime": {
|
||
|
|
"end_time": "2020-09-24T13:23:28.016777Z",
|
||
|
|
"start_time": "2020-09-24T13:23:28.013578Z"
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||
|
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},
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||
|
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"colab_type": "code",
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||
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|
"id": "eBYFpMD58Zg4",
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||
|
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"colab": {
|
||
|
|
"base_uri": "https://localhost:8080/",
|
||
|
|
"height": 34
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||
|
|
},
|
||
|
|
"outputId": "8182e49a-3300-49f1-edf2-5e29d69946e9"
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||
|
|
},
|
||
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"source": [
|
||
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"tmp = W[0][0][2] - (-2*(0-(predicted_value[0][0]))*(W[2][2][0])*hidden[0,2]*(1-hidden[0,2])*x[0][0])\n",
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"print(tmp, updated_weights[0][0][0])"
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],
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"execution_count": null,
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||
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"outputs": [
|
||
|
|
{
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"-0.304951263947996 0.037488014\n"
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||
|
|
],
|
||
|
|
"name": "stdout"
|
||
|
|
}
|
||
|
|
]
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||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"metadata": {
|
||
|
|
"ExecuteTime": {
|
||
|
|
"end_time": "2020-09-24T13:23:28.021124Z",
|
||
|
|
"start_time": "2020-09-24T13:23:28.018197Z"
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||
|
|
},
|
||
|
|
"colab_type": "code",
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||
|
|
"id": "e5bsJzF88ZrM",
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||
|
|
"colab": {
|
||
|
|
"base_uri": "https://localhost:8080/",
|
||
|
|
"height": 34
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||
|
|
},
|
||
|
|
"outputId": "021e7318-fc42-49f9-89d2-5565d362498f"
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||
|
|
},
|
||
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"source": [
|
||
|
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"tmp = W[0][1][0] - (-2*(0-(predicted_value[0][0]))*(W[2][0][0])*hidden[0,0]*(1-hidden[0,0])*x[0][1])\n",
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||
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"print(tmp, updated_weights[0][1][0])"
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],
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"execution_count": null,
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||
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"outputs": [
|
||
|
|
{
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"0.42208860145914084 0.42208242\n"
|
||
|
|
],
|
||
|
|
"name": "stdout"
|
||
|
|
}
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"metadata": {
|
||
|
|
"ExecuteTime": {
|
||
|
|
"end_time": "2020-09-24T13:23:28.025464Z",
|
||
|
|
"start_time": "2020-09-24T13:23:28.022264Z"
|
||
|
|
},
|
||
|
|
"colab_type": "code",
|
||
|
|
"id": "coHgQaMI9R3N",
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||
|
|
"colab": {
|
||
|
|
"base_uri": "https://localhost:8080/",
|
||
|
|
"height": 34
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||
|
|
},
|
||
|
|
"outputId": "021e7318-fc42-49f9-89d2-5565d362498f"
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"tmp = W[0][1][1] - (-2*(0-(predicted_value[0][0]))*(W[2][1][0])*hidden[0,1]*(1-hidden[0,1])*x[0][1])\n",
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||
|
|
"print(tmp, updated_weights[0][1][1])"
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|
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],
|
||
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|
"execution_count": null,
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||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"-0.5673373173880019 -0.5673459\n"
|
||
|
|
],
|
||
|
|
"name": "stdout"
|
||
|
|
}
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"metadata": {
|
||
|
|
"ExecuteTime": {
|
||
|
|
"end_time": "2020-09-24T13:23:28.030294Z",
|
||
|
|
"start_time": "2020-09-24T13:23:28.026871Z"
|
||
|
|
},
|
||
|
|
"colab_type": "code",
|
||
|
|
"id": "XEbiE6xc9R3P",
|
||
|
|
"colab": {
|
||
|
|
"base_uri": "https://localhost:8080/",
|
||
|
|
"height": 34
|
||
|
|
},
|
||
|
|
"outputId": "021e7318-fc42-49f9-89d2-5565d362498f"
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"tmp = W[0][1][2] - (-2*(0-(predicted_value[0][0]))*(W[2][2][0])*hidden[0,2]*(1-hidden[0,2])*x[0][1])\n",
|
||
|
|
"print(tmp, updated_weights[0][1][2])"
|
||
|
|
],
|
||
|
|
"execution_count": null,
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"0.15694874675699821 0.156948\n"
|
||
|
|
],
|
||
|
|
"name": "stdout"
|
||
|
|
}
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"metadata": {
|
||
|
|
"ExecuteTime": {
|
||
|
|
"end_time": "2020-09-24T13:23:28.035074Z",
|
||
|
|
"start_time": "2020-09-24T13:23:28.031407Z"
|
||
|
|
},
|
||
|
|
"colab_type": "code",
|
||
|
|
"id": "sD1NsccW9R3R",
|
||
|
|
"colab": {
|
||
|
|
"base_uri": "https://localhost:8080/",
|
||
|
|
"height": 34
|
||
|
|
},
|
||
|
|
"outputId": "021e7318-fc42-49f9-89d2-5565d362498f"
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"tmp = W[1][0] - (-2*(0-(predicted_value[0][0]))*hidden[0,0]*(1-hidden[0,0])*W[2][0][0])\n",
|
||
|
|
"print(tmp, updated_weights[1][0])"
|
||
|
|
],
|
||
|
|
"execution_count": null,
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"0.028788602743620932 0.028788012\n"
|
||
|
|
],
|
||
|
|
"name": "stdout"
|
||
|
|
}
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"metadata": {
|
||
|
|
"ExecuteTime": {
|
||
|
|
"end_time": "2020-09-24T13:23:28.038822Z",
|
||
|
|
"start_time": "2020-09-24T13:23:28.036075Z"
|
||
|
|
},
|
||
|
|
"colab_type": "code",
|
||
|
|
"id": "90aX0GVu9R3U",
|
||
|
|
"colab": {
|
||
|
|
"base_uri": "https://localhost:8080/",
|
||
|
|
"height": 34
|
||
|
|
},
|
||
|
|
"outputId": "021e7318-fc42-49f9-89d2-5565d362498f"
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"tmp = W[1][1] - (-2*(0-(predicted_value[0][0]))*hidden[0,1]*(1-hidden[0,1])*W[2][1][0])\n",
|
||
|
|
"print(tmp, updated_weights[1][1])"
|
||
|
|
],
|
||
|
|
"execution_count": null,
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"0.5137626696420274 0.51375407\n"
|
||
|
|
],
|
||
|
|
"name": "stdout"
|
||
|
|
}
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"metadata": {
|
||
|
|
"ExecuteTime": {
|
||
|
|
"end_time": "2020-09-24T13:23:28.042770Z",
|
||
|
|
"start_time": "2020-09-24T13:23:28.039723Z"
|
||
|
|
},
|
||
|
|
"colab_type": "code",
|
||
|
|
"id": "vP3P_DvO9R3W",
|
||
|
|
"colab": {
|
||
|
|
"base_uri": "https://localhost:8080/",
|
||
|
|
"height": 34
|
||
|
|
},
|
||
|
|
"outputId": "021e7318-fc42-49f9-89d2-5565d362498f"
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"tmp = W[1][2] - (-2*(0-(predicted_value[0][0]))*hidden[0,2]*(1-hidden[0,2])*W[2][2][0])\n",
