Python 如何有效地计算所有输出相对于参数的梯度

我有一个相对简单的要求，但令人惊讶的是，这似乎并不是在pytorch中直接实现的.假设一个带有$P$参数的神经网络输出长度为$Y$的矢量和一批$B$数据输入，我想计算输出相对于模型参数的梯度.

换句话说，我想要以下函数:

def calculate_gradients(model, X):
    """
    Args:
        nn module with P parameters in total that outputs a tensor of size (B, Y).
        torch tensor of shape (B, .).

    Returns:
        torch tensor of shape (B, Y, P)
    """
    # function logic here

不幸的是，我目前还看不到一种明显的有效计算方法，特别是在不对数据或目标维度进行聚合的情况下.下面的一个最小的工作示例涉及在输入和目标维度上循环，但肯定有更有效的方法？

import torch
from torchvision import datasets, transforms
import torch.nn as nn

###### SETUP ######

class MLP(nn.Module):
    def __init__(self, input_size, hidden_size, output_size):
        super(MLP, self).__init__()
        self.fc1 = nn.Linear(input_size, hidden_size)
        self.relu = nn.ReLU()
        self.fc2 = nn.Linear(hidden_size, output_size)
        
    def forward(self, x):
        h = self.fc1(x)
        pred = self.fc2(self.relu(h))
        return pred
    
train_dataset = datasets.MNIST(root='./data', train=True, download=True, 
                            transform=transforms.Compose(
                                [transforms.ToTensor(),
                                    transforms.Normalize((0.5,), (0.5,))
        ]))

train_dataloader = torch.utils.data.DataLoader(train_dataset, batch_size=2, shuffle=False)

X, y = next(iter(train_dataloader))  # take a random batch of data

net = MLP(28*28, 20, 10)  # define a network


###### CALCULATE GRADIENTS ######
def calculate_gradients(model, X):
    # Create a tensor to hold the gradients
    gradients = torch.zeros(X.shape[0], 10, sum(p.numel() for p in model.parameters()))

    # Calculate the gradients for each input and target dimension
    for i in range(X.shape[0]):
        for j in range(10):
            model.zero_grad()
            output = model(X[i])
            # Calculate the gradients
            grads = torch.autograd.grad(output[j], model.parameters())
            # Flatten the gradients and store them
            gradients[i, j, :] = torch.cat([g.view(-1) for g in grads])
            
    return gradients

grads = calculate_gradients(net, X.view(X.shape[0], -1))

Edit:个 我对Felix Zimmermann的解决方案运行了一些快速基准测试，它确实为我的机器上的这个玩具问题提供了一些很好的加速.

import time

start = time.time()
for _ in range(1000):
    grads = calculate_gradients(net, X.view(X.shape[0], -1))
end = time.time()
print('Loop solution', end - start)

start = time.time()
for _ in range(1000):
    params = {k: v.detach() for k, v in net.named_parameters()}
    buffers = {k: v.detach() for k, v in net.named_buffers()}
    grads2 = torch.vmap(one_sample)(X.flatten(1))
end = time.time()
print('Vmap solution', end - start)

哪一项输出

Loop solution 8.408899307250977
Vmap solution 2.355229139328003

请注意，在更现实的环境中，GPU上的批次更大，性能提升可能会更大.