在损失函数中点张量时不存在的 pytorch 梯度

Question

出于此 MWE 的目的，我尝试使用具有多个项的自定义损失函数来拟合线性回归。但是，当我试图通过在损失函数中点缀权重向量来对损失函数中的不同项进行加权时，我运行陷入了奇怪的行为。只需将损失相加就可以按预期工作；然而，当点权重和损失时，反向传播以某种方式被破坏并且损失函数没有减少。

我尝试在两个张量上启用和禁用 requires_grad，但无法复制预期的行为。

import torch
import torch.nn as nn
import numpy as np
import matplotlib.pyplot as plt


# Hyper-parameters
input_size = 1
output_size = 1
num_epochs = 60
learning_rate = 0.001

# Toy dataset
x_train = np.array([[3.3], [4.4], [5.5], [6.71], [6.93], [4.168], 
                    [9.779], [6.182], [7.59], [2.167], [7.042], 
                    [10.791], [5.313], [7.997], [3.1]], dtype=np.float32)

y_train = np.array([[1.7], [2.76], [2.09], [3.19], [1.694], [1.573], 
                    [3.366], [2.596], [2.53], [1.221], [2.827], 
                    [3.465], [1.65], [2.904], [1.3]], dtype=np.float32)

# Linear regression model
model = nn.Linear(input_size, output_size)

# Loss and optimizer
optimizer = torch.optim.SGD(model.parameters(), lr=learning_rate)  

def loss_fn(outputs, targets):
    l1loss = torch.norm(outputs - targets, 1)
    l2loss = torch.norm(outputs - targets, 2)

    # This works as expected
    # loss = 1 * l1loss + 1 * l2loss
    # Loss never changes, no matter what combination of
    # requires_grad I set
    loss = torch.dot(torch.tensor([1.0, 1.0], requires_grad=False),
            torch.tensor([l1loss, l2loss], requires_grad=True))
    return loss

# Train the model
for epoch in range(num_epochs):
    # Convert numpy arrays to torch tensors
    inputs = torch.from_numpy(x_train)
    targets = torch.from_numpy(y_train)

    # Forward pass
    outputs = model(inputs)
    loss = loss_fn(outputs, targets)

    # Backward and optimize
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()

    if (epoch+1) % 5 == 0:
        print ('Epoch [{}/{}], Loss: {:.4f}'.format(epoch+1, num_epochs, loss.item()))

# Plot the graph
predicted = model(torch.from_numpy(x_train)).detach().numpy()
plt.plot(x_train, y_train, 'ro', label='Original data')
plt.plot(x_train, predicted, label='Fitted line')
plt.legend()
plt.show()

预期结果：损失函数减小，线性回归拟合（见下面的输出）

Epoch [5/60], Loss: 7.9943
Epoch [10/60], Loss: 7.7597
Epoch [15/60], Loss: 7.6619
Epoch [20/60], Loss: 7.6102
Epoch [25/60], Loss: 7.4971
Epoch [30/60], Loss: 7.4106
Epoch [35/60], Loss: 7.3942
Epoch [40/60], Loss: 7.2438
Epoch [45/60], Loss: 7.2322
Epoch [50/60], Loss: 7.1012
Epoch [55/60], Loss: 7.0701
Epoch [60/60], Loss: 6.9612

实际结果：损失函数没有变化

Epoch [5/60], Loss: 73.7473
Epoch [10/60], Loss: 73.7473
Epoch [15/60], Loss: 73.7473
Epoch [20/60], Loss: 73.7473
Epoch [25/60], Loss: 73.7473
Epoch [30/60], Loss: 73.7473
Epoch [35/60], Loss: 73.7473
Epoch [40/60], Loss: 73.7473
Epoch [45/60], Loss: 73.7473
Epoch [50/60], Loss: 73.7473
Epoch [55/60], Loss: 73.7473
Epoch [60/60], Loss: 73.7473

我很困惑为什么这样一个简单的操作会破坏反向传播梯度，如果有人对为什么这不起作用有一些见解，我将不胜感激。

Answer 1

使用 torch.cat((loss1, loss2))，您正在从现有张量破坏图创建新张量。

无论如何你不应该这样做，除非你试图概括你的损失函数，它是非常不可读的。简单加法方式更好。

在损失函数中点张量时不存在的 pytorch 梯度

Nonexistant pytorch gradients when dotting tensors in loss function

python

machine-learning

neural-network

pytorch

autograd