{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from utils import Scalar, draw_graph\n", "from linear_model import Linear, mse" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "%3\n", "\n", "\n", "4398170656backward\n", "\n", "y1= 1.00\n", "\n", "\n", "4398171184backward\n", "\n", "grad=-5.50\n", "\n", "value= 0.00\n", "\n", "b\n", "\n", "\n", "4398171232backward\n", "\n", "grad=-1.00\n", "\n", "value= 0.00\n", "\n", "+\n", "\n", "\n", "4398171232backward->4398171184backward\n", "\n", "\n", "-1.00\n", "\n", "\n", "4398170992backward\n", "\n", "grad=-1.00\n", "\n", "value= 0.00\n", "\n", "*\n", "\n", "\n", "4398171232backward->4398170992backward\n", "\n", "\n", "-1.00\n", "\n", "\n", "4398170752backward\n", "\n", "y2= 4.50\n", "\n", "\n", "4398170800backward\n", "\n", "x1= 1.50\n", "\n", "\n", "4398170848backward\n", "\n", "x2= 2.00\n", "\n", "\n", "4398171376backward\n", "\n", "grad=-4.50\n", "\n", "value= 0.00\n", "\n", "+\n", "\n", "\n", "4398171376backward->4398171184backward\n", "\n", "\n", "-4.50\n", "\n", "\n", "4398170512backward\n", "\n", "grad=-4.50\n", "\n", "value= 0.00\n", "\n", "*\n", "\n", "\n", "4398171376backward->4398170512backward\n", "\n", "\n", "-4.50\n", "\n", "\n", "4398171424backward\n", "\n", "grad= 4.50\n", "\n", "value= 4.50\n", "\n", "-\n", "\n", "\n", "4398171424backward->4398170752backward\n", "\n", "\n", "\n", "4398171424backward->4398171376backward\n", "\n", "\n", "-4.50\n", "\n", "\n", "4398170992backward->4398170800backward\n", "\n", "\n", "\n", "4398171040backward\n", "\n", "grad=-10.50\n", "\n", "value= 0.00\n", "\n", "a\n", "\n", "\n", "4398170992backward->4398171040backward\n", "\n", "\n", "-1.50\n", "\n", "\n", "4398171520backward\n", "\n", "grad= 1.00\n", "\n", "value= 10.62\n", "\n", "mse\n", "\n", "\n", "4398171520backward->4398171424backward\n", "\n", "\n", " 4.50\n", "\n", "\n", "4398171088backward\n", "\n", "grad= 1.00\n", "\n", "value= 1.00\n", "\n", "-\n", "\n", "\n", "4398171520backward->4398171088backward\n", "\n", "\n", " 1.00\n", "\n", "\n", "4398170512backward->4398170848backward\n", "\n", "\n", "\n", "4398170512backward->4398171040backward\n", "\n", "\n", "-9.00\n", "\n", "\n", "4398171088backward->4398170656backward\n", "\n", "\n", "\n", "4398171088backward->4398171232backward\n", "\n", "\n", "-1.00\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x1 = Scalar(1.5, label='x1', requires_grad=False)\n", "y1 = Scalar(1.0, label='y1', requires_grad=False)\n", "x2 = Scalar(2.0, label='x2', requires_grad=False)\n", "y2 = Scalar(4.5, label='y2', requires_grad=False)\n", "# 反向传播\n", "model = Linear()\n", "loss = mse([model.error(x1, y1), model.error(x2, y2)])\n", "loss.backward()\n", "draw_graph(loss, 'backward')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "%3\n", "\n", "\n", "4387998736backward\n", "\n", "grad=-1.00\n", "\n", "value= 0.00\n", "\n", "+\n", "\n", "\n", "4387998640backward\n", "\n", "grad=-1.00\n", "\n", "value= 0.00\n", "\n", "*\n", "\n", "\n", "4387998736backward->4387998640backward\n", "\n", "\n", "-1.00\n", "\n", "\n", "4387997680backward\n", "\n", "grad=-5.50\n", "\n", "value= 0.00\n", "\n", "b\n", "\n", "\n", "4387998736backward->4387997680backward\n", "\n", "\n", "-1.00\n", "\n", "\n", "4398170656backward\n", "\n", "y1= 1.00\n", "\n", "\n", "4387998784backward\n", "\n", "x1= 0.00\n", "\n", "\n", "4387996768backward\n", "\n", "grad= 1.00\n", "\n", "value= 10.62\n", "\n", "mse\n", "\n", "\n", "4387995856backward\n", "\n", "grad= 