What if, at training time, we also backpropagate on the input data?

hello,everyone. I came across a strange mistake that drove me crazy.In linear regression,I set inputs X’s grad=True,and there was an error in the second backpropagation.Here is my code:

import random
import torch
from d2l import torch as d2l


def synthetic_data(w, b, num_examples):  # @save
    """生成y=Xw+b+噪声"""
    X = torch.normal(0, 1, (num_examples, len(w)), requires_grad=True)
    y = torch.matmul(X, w) + b
    y += torch.normal(0, 0.01, y.shape)
    return X, y.reshape((-1, 1))


true_w = torch.tensor([2, -3.4])
true_b = 4.2
features, labels = synthetic_data(true_w, true_b, 20)


def data_iter(batch_size, features, labels):
    num_examples = len(features)
    indices = list(range(num_examples))
    # 这些样本是随机读取的,没有特定的顺序
    random.shuffle(indices)
    for i in range(0, num_examples, batch_size):
        batch_indices = torch.tensor(
            indices[i: min(i + batch_size, num_examples)])
        yield features[batch_indices], labels[batch_indices]


w = torch.normal(0, 0.01, size=(2, 1), requires_grad=True)
b = torch.zeros(1, requires_grad=True)


def linreg(X, w, b):  # @save
    """线性回归模型"""
    return torch.matmul(X, w) + b


def squared_loss(y_hat, y):  # @save
    """均方损失"""
    return (y_hat - y.reshape(y_hat.shape)) ** 2 / 2


def sgd(params, lr, batch_size):  # @save
    """小批量随机梯度下降"""
    with torch.no_grad():
        for param in params:
            param -= lr * param.grad / batch_size
            param.grad.zero_()


lr = 0.03
num_epochs = 3
net = linreg
loss = squared_loss
batch_size = 10

for epoch in range(num_epochs):
    for X, y in data_iter(batch_size, features, labels):
        l = loss(net(X, w, b), y)  # X和y的小批量损失
        # 因为l形状是(batch_size,1),而不是一个标量。l中的所有元素被加到一起,
        # 并以此计算关于[w,b]的梯度
        l.sum().backward()
        sgd([w, b], lr, batch_size)  # 使用参数的梯度更新参数
    with torch.no_grad():
        train_l = loss(net(features, w, b), labels)
        print(f'epoch {epoch + 1}, loss {float(train_l.mean()):f}')

and I notice that the error appears in second backward,here is error:
RuntimeError: Trying to backward through the graph a second time (or directly access saved tensors after they have already been freed). Saved intermediate values of the graph are freed when you call .backward() or autograd.grad(). Specify retain_graph=True if you need to backward through the graph a second time or if you need to access saved tensors after calling backward.

Your code is unfortunately not properly formatted and thus not executable.
Could you post a minimal and executable code snippet to reproduce the issue by wrapping them into three backticks ```?

ok.My code is here:

import random
import torch
from d2l import torch as d2l


def synthetic_data(w, b, num_examples):  # @save
    """生成y=Xw+b+噪声"""
    X = torch.normal(0, 1, (num_examples, len(w)), requires_grad=True)
    y = torch.matmul(X, w) + b
    y += torch.normal(0, 0.01, y.shape)
    return X, y.reshape((-1, 1))


true_w = torch.tensor([2, -3.4])
true_b = 4.2
features, labels = synthetic_data(true_w, true_b, 20)


def data_iter(batch_size, features, labels):
    num_examples = len(features)
    indices = list(range(num_examples))
    # 这些样本是随机读取的,没有特定的顺序
    random.shuffle(indices)
    for i in range(0, num_examples, batch_size):
        batch_indices = torch.tensor(
            indices[i: min(i + batch_size, num_examples)])
        yield features[batch_indices], labels[batch_indices]


w = torch.normal(0, 0.01, size=(2, 1), requires_grad=True)
b = torch.zeros(1, requires_grad=True)


def linreg(X, w, b):  # @save
    """线性回归模型"""
    return torch.matmul(X, w) + b


def squared_loss(y_hat, y):  # @save
    """均方损失"""
    return (y_hat - y.reshape(y_hat.shape)) ** 2 / 2


def sgd(params, lr, batch_size):  # @save
    """小批量随机梯度下降"""
    with torch.no_grad():
        for param in params:
            param -= lr * param.grad / batch_size
            param.grad.zero_()


lr = 0.03
num_epochs = 3
net = linreg
loss = squared_loss
batch_size = 10

for epoch in range(num_epochs):
    for X, y in data_iter(batch_size, features, labels):
        l = loss(net(X, w, b), y)  # X和y的小批量损失
        # 因为l形状是(batch_size,1),而不是一个标量。l中的所有元素被加到一起,
        # 并以此计算关于[w,b]的梯度
        l.sum().backward()
        sgd([w, b], lr, batch_size)  # 使用参数的梯度更新参数
    with torch.no_grad():
        train_l = loss(net(features, w, b), labels)
        print(f'epoch {epoch + 1}, loss {float(train_l.mean()):f}')

Thanks for the code!
The issue is caused by using a non-leaf target tensor, which contains a gradient history.
Using l = loss(net(X, w, b), y.detach()) fixes the error.
To avoid it entirely you should check if you really want to initialize the input X with requires_grad=True (as it’s uncommon) and create the target y in a no_grad() context as the target is usually static.

Thank you! Actually,If you want to fix the bug,It seems that it’s easy.But I want to know why this error happens? Yesterday,I use the function make_dot which is in torchviz package to print the graph visualizations pass the backward.And find the reason.
Thanks again for your reply and help.Best wishes!!