{ "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": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "%3\n", "\n", "\n", "140231043894480backward\n", "\n", "grad=0.15\n", "\n", "value=1.00\n", "\n", "b\n", "\n", "\n", "140231043894528backward\n", "\n", "grad=0.15\n", "\n", "value=0.50\n", "\n", "*\n", "\n", "\n", "140231043894576backward\n", "\n", "grad=0.01\n", "\n", "value=5.00\n", "\n", "w\n", "\n", "\n", "140231043894528backward->140231043894576backward\n", "\n", "\n", "0.01\n", "\n", "\n", "140231043894624backward\n", "\n", "x=0.10\n", "\n", "\n", "140231043894528backward->140231043894624backward\n", "\n", "\n", "\n", "140231043894672backward\n", "\n", "grad=1.00\n", "\n", "value=0.82\n", "\n", "sigmoid\n", "\n", "\n", "140231043894720backward\n", "\n", "grad=0.15\n", "\n", "value=1.50\n", "\n", "+\n", "\n", "\n", "140231043894672backward->140231043894720backward\n", "\n", "\n", "0.15\n", "\n", "\n", "140231043894720backward->140231043894480backward\n", "\n", "\n", "0.15\n", "\n", "\n", "140231043894720backward->140231043894528backward\n", "\n", "\n", "0.15\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 为了图形简洁易懂，假设只有一个权重项参数\n", "## 当线性输出较小时，梯度不会溢出\n", "w = Scalar(5.0, label='w')\n", "b = Scalar(1.0, label='b')\n", "x = Scalar(0.1, label='x', requires_grad=False)\n", "h = w * x + b\n", "l = h.sigmoid()\n", "l.backward()\n", "draw_graph(l, 'backward')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "%3\n", "\n", "\n", "140231043891792backward\n", "\n", "grad=0.00\n", "\n", "value=100.50\n", "\n", "*\n", "\n", "\n", "140231043893472backward\n", "\n", "x=20.10\n", "\n", "\n", "140231043891792backward->140231043893472backward\n", "\n", "\n", "\n", "140231043893136backward\n", "\n", "grad=0.00\n", "\n", "value=5.00\n", "\n", "w\n", "\n", "\n", "140231043891792backward->140231043893136backward\n", "\n", "\n", "0.00\n", "\n", "\n", "140231043893328backward\n", "\n", "grad=0.00\n", "\n", "value=1.00\n", "\n", "b\n", "\n", "\n", "140231043893616backward\n", "\n", "grad=1.00\n", "\n", "value=1.00\n", "\n", "sigmoid\n", "\n", "\n", "140231043893664backward\n", "\n", "grad=0.00\n", "\n", "value=101.50\n", "\n", "+\n", "\n", "\n", "140231043893616backward->140231043893664backward\n", "\n", "\n", "0.00\n", "\n", "\n", "140231043893664backward->140231043891792backward\n", "\n", "\n", "0.00\n", "\n", "\n", "140231043893664backward->140231043893328backward\n", "\n", "\n", "0.00\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 当线性输出较大时，梯度溢出\n", "w = Scalar(5.0, label='w')\n", "b = Scalar(1.0, label='b')\n", "x = Scalar(20.1, label='x', requires_grad=False)\n", "h = w * x + b\n", "l = h.sigmoid()\n", "l.backward()\n", "draw_graph(l, 'backward')" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "%3\n", "\n", "\n", "140231043894768backward\n", "\n", "x2=-0.40\n", "\n", "\n", "140231044055104backward\n", "\n", "grad=1.00\n", "\n", "value=1.50\n", "\n", "+\n", "\n", "\n", "140231043894384backward\n", "\n", "grad=1.00\n", "\n", "value=1.00\n", "\n", "sigmoid\n", "\n", "\n", "140231044055104backward->140231043894384backward\n", "\n", "\n", "1.00\n", "\n", "\n", "140231043893184backward\n", "\n", "grad=1.00\n", "\n", "value=0.50\n", "\n", "sigmoid\n", "\n", "\n", "140231044055104backward->140231043893184backward\n", "\n", "\n", "1.00\n", "\n", "\n", "140231043892032backward\n", "\n", "grad=0.00\n", "\n", "value=75.00\n", "\n", "+\n", "\n", "\n", "140231043894384backward->140231043892032backward\n", "\n", "\n", "0.00\n", "\n", "\n", "140231043892416backward\n", "\n", "grad=0.25\n", "\n", "value=20.00\n", "\n", "b\n", "\n", "\n", "140231043892944backward\n", "\n", "grad=-0.10\n", "\n", "value=50.00\n", "\n", "w\n", "\n", "\n", "140231044055248backward\n", "\n", "grad=0.25\n", "\n", "value=0.00\n", "\n", "+\n", "\n", "\n", "140231044055248backward->140231043892416backward\n", "\n", "\n", "0.25\n", "\n