|
||
|
|
"print(tmp, updated_weights[1][2])"
|
||
|
|
],
|
||
|
|
"execution_count": null,
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"-0.0954512566166247 -0.09545201\n"
|
||
|
|
],
|
||
|
|
"name": "stdout"
|
||
|
|
}
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"metadata": {
|
||
|
|
"ExecuteTime": {
|
||
|
|
"end_time": "2020-09-24T13:23:28.046332Z",
|
||
|
|
"start_time": "2020-09-24T13:23:28.043797Z"
|
||
|
|
},
|
||
|
|
"colab_type": "code",
|
||
|
|
"id": "D0tTvkLV9R3Z",
|
||
|
|
"colab": {
|
||
|
|
"base_uri": "https://localhost:8080/",
|
||
|
|
"height": 34
|
||
|
|
},
|
||
|
|
"outputId": "021e7318-fc42-49f9-89d2-5565d362498f"
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"tmp = W[2][0][0]-(-2*(0-(predicted_value[0][0]))*hidden[0][0])\n",
|
||
|
|
"print(tmp, updated_weights[2][0][0])"
|
||
|
|
],
|
||
|
|
"execution_count": null,
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"0.8342055621416937 0.8341824\n"
|
||
|
|
],
|
||
|
|
"name": "stdout"
|
||
|
|
}
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"metadata": {
|
||
|
|
"ExecuteTime": {
|
||
|
|
"end_time": "2020-09-24T13:23:28.050423Z",
|
||
|
|
"start_time": "2020-09-24T13:23:28.047373Z"
|
||
|
|
},
|
||
|
|
"colab_type": "code",
|
||
|
|
"id": "eJkFiIgG9R3b",
|
||
|
|
"colab": {
|
||
|
|
"base_uri": "https://localhost:8080/",
|
||
|
|
"height": 34
|
||
|
|
},
|
||
|
|
"outputId": "021e7318-fc42-49f9-89d2-5565d362498f"
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"tmp = W[2][1][0]-(-2*(0-(predicted_value[0][0]))*hidden[0][1])\n",
|
||
|
|
"print(tmp, updated_weights[2][1][0])"
|
||
|
|
],
|
||
|
|
"execution_count": null,
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"0.2509642654210383 0.25095794\n"
|
||
|
|
],
|
||
|
|
"name": "stdout"
|
||
|
|
}
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"metadata": {
|
||
|
|
"ExecuteTime": {
|
||
|
|
"end_time": "2020-09-24T13:23:28.053986Z",
|
||
|
|
"start_time": "2020-09-24T13:23:28.051400Z"
|
||
|
|
},
|
||
|
|
"colab_type": "code",
|
||
|
|
"id": "YQ6B8fA-9R3d",
|
||
|
|
"colab": {
|
||
|
|
"base_uri": "https://localhost:8080/",
|
||
|
|
"height": 34
|
||
|
|
},
|
||
|
|
"outputId": "021e7318-fc42-49f9-89d2-5565d362498f"
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"tmp = W[2][2][0]-(-2*(0-(predicted_value[0][0]))*hidden[0][2])\n",
|
||
|
|
"print(tmp, updated_weights[2][2][0])"
|
||
|
|
],
|
||
|
|
"execution_count": null,
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"0.422898309408289 0.4228859\n"
|
||
|
|
],
|
||
|
|
"name": "stdout"
|
||
|
|
}
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"metadata": {
|
||
|
|
"ExecuteTime": {
|
||
|
|
"end_time": "2020-09-24T13:23:28.057470Z",
|
||
|
|
"start_time": "2020-09-24T13:23:28.054896Z"
|
||
|
|
},
|
||
|
|
"colab_type": "code",
|
||
|
|
"id": "DYInbxAt9R3g",
|
||
|
|
"colab": {
|
||
|
|
"base_uri": "https://localhost:8080/",
|
||
|
|
"height": 34
|
||
|
|
},
|
||
|
|
"outputId": "021e7318-fc42-49f9-89d2-5565d362498f"
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"tmp = W[3][0]-(-2*(0-(predicted_value[0][0])))\n",
|
||
|
|
"print(tmp, updated_weights[3][0])"
|
||
|
|
],
|
||
|
|
"execution_count": null,
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"0.6052061234525776 0.60529804\n"
|
||
|
|
],
|
||
|
|
"name": "stdout"
|
||
|
|
}
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"metadata": {
|
||
|
|
"colab_type": "code",
|
||
|
|
"id": "7LtMWS6c3nBP",
|
||
|
|
"colab": {}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
""
|
||
|
|
],
|
||
|
|
"execution_count": null,
|
||
|
|
"outputs": []
|
||
|
|
}
|
||
|
|
]
|
||
|
|
}
|