PyTorch深度学习实践——4.反向传播＆作业
课程链接：《PyTorch深度学习实践》4.反向传播
思路：
1、先算损失loss
2、算反向传播 backward
loss.backward(): dloss \ dw == w.grad （Tensor）
3、更新权重w
w.data = w.data - 0.01 * w.grad.data
4、更新之后必须对权重w的梯度值（w.grad）清零，否则新的梯度值与之前的梯度值相加
w.grad.data.zero_()
课上示例
示例程序源代码+注释（根据个人理解）
import torch
x_data = [1.0, 2.0, 3.0]
y_data = [2.0, 4.0, 6.0]
w = torch.Tensor([1.0]) # w值为1.0
w.requires_grad = True # 需要计算梯度
def forward(x):
return x * w # w为Tensor类型，*为Tensor与Tensor之间的数乘，自动把x转换为Tensor类型
def loss(x, y):
y_pred = forward(x) # 求 y_hat
return (y_pred - y) ** 2 # 求损失 loss = (y_hat - y) ^ 2
print('Predict (before training)', 4, forward(4).item()) # 训练前 x = 4 时的 y_hat 值 (y_hat = 4 * w)
for epoch in range(100):
l = 0
for x, y in zip(x_data, y_data):
l = loss(x, y) # 前馈过程，只计算loss，loss(l)是Tensor类型的张量
l.backward() # 调用张量的成员函数 backward()，自动计算所有梯度，存到w里
print('\tgrad:', x, y, w.grad.item()) # 获得梯度 w.grad，用 .item() 将Tensor里的数值拿出来，作为Python的标量
w.data = w.data - 0.01 * w.grad.data # w.grad 是一个Tensor的张量，需要取data数值进行计算，不会建立计算图
# 计算时使用的Tensor张量，自动构建计算图，用于求反向传播（梯度）；而更新权重时，需要使用标量
w.grad.data.zero_() # 权重w中梯度的数据全都清零
print("progress:", epoch, l.item())
print('Predict (after training)', 4, forward(4).item()) # 训练后 x = 4 时的 y_hat 值 (y_hat = 4 * w)
输出结果：
Predict (before training) 4 4.0
grad: 1.0 2.0 -2.0
grad: 2.0 4.0 -7.840000152587891
grad: 3.0 6.0 -16.228801727294922
progress: 0 7.315943717956543
grad: 1.0 2.0 -1.478623867034912
grad: 2.0 4.0 -5.796205520629883
grad: 3.0 6.0 -11.998146057128906
progress: 1 3.9987640380859375
grad: 1.0 2.0 -1.0931644439697266
grad: 2.0 4.0 -4.285204887390137
grad: 3.0 6.0 -8.870372772216797
progress: 2 2.1856532096862793
grad: 1.0 2.0 -0.8081896305084229
grad: 2.0 4.0 -3.1681032180786133
grad: 3.0 6.0 -6.557973861694336
progress: 3 1.1946394443511963
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grad: 1.0 2.0 -7.152557373046875e-07
grad: 2.0 4.0 -2.86102294921875e-06
grad: 3.0 6.0 -5.7220458984375e-06
progress: 91 9.094947017729282e-13
grad: 1.0 2.0 -7.152557373046875e-07
grad: 2.0 4.0 -2.86102294921875e-06
grad: 3.0 6.0 -5.7220458984375e-06
progress: 92 9.094947017729282e-13
grad: 1.0 2.0 -7.152557373046875e-07
grad: 2.0 4.0 -2.86102294921875e-06
grad: 3.0 6.0 -5.7220458984375e-06
progress: 93 9.094947017729282e-13
grad: 1.0 2.0 -7.152557373046875e-07
grad: 2.0 4.0 -2.86102294921875e-06
grad: 3.0 6.0 -5.7220458984375e-06
progress: 94 9.094947017729282e-13
grad: 1.0 2.0 -7.152557373046875e-07
grad: 2.0 4.0 -2.86102294921875e-06
grad: 3.0 6.0 -5.7220458984375e-06
progress: 95 9.094947017729282e-13
grad: 1.0 2.0 -7.152557373046875e-07
grad: 2.0 4.0 -2.86102294921875e-06
grad: 3.0 6.0 -5.7220458984375e-06
progress: 96 9.094947017729282e-13
grad: 1.0 2.0 -7.152557373046875e-07
grad: 2.0 4.0 -2.86102294921875e-06
grad: 3.0 6.0 -5.7220458984375e-06
progress: 97 9.094947017729282e-13
grad: 1.0 2.0 -7.152557373046875e-07
grad: 2.0 4.0 -2.86102294921875e-06
grad: 3.0 6.0 -5.7220458984375e-06
progress: 98 9.094947017729282e-13
grad: 1.0 2.0 -7.152557373046875e-07
grad: 2.0 4.0 -2.86102294921875e-06
grad: 3.0 6.0 -5.7220458984375e-06
progress: 99 9.094947017729282e-13
Predict (after training) 4 7.999998569488525
注意：
使用.data避免构建计算图，仍是Tensor张量类型；
.item()将其转换成Python数值类型的标量。
简单来说：.data返回的扔是一个Tensor，而.item()返回的是一个具体的数值。
课后作业
补充知识：
torch.rand是均匀分布的随机变量
torch.randn是标准正太分布的随机变量
例如：
torch.randn(4)
tensor([-2.1436, 0.9966, 2.3426, -0.6366])
torch.randn(2, 3)
tensor([[1.5954, 2.8929, -1.0923],
[1.1719, -0.4709, -0.1996]])
import torch
x_data = [-3.0, -2.0, -1.0, 0.0, 1.0, 2.0, 3.0]
y_data = [12.0, 4.0, 0.0, 0.0, 4.0, 12.0]
w1 = torch.randn(1) # 标准正太分布的随机变量，一维向量
w1.requires_grad = True
w2 = torch.randn(1)
w2.requires_grad = True
b = torch.Tensor([0.0]) # 偏移量默认为0
b.requires_grad = True
def forward(x):
return w1 * (x ** 2) + w2 * x + b # 预设值为 w1 = 2, w2 = 2, b = 0
# y = 2 x^2 + 2x
def loss(x, y):
y_pred = forward(x)
return (y_pred - y) ** 2
print('Predict (before training)', 4, forward(4).item())
for epoch in range(100):
l = 0
for x, y in zip(x_data, y_data):
l = loss(x, y)
l.backward()
print('\tgrad:', x, y, w1.grad.item(), w2.grad.item(), b.grad.item())
w1.data = w1.data - 0.01 * w1.grad.data
w1.grad.data.zero_() # 必须要清零，否则会一直累加，梯度值变大
w2.data = w2.data - 0.01 * w2.grad.data
w2.grad.data.zero_()
b.data = b.data - 0.01 * b.grad.data
b.grad.data.zero_()
print("progress:", epoch, l.item())
print('Predict (after training)', 4, forward(4).item())
输出结果：
Predict (before training) 4 -8.422724723815918
grad: -3.0 12.0 -273.0215148925781 91.00717163085938 -30.335723876953125
grad: -2.0 4.0 62.68621826171875 -31.343109130859375 15.671554565429688
grad: -1.0 0.0 5.388011455535889 -5.388011455535889 5.388011455535889
grad: 0.0 0.0 0.0 0.0 0.18552318215370178
grad: 1.0 4.0 -6.306151866912842 -6.306151866912842 -6.306151866912842
grad: 2.0 12.0 -54.080047607421875 -27.040023803710938 -13.520011901855469
progress: 0 45.69768142700195
grad: -3.0 12.0 173.32583618164062 -57.7752799987793 19.258426666259766
grad: -2.0 4.0 -17.348819732666016 8.674409866333008 -4.337204933166504
grad: -1.0 0.0 1.5983614921569824 -1.5983614921569824 1.5983614921569824
grad: 0.0 0.0 0.0 0.0 0.24794435501098633
grad: 1.0 4.0 -6.50785493850708 -6.50785493850708 -6.50785493850708
grad: 2.0 12.0 -71.37567901611328 -35.68783950805664 -17.84391975402832
progress: 1 79.60137176513672
grad: -3.0 12.0 -4.573007583618164 1.5243358612060547 -0.5081119537353516
grad: -2.0 4.0 10.890235900878906 -5.445117950439453 2.7225589752197266
grad: -1.0 0.0 2.449244260787964 -2.449244260787964 2.449244260787964
grad: 0.0 0.0 0.0 0.0 0.6367471814155579
grad: 1.0 4.0 -3.773172378540039 -3.773172378540039 -3.773172378540039
grad: 2.0 12.0 -41.495018005371094 -20.747509002685547 -10.373754501342773
progress: 2 26.903696060180664
grad: -3.0 12.0 39.47118377685547 -13.157060623168945 4.385686874389648
