PyTorch梯度下降反向传播实例分析

魁首哥

作者

PyTorch梯度下降反向传播实例分析

本文小编为大家详细介绍“PyTorch梯度下降反向传播实例分析”，内容详细，步骤清晰，细节处理妥当，希望这篇“PyTorch梯度下降反向传播实例分析”文章能帮助大家解决疑惑，下面跟着小编的思路慢慢深入，一起来学习新知识吧。

前言：

反向传播的目的是计算成本函数C对网络中任意w或b的偏导数。一旦我们有了这些偏导数，我们将通过一些常数 α的乘积和该数量相对于成本函数的偏导数来更新网络中的权重和偏差。这是流行的梯度下降算法。而偏导数给出了最大上升的方向。因此，关于反向传播算法，我们继续查看下文。

我们向相反的方向迈出了一小步——最大下降的方向，也就是将我们带到成本函数的局部最小值的方向

如题：

意思是利用这个二次模型来预测数据，减小损失函数(MSE)的值。

代码如下：

importtorchimportmatplotlib.pyplotaspltimportosos.environ["KMP_DUPLICATE_LIB_OK"]="TRUE"#数据集x_data=[1.0,2.0,3.0]y_data=[2.0,4.0,6.0]#权重参数初始值均为1w=torch.tensor([1.0,1.0,1.0])w.requires_grad=True#需要计算梯度#前向传播defforward(x):returnw[0]*(x**2)+w[1]*x+w[2]#计算损失defloss(x,y):y_pred=forward(x)return(y_pred-y)**2#训练模块print('predict(beforetranining)',4,forward(4).item())epoch_list=[]w_list=[]loss_list=[]forepochinrange(1000):forx,yinzip(x_data,y_data):l=loss(x,y)l.backward()#后向传播print('\tgrad:',x,y,w.grad.data)w.data=w.data-0.01*w.grad.data#梯度下降w.grad.data.zero_()#梯度清零操作print('progress:',epoch,l.item())epoch_list.append(epoch)w_list.append(w.data)loss_list.append(l.item())print('predict(aftertranining)',4,forward(4).item())#绘图plt.plot(epoch_list,loss_list,'b')plt.xlabel('Epoch')plt.ylabel('Loss')plt.grid()plt.show()