", "\n", "140231044058608backward\n", "\n", "grad=0.25\n", "\n", "value=-20.00\n", "\n", "*\n", "\n", "\n", "140231044055248backward->140231044058608backward\n", "\n", "\n", "0.25\n", "\n", "\n", "140231043891984backward\n", "\n", "x1=1.10\n", "\n", "\n", "140231043892032backward->140231043892416backward\n", "\n", "\n", "0.00\n", "\n", "\n", "140231043892080backward\n", "\n", "grad=0.00\n", "\n", "value=55.00\n", "\n", "*\n", "\n", "\n", "140231043892032backward->140231043892080backward\n", "\n", "\n", "0.00\n", "\n", "\n", "140231043892080backward->140231043892944backward\n", "\n", "\n", "0.00\n", "\n", "\n", "140231043892080backward->140231043891984backward\n", "\n", "\n", "\n", "140231043893184backward->140231044055248backward\n", "\n", "\n", "0.25\n", "\n", "\n", "140231044058608backward->140231043894768backward\n", "\n", "\n", "\n", "140231044058608backward->140231043892944backward\n", "\n", "\n", "-0.10\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 不同数据点的反向传播是相互独立的\n", "w = Scalar(50.0, label='w')\n", "b = Scalar(20.0, label='b')\n", "x1 = Scalar(1.1, label='x1', requires_grad=False)\n", "x2 = Scalar(-0.4, label='x2', requires_grad=False)\n", "h1 = w * x1 + b\n", "l1 = h1.sigmoid()\n", "h2 = w * x2 + b\n", "l2 = h2.sigmoid()\n", "l = l1 + l2\n", "l.backward()\n", "draw_graph(l, 'backward')" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "%3\n", "\n", "\n", "140231044056592backward\n", "\n", "grad=0.00\n", "\n", "value=85.00\n", "\n", "+\n", "\n", "\n", "140231044056160backward\n", "\n", "grad=0.00\n", "\n", "value=65.00\n", "\n", "*\n", "\n", "\n", "140231044056592backward->140231044056160backward\n", "\n", "\n", "0.00\n", "\n", "\n", "140231044056256backward\n", "\n", "grad=0.00\n", "\n", "value=20.00\n", "\n", "b\n", "\n", "\n", "140231044056592backward->140231044056256backward\n", "\n", "\n", "0.00\n", "\n", "\n", "140231044056400backward\n", "\n", "x3=1.30\n", "\n", "\n", "140231044056160backward->140231044056400backward\n", "\n", "\n", "\n", "140231044056496backward\n", "\n", "grad=0.00\n", "\n", "value=50.00\n", "\n", "w\n", "\n", "\n", "140231044056160backward->140231044056496backward\n", "\n", "\n", "0.00\n", "\n", "\n", "140231044057264backward\n", "\n", "grad=0.00\n", "\n", "value=90.00\n", "\n", "+\n", "\n", "\n", "140231044057264backward->140231044056256backward\n", "\n", "\n", "0.00\n", "\n", "\n", "140231044055728backward\n", "\n", "grad=0.00\n", "\n", "value=70.00\n", "\n", "*\n", "\n", "\n", "140231044057264backward->140231044055728backward\n", "\n", "\n", "0.00\n", "\n", "\n", "140231044056352backward\n", "\n", "x4=1.40\n", "\n", "\n", "140231044055728backward->140231044056352backward\n", "\n", "\n", "\n", "140231044055728backward->140231044056496backward\n", "\n", "\n", "0.00\n", "\n", "\n", "140231044056928backward\n", "\n", "grad=1.00\n", "\n", "value=1.00\n", "\n", "sigmoid\n", "\n", "\n", "140231044056928backward->140231044057264backward\n", "\n", "\n", "0.00\n", "\n", "\n", "140231044056448backward\n", "\n", "grad=1.00\n", "\n", "value=1.00\n", "\n", "sigmoid\n", "\n", "\n", "140231044056448backward->140231044056592backward\n", "\n", "\n", "0.00\n", "\n", "\n", "140231044057072backward\n", "\n", "grad=1.00\n", "\n", "value=2.00\n", "\n", "+\n", "\n", "\n", "140231044057072backward->140231044056928backward\n", "\n", "\n", "1.00\n", "\n", "\n", "140231044057072backward->140231044056448backward\n", "\n", "\n", "1.00\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 当对于所有数据，相应的线性输出都较大时，该神经元相当于坏死掉\n", "w = Scalar(50.0, label='w')\n", "b = Scalar(20.0, label='b')\n", "x3 = Scalar(1.3, label='x3', requires_grad=False)\n", "x4 = Scalar(1.4, label='x4', requires_grad=False)\n", "h3 = w * x3 + b\n", "l3 = h3.sigmoid()\n", "h4 = w * x4 + b\n", "l4 = h4.sigmoid()\n", "l = l3 + l4\n", "l.backward()\n", "draw_graph(l, '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 }