grad: -2.0 4.0 1.5013236999511719 -0.7506618499755859 0.37533092498779297
grad: -1.0 0.0 1.7946186065673828 -1.7946186065673828 1.7946186065673828
grad: 0.0 0.0 0.0 0.0 0.7758380174636841
grad: 1.0 4.0 -2.782381534576416 -2.782381534576416 -2.782381534576416
grad: 2.0 12.0 -34.26860427856445 -17.134302139282227 -8.567151069641113
progress: 3 18.34902000427246
grad: -3.0 12.0 11.700010299682617 -3.900003433227539 1.3000011444091797
grad: -2.0 4.0 4.909320831298828 -2.454660415649414 1.227330207824707
grad: -1.0 0.0 1.7312746047973633 -1.7312746047973633 1.7312746047973633
grad: 0.0 0.0 0.0 0.0 0.9021397829055786
grad: 1.0 4.0 -1.7243456840515137 -1.7243456840515137 -1.7243456840515137
grad: 2.0 12.0 -23.89825439453125 -11.949127197265625 -5.9745635986328125
progress: 4 8.923852920532227
grad: -3.0 12.0 12.203630447387695 -4.067876815795898 1.3559589385986328
grad: -2.0 4.0 3.7686080932617188 -1.8843040466308594 0.9421520233154297
grad: -1.0 0.0 1.5178654193878174 -1.5178654193878174 1.5178654193878174
grad: 0.0 0.0 0.0 0.0 0.9617555737495422
grad: 1.0 4.0 -1.08040189743042 -1.08040189743042 -1.08040189743042
grad: 2.0 12.0 -18.039810180664062 -9.019905090332031 -4.509952545166016
progress: 5 5.084918022155762
grad: -3.0 12.0 5.502656936645508 -1.834218978881836 0.6114063262939453
grad: -2.0 4.0 4.105258941650391 -2.0526294708251953 1.0263147354125977
grad: -1.0 0.0 1.3971140384674072 -1.3971140384674072 1.3971140384674072
grad: 0.0 0.0 0.0 0.0 0.9936307668685913
grad: 1.0 4.0 -0.5791754722595215 -0.5791754722595215 -0.5791754722595215
grad: 2.0 12.0 -13.137199401855469 -6.568599700927734 -3.284299850463867
progress: 6 2.6966564655303955
grad: -3.0 12.0 3.1522178649902344 -1.0507392883300781 0.3502464294433594
grad: -2.0 4.0 3.869007110595703 -1.9345035552978516 0.9672517776489258
grad: -1.0 0.0 1.2755769491195679 -1.2755769491195679 1.2755769491195679
grad: 0.0 0.0 0.0 0.0 0.9991660714149475
grad: 1.0 4.0 -0.23718738555908203 -0.23718738555908203 -0.23718738555908203
grad: 2.0 12.0 -9.74737548828125 -4.873687744140625 -2.4368438720703125
progress: 7 1.484552025794983
grad: -3.0 12.0 0.6604156494140625 -0.2201385498046875 0.0733795166015625
grad: -2.0 4.0 3.7885818481445312 -1.8942909240722656 0.9471454620361328
grad: -1.0 0.0 1.1783339977264404 -1.1783339977264404 1.1783339977264404
grad: 0.0 0.0 0.0 0.0 0.9886861443519592
grad: 1.0 4.0 0.007760047912597656 0.007760047912597656 0.007760047912597656
grad: 2.0 12.0 -7.186729431152344 -3.593364715576172 -1.796682357788086
progress: 8 0.8070168495178223
grad: -3.0 12.0 -0.7919940948486328 0.26399803161621094 -0.08799934387207031
grad: -2.0 4.0 3.627819061279297 -1.8139095306396484 0.9069547653198242
grad: -1.0 0.0 1.09141206741333 -1.09141206741333 1.09141206741333
grad: 0.0 0.0 0.0 0.0 0.9664835333824158
grad: 1.0 4.0 0.17557430267333984 0.17557430267333984 0.17557430267333984
grad: 2.0 12.0 -5.3308868408203125 -2.6654434204101562 -1.3327217102050781