4.50\n", "\n", "value= 4.50\n", "\n", "-\n", "\n", "\n", "4387996768backward->4387995856backward\n", "\n", "\n", " 4.50\n", "\n", "\n", "4387998448backward\n", "\n", "grad= 1.00\n", "\n", "value= 1.00\n", "\n", "-\n", "\n", "\n", "4387996768backward->4387998448backward\n", "\n", "\n", " 1.00\n", "\n", "\n", "4398170752backward\n", "\n", "y2= 4.50\n", "\n", "\n", "4387995856backward->4398170752backward\n", "\n", "\n", "\n", "4387998544backward\n", "\n", "grad=-4.50\n", "\n", "value= 0.00\n", "\n", "+\n", "\n", "\n", "4387995856backward->4387998544backward\n", "\n", "\n", "-4.50\n", "\n", "\n", "4398170848backward\n", "\n", "x2= 2.00\n", "\n", "\n", "4387998448backward->4387998736backward\n", "\n", "\n", "-1.00\n", "\n", "\n", "4387998448backward->4398170656backward\n", "\n", "\n", "\n", "4387997968backward\n", "\n", "grad=-9.00\n", "\n", "value= 0.00\n", "\n", "a\n", "\n", "\n", "4387998688backward\n", "\n", "grad=-4.50\n", "\n", "value= 0.00\n", "\n", "*\n", "\n", "\n", "4387998544backward->4387998688backward\n", "\n", "\n", "-4.50\n", "\n", "\n", "4387998544backward->4387997680backward\n", "\n", "\n", "-4.50\n", "\n", "\n", "4387998640backward->4387998784backward\n", "\n", "\n", "\n", "4387998640backward->4387997968backward\n", "\n", "\n", " 0.00\n", "\n", "\n", "4387998688backward->4398170848backward\n", "\n", "\n", "\n", "4387998688backward->4387997968backward\n", "\n", "\n", "-9.00\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 将变量x1设置成0\n", "x1 = Scalar(0.0, label='x1', requires_grad=False)\n", "# 反向传播\n", "model = Linear()\n", "loss = mse([model.error(x1, y1), model.error(x2, y2)])\n", "loss.backward()\n", "draw_graph(loss, 'backward')" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "%3\n", "\n", "\n", "4398102032backward\n", "\n", "x1= 1.50\n", "\n", "\n", "4398102080backward\n", "\n", "grad=-8.00\n", "\n", "value= 0.00\n", "\n", "a\n", "\n", "\n", "4398313536backward\n", "\n", "grad= 4.00\n", "\n", "value= 4.00\n", "\n", "-\n", "\n", "\n", "4398313680backward\n", "\n", "grad=-4.00\n", "\n", "value= 0.00\n", "\n", "+\n", "\n", "\n", "4398313536backward->4398313680backward\n", "\n", "\n", "-4.00\n", "\n", "\n", "4398104288backward\n", "\n", "y2= 4.00\n", "\n", "\n", "4398313536backward->4398104288backward\n", "\n", "\n", "\n", "4398313584backward\n", "\n", "grad= 1.00\n", "\n", "value= 8.00\n", "\n", "mse\n", "\n", "\n", "4398313584backward->4398313536backward\n", "\n", "\n", " 4.00\n", "\n", "\n", "4398102320backward\n", "\n", "grad= 0.00\n", "\n", "value= 0.00\n", "\n", "-\n", "\n", "\n", "4398313584backward->4398102320backward\n", "\n", "\n", " 0.00\n", "\n", "\n", "4398103184backward\n", "\n", "grad= 0.00\n", "\n", "value= 0.00\n", "\n", "+\n", "\n", "\n", "4398102800backward\n", "\n", "grad=-4.00\n", "\n", "value= 0.00\n", "\n", "b\n", "\n", "\n", "4398103184backward->4398102800backward\n", "\n", "\n", " 0.00\n", "\n", "\n", "4398103376backward\n", "\n", "grad= 0.00\n", "\n", "value= 0.00\n", "\n", "*\n", "\n", "\n", "4398103184backward->4398103376backward\n", "\n", "\n", " 0.00\n", "\n", "\n", "4398313680backward->4398102800backward\n", "\n", "\n", "-4.00\n", "\n", "\n", "4398103472backward\n", "\n", "grad=-4.00\n", "\n", "value= 0.00\n", "\n", "*\n", "\n", "\n", "4398313680backward->4398103472backward\n", "\n", "\n", "-4.00\n", "\n", "\n", "4398102320backward->4398103184backward\n", "\n", "\n", " 0.00\n", "\n", "\n", "4398104528backward\n", "\n", "y1= 