{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import os\n", "import sys\n", "sys.path.append(os.path.abspath(os.path.join('..')))\n", "from ch07_autograd.utils import Scalar, draw_graph" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# 定义计算图\n", "w = Scalar(0.3, label='w')\n", "wh = Scalar(0.5, label='wh')\n", "x1 = Scalar(1., label='x1', requires_grad=False)\n", "x2 = Scalar(1., label='x2', requires_grad=False)\n", "x3 = Scalar(1., label='x3', requires_grad=False)\n", "# 可以将h1,h2,h3理解为隐藏状态\n", "# 它们分别表示第一步、第二步、第三步的隐藏状态\n", "h1 = w * x1\n", "h2 = w * x2 + wh * h1\n", "h3 = w * x3 + wh * h2" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "%3\n", "\n", "\n", "140454734443904backward\n", "\n", "grad= 1.00\n", "\n", "value= 0.30\n", "\n", "*\n", "\n", "\n", "140454734443808backward\n", "\n", "x1= 1.00\n", "\n", "\n", "140454734443904backward->140454734443808backward\n", "\n", "\n", "\n", "140454734443760backward\n", "\n", "grad= 1.00\n", "\n", "value= 0.30\n", "\n", "w\n", "\n", "\n", "140454734443904backward->140454734443760backward\n", "\n", "\n", " 1.00\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 对第一步的隐藏状态进行反向传播\n", "h1.backward()\n", "draw_graph(h1, 'backward')" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "%3\n", "\n", "\n", "140454734444048backward\n", "\n", "grad= 1.00\n", "\n", "value= 0.45\n", "\n", "+\n", "\n", "\n", "140454734444192backward\n", "\n", "grad= 1.00\n", "\n", "value= 0.15\n", "\n", "*\n", "\n", "\n", "140454734444048backward->140454734444192backward\n", "\n", "\n", " 1.00\n", "\n", "\n", "140454734443952backward\n", "\n", "grad= 1.00\n", "\n", "value= 0.30\n", "\n", "*\n", "\n", "\n", "140454734444048backward->140454734443952backward\n", "\n", "\n", " 1.00\n", "\n", "\n", "140454734443664backward\n", "\n", "grad= 0.30\n", "\n", "value= 0.50\n", "\n", "wh\n", "\n", "\n", "140454734444192backward->140454734443664backward\n", "\n", "\n", " 0.30\n", "\n", "\n", "140454734443904backward\n", "\n", "grad= 1.50\n", "\n", "value= 0.30\n", "\n", "*\n", "\n", "\n", "140454734444192backward->140454734443904backward\n", "\n", "\n", " 0.50\n", "\n", "\n", "140454734443712backward\n", "\n", "x2= 1.00\n", "\n", "\n", "140454734443760backward\n", "\n", "grad= 2.50\n", "\n", "value= 0.30\n", "\n", "w\n", "\n", "\n", "140454734443808backward\n", "\n", "x1= 1.00\n", "\n", "\n", "140454734443904backward->140454734443760backward\n", "\n", "\n", " 0.50\n", "\n", "\n", "140454734443904backward->140454734443808backward\n", "\n", "\n", "\n", "140454734443952backward->140454734443712backward\n", "\n", "\n", "\n", "140454734443952backward->140454734443760backward\n", "\n", "\n", " 1.00\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 对第二步的隐藏状态进行反向传播\n", "h2.backward()\n", "draw_graph(h2, 'backward')" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "%3\n", "\n", "\n", "140454734444048backward\n", "\n", "grad= 1.50\n", "\n", "value= 0.45\n", "\n", "+\n", "\n", "\n", "140454734444192backward\n", "\n", "grad= 1.50\n", "\n", "value= 0.15\n", "\n", "*\n", "\n", "\n", "140454734444048backward->140454734444192backward\n", "\n", "\n", " 0.50\n", "\n", "\n", "140454734443952backward\n", "\n", "grad= 1.50\n", "\n", "value= 0.30\n", "\n", "*\n", "\n", "\n", "140454734444048backward->140454734443952backward\n", "\n", "\n", " 0.50\n", "\n", "\n", "140454734444096backward\n", "\n", "grad= 1.00\n", "\n", "value= 0.22\n", "\n", "*\n", "\n", "\n", "140454734444096backward->140454734444048backward\n", "\n", "\n", " 0.50\n", "\n", "\n", "140454734443664backward\n", "\n", "grad= 0.90\n", "\n", "value= 0.50\n", "\n", "wh\n", "\n", "\n", "140454734444096backward->140454734443664backward\n", "\n", "\n", " 0.45\n", "\n", "\n", "140454734444192backward->140454734443664backward\n", "\n", "\n", " 0.15\n", "\n", "\n", "140454734443904backward\n", "\n", "grad= 1.75\n", "\n", "value= 0.30\n", "\n", "*\n", "\n", "\n", "140454734444192backward->140454734443904backward\n", "\n", "\n", " 0.25\n", "\n", "\n", "140454734443712backward\n", "\n", "x2= 1.00\n", "\n", "\n", "140454734443760backward\n", "\n", "grad= 4.25\n", "\n", "value= 0.30\n", "\n", "w\n", "\n", "\n", "140454734444288backward\n", "\n", "grad= 1.00\n", "\n", "value= 0.52\n", "\n", "+\n", "\n", "\n", "140454734444288backward->140454734444096backward\n", "\n", "\n", " 1.00\n", "\n", "\n", "140454734444000backward\n", "\n", "grad= 1.00\n", "\n", "value= 0.30\n", "\n", "*\n", "\n", "\n", "140454734444288backward->140454734444000backward\n", "\n", "\n", " 1.00\n", "\n", "\n", "140454734443808backward\n", "\n", "x1= 1.00\n", "\n", "\n", "140454734443856backward\n", "\n", "x3= 1.00\n", "\n", "\n", "140454734443904backward->140454734443760backward\n", "\n", "\n", " 0.25\n", "\n", "\n", "140454734443904backward->140454734443808backward\n", "\n", "\n", "\n", "140454734443952backward->140454734443712backward\n", "\n", "\n", "\n", "140454734443952backward->140454734443760backward\n", "\n", "\n", " 0.50\n", "\n", "\n", "140454734444000backward->140454734443760backward\n", "\n", "\n", " 1.00\n", "\n", "\n", "140454734444000backward->140454734443856backward\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 对第三步的隐藏状态进行反向传播\n", "h3.backward()\n", "draw_graph(h3, 'backward')" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }