# 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)

def linreg(X, w, b):  # @save
"""线性回归模型"""

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"""
for param in params:
param -= lr * param.grad / batch_size

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
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)

def linreg(X, w, b):  # @save
"""线性回归模型"""

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"""
for param in params:
param -= lr * param.grad / batch_size

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
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.