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：
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：
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 tensor([0.0148, 0.0148, 0.0148]) grad: 2.0 4.0 tensor([-2.8174, -1.4087, -0.7043]) grad: 3.0 6.0 tensor([2.9260, 0.9753, 0.3251])progress: 11 0.02642466314136982 grad: 1.0 2.0 tensor([0.0280, 0.0280, 0.0280]) grad: 2.0 4.0 tensor([-2.7682, -1.3841, -0.6920]) grad: 3.0 6.0 tensor([2.8915, 0.9638, 0.3213])progress: 12 0.025804826989769936 grad: 1.0 2.0 tensor([0.0397, 0.0397, 0.0397]) grad: 2.0 4.0 tensor([-2.7330, -1.3665, -0.6832]) grad: 3.0 6.0 tensor([2.8243, 0.9414, 0.3138])progress: 13 0.02462013065814972 grad: 1.0 2.0 tensor([0.0514, 0.0514, 0.0514]) grad: 2.0 4.0 tensor([-2.6934, -1.3467, -0.6734]) grad: 3.0 6.0 tensor([2.7756, 0.9252, 0.3084])progress: 14 0.023777369409799576 grad: 1.0 2.0 tensor([0.0624, 0.0624, 0.0624]) grad: 2.0 4.0 tensor([-2.6580, -1.3290, -0.6645]) grad: 3.0 6.0 tensor([2.7213, 0.9071, 0.3024])progress: 15 0.0228563379496336 grad: 1.0 2.0 tensor([0.0731, 0.0731, 0.0731]) grad: 2.0 4.0 tensor([-2.6227, -1.3113, -0.6557]) grad: 3.0 6.0 tensor([2.6725, 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tensor([-2.4392, -1.2196, -0.6098]) grad: 3.0 6.0 tensor([2.4101, 0.8034, 0.2678])progress: 22 0.017927465960383415 grad: 1.0 2.0 tensor([0.1367, 0.1367, 0.1367]) grad: 2.0 4.0 tensor([-2.4124, -1.2062, -0.6031]) grad: 3.0 6.0 tensor([2.3720, 0.7907, 0.2636])progress: 23 0.01736525259912014 grad: 1.0 2.0 tensor([0.1444, 0.1444, 0.1444]) grad: 2.0 4.0 tensor([-2.3867, -1.1933, -0.5967]) grad: 3.0 6.0 tensor([2.3354, 0.7785, 0.2595])progress: 24 0.016833148896694183 grad: 1.0 2.0 tensor([0.1518, 0.1518, 0.1518]) grad: 2.0 4.0 tensor([-2.3619, -1.1810, -0.5905]) grad: 3.0 6.0 tensor([2.3001, 0.7667, 0.2556])progress: 25 0.01632905937731266 grad: 1.0 2.0 tensor([0.1589, 0.1589, 0.1589]) grad: 2.0 4.0 tensor([-2.3380, -1.1690, -0.5845]) grad: 3.0 6.0 tensor([2.2662, 0.7554, 0.2518])progress: 26 0.01585075818002224 grad: 1.0 2.0 tensor([0.1657, 0.1657, 0.1657]) grad: 2.0 4.0 tensor([-2.3151, -1.1575, -0.5788]) grad: 3.0 6.0 tensor([2.2336, 0.7445, 0.2482])progress: 27 0.015397666022181511 grad: 1.0 2.0 tensor([0.1723, 0.1723, 0.1723]) grad: 2.0 4.0 tensor([-2.2929, -1.1465, -0.5732]) grad: 3.0 6.0 tensor([2.2022, 0.7341, 0.2447])progress: 28 0.014967591501772404 grad: 1.0 2.0 tensor([0.1786, 0.1786, 0.1786]) grad: 2.0 4.0 tensor([-2.2716, -1.1358, -0.5679]) grad: 3.0 6.0 tensor([2.1719, 0.7240, 0.2413])progress: 29 0.014559715054929256 grad: 1.0 2.0 tensor([0.1846, 0.1846, 0.1846]) grad: 2.0 4.0 tensor([-2.2511, -1.1255, -0.5628]) grad: 3.0 6.0 tensor([2.1429, 0.7143, 0.2381])progress: 30 0.014172340743243694 grad: 1.0 2.0 tensor([0.1904, 0.1904, 0.1904]) grad: 2.0 4.0 tensor([-2.2313, -1.1157, -0.5578]) grad: 3.0 6.0 tensor([2.1149, 0.7050, 0.2350])progress: 31 0.013804304413497448 grad: 1.0 2.0 tensor([0.1960, 0.1960, 0.1960]) grad: 2.0 4.0 tensor([-2.2123, -1.1061, -0.5531]) grad: 3.0 6.0 tensor([2.0879, 0.6960, 0.2320])progress: 32 0.013455045409500599 grad: 1.0 2.0 tensor([0.2014, 0.2014, 0.2014]) grad: 2.0 4.0 tensor([-2.1939, -1.0970, -0.5485]) grad: 3.0 6.0 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0.0065881176851689816 grad: 1.0 2.0 tensor([0.3139, 0.3139, 0.3139]) grad: 2.0 4.0 tensor([-1.7520, -0.8760, -0.4380]) grad: 3.0 6.0 tensor([1.4576, 0.4859, 0.1620])progress: 90 0.0065572685562074184 grad: 1.0 2.0 tensor([0.3143, 0.3143, 0.3143]) grad: 2.0 4.0 tensor([-1.7493, -0.8747, -0.4373]) grad: 3.0 6.0 tensor([1.4542, 0.4847, 0.1616])progress: 91 0.0065271081402897835 grad: 1.0 2.0 tensor([0.3147, 0.3147, 0.3147]) grad: 2.0 4.0 tensor([-1.7466, -0.8733, -0.4367]) grad: 3.0 6.0 tensor([1.4510, 0.4837, 0.1612])progress: 92 0.00649801641702652 grad: 1.0 2.0 tensor([0.3150, 0.3150, 0.3150]) grad: 2.0 4.0 tensor([-1.7441, -0.8720, -0.4360]) grad: 3.0 6.0 tensor([1.4478, 0.4826, 0.1609])progress: 93 0.0064699104987084866 grad: 1.0 2.0 tensor([0.3153, 0.3153, 0.3153]) grad: 2.0 4.0 tensor([-1.7415, -0.8708, -0.4354]) grad: 3.0 6.0 tensor([1.4448, 0.4816, 0.1605])progress: 94 0.006442630663514137 grad: 1.0 2.0 tensor([0.3156, 0.3156, 0.3156]) grad: 2.0 4.0 tensor([-1.7391, -0.8695, -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。
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