progress: 9 0.4440367817878723
grad: -3.0 12.0 -1.8829364776611328 0.6276454925537109 -0.2092151641845703
grad: -2.0 4.0 3.479217529296875 -1.7396087646484375 0.8698043823242188
grad: -1.0 0.0 1.0156728029251099 -1.0156728029251099 1.0156728029251099
grad: 0.0 0.0 0.0 0.0 0.9367715716362
grad: 1.0 4.0 0.2896747589111328 0.2896747589111328 0.2896747589111328
grad: 2.0 12.0 -3.9585723876953125 -1.9792861938476562 -0.9896430969238281
progress: 10 0.244848370552063
grad: -3.0 12.0 -2.576345443725586 0.8587818145751953 -0.28626060485839844
grad: -2.0 4.0 3.3186683654785156 -1.6593341827392578 0.8296670913696289
grad: -1.0 0.0 0.9478564262390137 -0.9478564262390137 0.9478564262390137
grad: 0.0 0.0 0.0 0.0 0.9022102355957031
grad: 1.0 4.0 0.3641386032104492 0.3641386032104492 0.3641386032104492
grad: 2.0 12.0 -2.952484130859375 -1.4762420654296875 -0.7381210327148438
progress: 11 0.13620565831661224
grad: -3.0 12.0 -3.0294971466064453 1.0098323822021484 -0.3366107940673828
grad: -2.0 4.0 3.160045623779297 -1.5800228118896484 0.7900114059448242
grad: -1.0 0.0 0.8868624567985535 -0.8868624567985535 0.8868624567985535
grad: 0.0 0.0 0.0 0.0 0.8648403286933899
grad: 1.0 4.0 0.41031837463378906 0.41031837463378906 0.41031837463378906
grad: 2.0 12.0 -2.2110671997070312 -1.1055335998535156 -0.5527667999267578
progress: 12 0.07638778537511826
grad: -3.0 12.0 -3.2939586639404297 1.0979862213134766 -0.3659954071044922
grad: -2.0 4.0 3.0024261474609375 -1.5012130737304688 0.7506065368652344
grad: -1.0 0.0 0.8313875794410706 -0.8313875794410706 0.8313875794410706
grad: 0.0 0.0 0.0 0.0 0.8260725736618042
grad: 1.0 4.0 0.4361400604248047 0.4361400604248047 0.4361400604248047
grad: 2.0 12.0 -1.6652374267578125 -0.8326187133789062 -0.4163093566894531
progress: 13 0.04332837089896202
grad: -3.0 12.0 -3.4293479919433594 1.1431159973144531 -0.3810386657714844
grad: -2.0 4.0 2.848804473876953 -1.4244022369384766 0.7122011184692383
grad: -1.0 0.0 0.7806005477905273 -0.7806005477905273 0.7806005477905273
grad: 0.0 0.0 0.0 0.0 0.7869192361831665
grad: 1.0 4.0 0.44751834869384766 0.44751834869384766 0.44751834869384766
grad: 2.0 12.0 -1.2624664306640625 -0.6312332153320312 -0.3156166076660156
progress: 14 0.02490346133708954
grad: -3.0 12.0 -3.4713878631591797 1.1571292877197266 -0.3857097625732422
grad: -2.0 4.0 2.69989013671875 -1.349945068359375 0.6749725341796875
grad: -1.0 0.0 0.7338007092475891 -0.7338007092475891 0.7338007092475891
grad: 0.0 0.0 0.0 0.0 0.7480815649032593
grad: 1.0 4.0 0.4487161636352539 0.4487161636352539 0.4487161636352539
grad: 2.0 12.0 -0.964874267578125 -0.4824371337890625 -0.24121856689453125
progress: 15 0.014546599239110947
grad: -3.0 12.0 -3.4488658905029297 1.1496219635009766 -0.3832073211669922
grad: -2.0 4.0 2.556568145751953 -1.2782840728759766 0.6391420364379883
grad: -1.0 0.0 0.6904639005661011 -0.6904639005661011 0.6904639005661011