1.00\n", "\n", "\n", "4398102320backward->4398104528backward\n", "\n", "\n", "\n", "4398103376backward->4398102032backward\n", "\n", "\n", "\n", "4398103376backward->4398102080backward\n", "\n", "\n", " 0.00\n", "\n", "\n", "4398103472backward->4398102080backward\n", "\n", "\n", "-8.00\n", "\n", "\n", "4398102512backward\n", "\n", "x2= 2.00\n", "\n", "\n", "4398103472backward->4398102512backward\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x1 = Scalar(1.5, label='x1', requires_grad=False)\n", "y1 = Scalar(1.0, label='y1', requires_grad=False)\n", "x2 = Scalar(2.0, label='x2', requires_grad=False)\n", "y2 = Scalar(4.0, label='y2', requires_grad=False)\n", "# 反向传播\n", "model = Linear()\n", "l = model.error(x1, y1)\n", "# 将变量x1，y1的损失设置成0\n", "l.value = 0.0\n", "loss = mse([l, model.error(x2, y2)])\n", "loss.backward()\n", "draw_graph(loss, 'backward')" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "%3\n", "\n", "\n", "4398315552backward\n", "\n", "grad=-9.50\n", "\n", "value= 0.00\n", "\n", "a\n", "\n", "\n", "4398315648backward\n", "\n", "grad= 1.00\n", "\n", "value= 1.00\n", "\n", "-\n", "\n", "\n", "4398314784backward\n", "\n", "y1= 1.00\n", "\n", "\n", "4398315648backward->4398314784backward\n", "\n", "\n", "\n", "4398314832backward\n", "\n", "grad=-1.00\n", "\n", "value= 0.00\n", "\n", "+\n", "\n", "\n", "4398315648backward->4398314832backward\n", "\n", "\n", "-1.00\n", "\n", "\n", "4398315264backward\n", "\n", "y2= 4.00\n", "\n", "\n", "4398315792backward\n", "\n", "grad= 4.00\n", "\n", "value= 4.00\n", "\n", "-\n", "\n", "\n", "4398315792backward->4398315264backward\n", "\n", "\n", "\n", "4398314400backward\n", "\n", "grad=-4.00\n", "\n", "value= 0.00\n", "\n", "+\n", "\n", "\n", "4398315792backward->4398314400backward\n", "\n", "\n", "-4.00\n", "\n", "\n", "4398315840backward\n", "\n", "grad= 1.00\n", "\n", "value= 0.00\n", "\n", "mse\n", "\n", "\n", "4398315840backward->4398315648backward\n", "\n", "\n", " 1.00\n", "\n", "\n", "4398315840backward->4398315792backward\n", "\n", "\n", " 4.00\n", "\n", "\n", "4398314928backward\n", "\n", "grad=-5.00\n", "\n", "value= 0.00\n", "\n", "b\n", "\n", "\n", "4398314832backward->4398314928backward\n", "\n", "\n", "-1.00\n", "\n", "\n", "4398315456backward\n", "\n", "grad=-1.00\n", "\n", "value= 0.00\n", "\n", "*\n", "\n", "\n", "4398314832backward->4398315456backward\n", "\n", "\n", "-1.00\n", "\n", "\n", "4398315360backward\n", "\n", "x1= 1.50\n", "\n", "\n", "4398315888backward\n", "\n", "grad=-4.00\n", "\n", "value= 0.00\n", "\n", "*\n", "\n", "\n", "4398315888backward->4398315552backward\n", "\n", "\n", "-8.00\n", "\n", "\n", "4398315408backward\n", "\n", "x2= 2.00\n", "\n", "\n", "4398315888backward->4398315408backward\n", "\n", "\n", "\n", "4398314400backward->4398315888backward\n", "\n", "\n", "-4.00\n", "\n", "\n", "4398314400backward->4398314928backward\n", "\n", "\n", "-4.00\n", "\n", "\n", "4398315456backward->4398315552backward\n", "\n", "\n", "-1.50\n", "\n", "\n", "4398315456backward->4398315360backward\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x1 = Scalar(1.5, label='x1', requires_grad=False)\n", "y1 = Scalar(1.0, label='y1', requires_grad=False)\n", "x2 = Scalar(2.0, label='x2', requires_grad=False)\n", "y2 = Scalar(4.0, label='y2', requires_grad=False)\n", "# 反向传播\n", "model = Linear()\n", "loss = mse([model.error(x1, y1), model.error(x2, y2)])\n", "loss.value = 0\n", "loss.backward()\n", "draw_graph(loss, '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 }