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服务器之家络中的权重和偏差。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：
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import torchimport matplotlib.pyplot as pltimport osos.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def forward(x): return w[0]*(x**2)+w[1]*x+w[2]# 计算损失def loss(x,y): y_pred = forward(x) return (y_pred-y) ** 2# 训练模块print('predict (before tranining) ',4, forward(4).item())epoch_list = []w_list = []loss_list = []for epoch in range(1000): for x,y in zip(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 (after tranining) ',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：
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predict (before tranining) 4 21.0 grad: 1.0 2.0 tensor([2., 2., 2.]) grad: 2.0 4.0 tensor([22.8800, 11.4400, 5.7200]) grad: 3.0 6.0 tensor([77.0472, 25.6824, 8.5608])progress: 0 18.321826934814453 grad: 1.0 2.0 tensor([-1.1466, -1.1466, -1.1466]) grad: 2.0 4.0 tensor([-15.5367, -7.7683, -3.8842]) grad: 3.0 6.0 tensor([-30.4322, -10.1441, -3.3814])progress: 1 2.858394145965576 grad: 1.0 2.0 tensor([0.3451, 0.3451, 0.3451]) grad: 2.0 4.0 tensor([2.4273, 1.2137, 0.6068]) grad: 3.0 6.0 tensor([19.4499, 6.4833, 2.1611])progress: 2 1.1675907373428345 grad: 1.0 2.0 tensor([-0.3224, -0.3224, -0.3224]) grad: 2.0 4.0 tensor([-5.8458, -2.9229, -1.4614]) grad: 3.0 6.0 tensor([-3.8829, -1.2943, -0.4314])progress: 3 0.04653334245085716 grad: 1.0 2.0 tensor([0.0137, 0.0137, 0.0137]) grad: 2.0 4.0 tensor([-1.9141, -0.9570, -0.4785]) grad: 3.0 6.0 tensor([6.8557, 2.2852, 0.7617])progress: 4 0.14506366848945618 grad: 1.0 2.0 tensor([-0.1182, -0.1182, -0.1182]) grad: 2.0 4.0 tensor([-3.6644, -1.8322, -0.9161]) grad: 3.0 6.0 tensor([1.7455, 0.5818, 0.1939])progress: 5 0.009403289295732975 grad: 1.0 2.0 tensor([-0.0333, -0.0333, -0.0333]) grad: 2.0 4.0 tensor([-2.7739, -1.3869, -0.6935]) grad: 3.0 6.0 tensor([4.0140, 1.3380, 0.4460])progress: 6 0.04972923547029495 grad: 1.0 2.0 tensor([-0.0501, -0.0501, -0.0501]) grad: 2.0 4.0 tensor([-3.1150, -1.5575, -0.7788]) grad: 3.0 6.0 tensor([2.8534, 0.9511, 0.3170])progress: 7 0.025129113346338272 grad: 1.0 2.0 tensor([-0.0205, -0.0205, -0.0205]) grad: 2.0 4.0 tensor([-2.8858, -1.4429, -0.7215]) grad: 3.0 6.0 tensor([3.2924, 1.0975, 0.3658])progress: 8 0.03345605731010437 grad: 1.0 2.0 tensor([-0.0134, -0.0134, -0.0134]) grad: 2.0 4.0 tensor([-2.9247, -1.4623, -0.7312]) grad: 3.0 6.0 tensor([2.9909, 0.9970, 0.3323])progress: 9 0.027609655633568764 grad: 1.0 2.0 tensor([0.0033, 0.0033, 0.0033]) grad: 2.0 4.0 tensor([-2.8414, -1.4207, -0.7103]) grad: 3.0 6.0 tensor([3.0377, 1.0126, 0.3375])progress: 10 0.02848036028444767 grad: 1.0 2.0 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-0.4348]) grad: 3.0 6.0 tensor([1.4418, 0.4806, 0.1602])progress: 95 0.006416172254830599 grad: 1.0 2.0 tensor([0.3159, 0.3159, 0.3159]) grad: 2.0 4.0 tensor([-1.7366, -0.8683, -0.4342]) grad: 3.0 6.0 tensor([1.4389, 0.4796, 0.1599])progress: 96 0.006390606984496117 grad: 1.0 2.0 tensor([0.3161, 0.3161, 0.3161]) grad: 2.0 4.0 tensor([-1.7343, -0.8671, -0.4336]) grad: 3.0 6.0 tensor([1.4361, 0.4787, 0.1596])progress: 97 0.0063657015562057495 grad: 1.0 2.0 tensor([0.3164, 0.3164, 0.3164]) grad: 2.0 4.0 tensor([-1.7320, -0.8660, -0.4330]) grad: 3.0 6.0 tensor([1.4334, 0.4778, 0.1593])progress: 98 0.0063416799530386925 grad: 1.0 2.0 tensor([0.3166, 0.3166, 0.3166]) grad: 2.0 4.0 tensor([-1.7297, -0.8649, -0.4324]) grad: 3.0 6.0 tensor([1.4308, 0.4769, 0.1590])progress: 99 0.00631808303296566predict (after tranining) 4 8.544171333312988 |
损失值随着迭代次数的增加呈递减趋势，如下图所示：
可以看出：x=4时的预测值约为8.5，与真实值8有所差距，可通过提高迭代次数或者调整学习率、初始参数等方法来减小差距。
参考文献：
到此这篇关于PyTorch反向传播的文章就介绍到这了,更多相关PyTorch反向传播内容请搜索服务器之家以前的文章或继续浏览下面的相关文章希望大家以后多多支持服务器之家！
原文链接：https://blog.csdn.net/weixin_43821559/article/details/123296140