grad: 0.0 0.0 0.0 0.0 0.7100420594215393
grad: 1.0 4.0 0.4428548812866211 0.4428548812866211 0.4428548812866211
grad: 2.0 12.0 -0.7444839477539062 -0.3722419738769531 -0.18612098693847656
progress: 16 0.008660254999995232
grad: -3.0 12.0 -3.381814956665039 1.1272716522216797 -0.37575721740722656
grad: -2.0 4.0 2.4192352294921875 -1.2096176147460938 0.6048088073730469
grad: -1.0 0.0 0.6501691341400146 -0.6501691341400146 0.6501691341400146
grad: 0.0 0.0 0.0 0.0 0.6731221079826355
grad: 1.0 4.0 0.4321928024291992 0.4321928024291992 0.4321928024291992
grad: 2.0 12.0 -0.580841064453125 -0.2904205322265625 -0.14521026611328125
progress: 17 0.005271505564451218
grad: -3.0 12.0 -3.2849807739257812 1.0949935913085938 -0.36499786376953125
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grad: 0.0 0.0 0.0 0.0 0.6375278234481812
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progress: 18 0.0032906816340982914
grad: -3.0 12.0 -3.1689376831054688 1.0563125610351562 -0.35210418701171875
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grad: -2.0 4.0 0.025928497314453125 -0.012964248657226562 0.006482124328613281
grad: -1.0 0.0 0.0068511334247887135 -0.0068511334247887135 0.0068511334247887135
grad: 0.0 0.0 0.0 0.0 0.007260804530233145
grad: 1.0 4.0 0.0051174163818359375 0.0051174163818359375 0.0051174163818359375
grad: 2.0 12.0 -0.0016632080078125 -0.00083160400390625 -0.000415802001953125
progress: 96 4.322282620705664e-08
grad: -3.0 12.0 -0.03836631774902344 0.012788772583007812 -0.0042629241943359375
grad: -2.0 4.0 0.0244903564453125 -0.01224517822265625 0.006122589111328125
grad: -1.0 0.0 0.006468663923442364 -0.006468663923442364 0.006468663923442364
grad: 0.0 0.0 0.0 0.0 0.006854990031570196
grad: 1.0 4.0 0.0048313140869140625 0.0048313140869140625 0.0048313140869140625
grad: 2.0 12.0 -0.00156402587890625 -0.000782012939453125 -0.0003910064697265625
progress: 97 3.822151484200731e-08
grad: -3.0 12.0 -0.03620338439941406 0.012067794799804688 -0.0040225982666015625
grad: -2.0 4.0 0.023113250732421875 -0.011556625366210938 0.005778312683105469
grad: -1.0 0.0 0.006106880493462086 -0.006106880493462086 0.006106880493462086
grad: 0.0 0.0 0.0 0.0 0.006471832282841206
grad: 1.0 4.0 0.004561424255371094 0.004561424255371094 0.004561424255371094
grad: 2.0 12.0 -0.00148773193359375 -0.000743865966796875 -0.0003719329833984375
progress: 98 3.4583536034915596e-08
grad: -3.0 12.0 -0.03414344787597656 0.011381149291992188 -0.0037937164306640625
grad: -2.0 4.0 0.021816253662109375 -0.010908126831054688 0.005454063415527344
grad: -1.0 0.0 0.005765250883996487 -0.005765250883996487 0.005765250883996487
grad: 0.0 0.0 0.0 0.0 0.006110093556344509
grad: 1.0 4.0 0.004305839538574219 0.004305839538574219 0.004305839538574219
grad: 2.0 12.0 -0.00140380859375 -0.000701904296875 -0.0003509521484375
progress: 99 3.079185262322426e-08
Predict (after training) 4 39.99186325073242