PyTorchの自動微分

In [1]:

    

import numpy as np
import torch
import torch.nn as nn
from torch.autograd import Variable


    

In [2]:

    

# テンソルを作成
# Variableはgradプロパティを持ち自動微分の対象になる
# requires_grad=Falseだと微分の対象にならず勾配はNoneが返る
x = Variable(torch.Tensor([1]), requires_grad=True)
w = Variable(torch.Tensor([2]), requires_grad=True)
b = Variable(torch.Tensor([3]), requires_grad=True)

# 計算グラフを構築
# y = 2 * x + 3
y = w * x + b

# 勾配を計算
y.backward()

# 勾配を表示
print(x.grad)  # dy/dx = w = 2
print(w.grad)  # dy/dw = x = 1
print(b.grad)  # dy/db = 1


    

    




Variable containing:
 2
[torch.FloatTensor of size 1]

Variable containing:
 1
[torch.FloatTensor of size 1]

Variable containing:
 1
[torch.FloatTensor of size 1]

In [3]:

    

x = Variable(torch.Tensor([2]), requires_grad=True)
y = x ** 2
y.backward()
print(x.grad)


    

    




Variable containing:
 4
[torch.FloatTensor of size 1]

In [4]:

    

x = Variable(torch.Tensor([2]), requires_grad=True)
y = torch.exp(x)
y.backward()
print(x.grad)


    

    




Variable containing:
 7.3891
[torch.FloatTensor of size 1]

In [5]:

    

x = Variable(torch.Tensor([np.pi]), requires_grad=True)
y = torch.sin(x)
y.backward()
print(x.grad)


    

    




Variable containing:
-1
[torch.FloatTensor of size 1]

In [6]:

    

x = Variable(torch.Tensor([0]), requires_grad=True)
y = (x - 4) * (x ** 2 + 6)
y.backward()
print(x.grad)


    

    




Variable containing:
 6
[torch.FloatTensor of size 1]

In [7]:

    

x = Variable(torch.Tensor([2]), requires_grad=True)
y = (torch.sqrt(x) + 1) ** 3
y.backward()
print(x.grad)


    

    




Variable containing:
 6.1820
[torch.FloatTensor of size 1]

In [8]:

    

x = Variable(torch.Tensor([1]), requires_grad=True)
y = Variable(torch.Tensor([2]), requires_grad=True)
z = (x + 2 * y) ** 2
z.backward()
print(x.grad)  # dz/dx
print(y.grad)  # dz/dy


    

    




Variable containing:
 10
[torch.FloatTensor of size 1]

Variable containing:
 20
[torch.FloatTensor of size 1]

In [9]:

    

# バッチサンプル数=5、入力特徴量の次元数=3
x = Variable(torch.randn(5, 3))
# バッチサンプル数=5、出力特徴量の次元数=2
y = Variable(torch.randn(5, 2))

# Linear層を作成
# 3ユニット => 2ユニット
linear = nn.Linear(3, 2)

# Linear層のパラメータ
print('w:', linear.weight)
print('b:', linear.bias)

# lossとoptimizer
criterion = nn.MSELoss()
optimizer = torch.optim.SGD(linear.parameters(), lr=0.01)

# forward
pred = linear(x)

# loss = L
loss = criterion(pred, y)
print('loss:', loss)

# backpropagation
loss.backward()

# 勾配を表示
print('dL/dw:', linear.weight.grad)
print('dL/db:', linear.bias.grad)

# 勾配を用いてパラメータを更新
print('*** by hand')
print(linear.weight.sub(0.01 * linear.weight.grad))
print(linear.bias.sub(0.01 * linear.bias.grad))

# 勾配降下法
optimizer.step()

# 1ステップ更新後のパラメータを表示
# 上の式と結果が一致することがわかる
print('*** by optimizer.step()')
print(linear.weight)
print(linear.bias)


    

    




w: Parameter containing:
 0.4997 -0.5219 -0.4392
 0.3093  0.1686 -0.4614
[torch.FloatTensor of size 2x3]

b: Parameter containing:
 0.4723
-0.4395
[torch.FloatTensor of size 2]

loss: Variable containing:
 1.3311
[torch.FloatTensor of size 1]

dL/dw: Variable containing:
 0.1397 -0.8410 -0.2321
 0.8261  0.3623 -0.4528
[torch.FloatTensor of size 2x3]

dL/db: Variable containing:
 0.9104
-0.2471
[torch.FloatTensor of size 2]

*** by hand
Variable containing:
 0.4983 -0.5135 -0.4369
 0.3010  0.1650 -0.4569
[torch.FloatTensor of size 2x3]

Variable containing:
 0.4632
-0.4370
[torch.FloatTensor of size 2]

*** by optimizer.step()
Parameter containing:
 0.4983 -0.5135 -0.4369
 0.3010  0.1650 -0.4569
[torch.FloatTensor of size 2x3]

Parameter containing:
 0.4632
-0.4370
[torch.FloatTensor of size 2]