结果如下：

predict(beforetranining)421.0grad:1.02.0tensor([2.,2.,2.])grad:2.04.0tensor([22.8800,11.4400,5.7200])grad:3.06.0tensor([77.0472,25.6824,8.5608])progress:018.321826934814453grad:1.02.0tensor([-1.1466,-1.1466,-1.1466])grad:2.04.0tensor([-15.5367,-7.7683,-3.8842])grad:3.06.0tensor([-30.4322,-10.1441,-3.3814])progress:12.858394145965576grad:1.02.0tensor([0.3451,0.3451,0.3451])grad:2.04.0tensor([2.4273,1.2137,0.6068])grad:3.06.0tensor([19.4499,6.4833,2.1611])progress:21.1675907373428345grad:1.02.0tensor([-0.3224,-0.3224,-0.3224])grad:2.04.0tensor([-5.8458,-2.9229,-1.4614])grad:3.06.0tensor([-3.8829,-1.2943,-0.4314])progress:30.04653334245085716grad:1.02.0tensor([0.0137,0.0137,0.0137])grad:2.04.0tensor([-1.9141,-0.9570,-0.4785])grad:3.06.0tensor([6.8557,2.2852,0.7617])progress:40.14506366848945618grad:1.02.0tensor([-0.1182,-0.1182,-0.1182])grad:2.04.0tensor([-3.6644,-1.8322,-0.9161])grad:3.06.0tensor([1.7455,0.5818,0.1939])progress:50.009403289295732975grad:1.02.0tensor([-0.0333,-0.0333,-0.0333])grad:2.04.0tensor([-2.7739,-1.3869,-0.6935])grad:3.06.0tensor([4.0140,1.3380,0.4460])progress:60.04972923547029495grad:1.02.0tensor([-0.0501,-0.0501,-0.0501])grad:2.04.0tensor([-3.1150,-1.5575,-0.7788])grad:3.06.0tensor([2.8534,0.9511,0.3170])progress:70.025129113346338272grad:1.02.0tensor([-0.0205,-0.0205,-0.0205])grad:2.04.0tensor([-2.8858,-1.4429,-0.7215])grad:3.06.0tensor([3.2924,1.0975,0.3658])progress:80.03345605731010437grad:1.02.0tensor([-0.0134,-0.0134,-0.0134])grad:2.04.0tensor([-2.9247,-1.4623,-0.7312])grad:3.06.0tensor([2.9909,0.9970,0.3323])progress:90.027609655633568764grad:1.02.0tensor([0.0033,0.0033,0.0033])grad:2.04.0tensor([-2.8414,-1.4207,-0.7103])grad:3.06.0tensor([3.0377,1.0126,0.3375])progress:100.02848036028444767grad:1.02.0tensor([0.0148,0.0148,0.0148])grad:2.04.0tensor([-2.8174,-1.4087,-0.7043])grad:3.06.0tensor([2.9260,0.9753,0.3251])progress:110.02642466314136982grad:1.02.0tensor([0.0280,0.0280,0.0280])grad:2.04.0tensor([-2.7682,-1.3841,-0.6920])grad:3.06.0tensor([2.8915,0.9638,0.3213])progress:120.025804826989769936grad:1.02.0tensor([0.0397,0.0397,0.0397])grad:2.04.0tensor([-2.7330,-1.3665,-0.6832])grad:3.06.0tensor([2.8243,0.9414,0.3138])progress:130.02462013065814972grad:1.02.0tensor([0.0514,0.0514,0.0514])grad:2.04.0tensor([-2.6934,-1.3467,-0.6734])grad:3.06.0tensor([2.7756,0.9252,0.3084])progress:140.023777369409799576grad:1.02.0tensor([0.0624,0.0624,0.0624])grad:2.04.0tensor([-2.6580,-1.3290,-0.6645])grad:3.06.0tensor([2.7213,0.9071,0.3024])progress:150.0228563379496336grad:1.02.0tensor([0.0731,0.0731,0.0731])grad:2.04.0tensor([-2.6227,-1.3113,-0.6557])grad:3.06.0tensor([2.6725,0.8908,0.2969])progress:160.022044027224183083grad:1.02.0tensor([0.0833,0.0833,0.0833])grad:2.04.0tensor([-2.5893,-1.2946,-0.6473])grad:3.06.0tensor([2.6240,0.8747,0.2916])progress:170.02125072106719017grad:1.02.0tensor([0.0931,0.0931,0.0931])grad:2.04.0tensor([-2.5568,-1.2784,-0.6392])grad:3.06.0tensor([2.5780,0.8593,0.2864])progress:180.020513182505965233grad:1.02.0tensor([0.1025,0.1025,0.1025])grad:2.04.0tensor([-2.5258,-1.2629,-0.6314])grad:3.06.0tensor([2.5335,0.8445,0.2815])progress:190.019810274243354797grad:1.02.0tensor([0.1116,0.1116,0.1116])grad:2.04.0tensor([-2.4958,-1.2479,-0.6239])grad:3.06.0tensor([2.4908,0.8303,0.2768])progress:200.019148115068674088grad:1.02.0tensor([0.1203,0.1203,0.1203])grad:2.04.0tensor([-2.4669,-1.2335,-0.6167])grad:3.06.0tensor([2.4496,0.8165,0.2722])progress:210.018520694226026535grad:1.02.0tensor([0.1286,0.1286,0.1286])grad:2.04.0tensor([-2.4392,-1.2196,-0.6098])grad:3.06.0tensor([2.4101,0.8034,0.2678])progress:220.017927465960383415grad:1.02.0tensor([0.1367,0.1367,0.1367])grad:2.04.0tensor([-2.4124,-1.2062,-0.6031])grad:3.06.0tensor([2.3720,0.7907,0.2636])progress:230.01736525259912014grad:1.02.0tensor([0.1444,0.1444,0.1444])grad:2.04.0tensor([-2.3867,-1.1933,-0.5967])grad:3.06.0tensor([2.3354,0.7785,0.2595])progress:240.016833148896694183grad:1.02.0tensor([0.1518,0.1518,0.1518])grad:2.04.0tensor([-2.3619,-1.1810,-0.5905])grad:3.06.0tensor([2.3001,0.7667,0.2556])progress:250.01632905937731266grad:1.02.0tensor([0.1589,0.1589,0.1589])grad:2.04.0tensor([-2.3380,-1.1690,-0.5845])grad:3.06.0tensor([2.2662,0.7554,0.2518])progress:260.01585075818002224grad:1.02.0tensor([0.1657,0.1657,0.1657])grad:2.04.0tensor([-2.3151,-1.1575,-0.5788])grad:3.06.0tensor([2.2336,0.7445,0.2482])progress:270.015397666022181511grad:1.02.0tensor([0.1723,0.1723,0.1723])grad:2.04.0tensor([-2.2929,-1.1465,-0.5732])grad:3.06.0tensor([2.2022,0.7341,0.2447])progress:280.014967591501772404grad:1.02.0tensor([0.1786,0.1786,0.1786])grad:2.04.0tensor([-2.2716,-1.1358,-0.5679])grad:3.06.0tensor([2.1719,0.7240,0.2413])progress:290.014559715054929256grad:1.02.0tensor([0.1846,0.1846,0.1846])grad:2.04.0tensor([-2.2511,-1.1255,-0.5628])grad:3.06.0tensor([2.1429,0.7143,0.2381])progress:300.014172340743243694grad:1.02.0tensor([0.1904,0.1904,0.1904])grad:2.04.0tensor([-2.2313,-1.1157,-0.5578])grad:3.06.0tensor([2.1149,0.7050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损失值随着迭代次数的增加呈递减趋势，如下图所示：