Backward pass (loss.backward) in PyTorch

Introduction

The backward pass calculates how much each part of the model contributed to the error. This helps the model learn by adjusting itself to make better predictions.

When training a neural network to update its weights.

After calculating the loss to find gradients for optimization.

When you want to perform gradient descent to improve model accuracy.

To compute gradients for all parameters before calling the optimizer step.

Syntax

PyTorch

loss.backward()

This function computes gradients of the loss with respect to model parameters.

It must be called after computing the loss and before updating weights.

Examples

Calculate loss and then compute gradients for all model parameters.

PyTorch

loss = criterion(output, target)
loss.backward()

Use a functional loss and then call backward to get gradients.

PyTorch

loss = torch.nn.functional.mse_loss(predictions, labels)
loss.backward()

Sample Model

This code shows a simple linear model learning to fit points. It calculates loss, calls loss.backward() to get gradients, prints them, updates weights, and shows loss improvement.

PyTorch

import torch
import torch.nn as nn
import torch.optim as optim

# Simple linear model
model = nn.Linear(1, 1)

# Sample input and target
x = torch.tensor([[1.0], [2.0], [3.0]])
y = torch.tensor([[2.0], [4.0], [6.0]])

# Mean squared error loss
criterion = nn.MSELoss()

# Optimizer
optimizer = optim.SGD(model.parameters(), lr=0.1)

# Forward pass
output = model(x)

# Compute loss
loss = criterion(output, y)
print(f"Loss before backward: {loss.item():.4f}")

# Backward pass to compute gradients
loss.backward()

# Print gradients of model parameters
for name, param in model.named_parameters():
    print(f"Gradients for {name}: {param.grad}")

# Update weights
optimizer.step()

# Forward pass after update
output2 = model(x)
loss2 = criterion(output2, y)
print(f"Loss after one update: {loss2.item():.4f}")

Important Notes

Always zero gradients before backward pass if running multiple iterations: optimizer.zero_grad().

Calling loss.backward() accumulates gradients, so clear them to avoid mixing.

Summary

Backward pass computes gradients needed to update model weights.

Call loss.backward() after computing loss.

Use gradients with an optimizer to improve model predictions.

Practice

1. What does the loss.backward() function do in PyTorch?

easy

A. It computes gradients of the loss with respect to model parameters.

B. It updates the model weights directly.

C. It calculates the loss value from predictions and targets.

D. It initializes the model parameters.

Solution

1. Step 1: Understand the role of loss.backward()

   This function computes gradients needed for updating model weights by backpropagation.

2. Step 2: Differentiate from other functions

   Updating weights is done by the optimizer, not loss.backward(). Calculating loss or initializing parameters are separate steps.

3. Final Answer:

   It computes gradients of the loss with respect to model parameters. -> Option A

4. Quick Check:

   Backward pass = compute gradients [OK]

Hint: Remember: backward() computes gradients, optimizer updates weights [OK]

Common Mistakes:

• Confusing backward() with optimizer step
• Thinking backward() calculates loss value
• Assuming backward() initializes parameters

2. Which of the following is the correct way to call the backward pass on a loss tensor named loss in PyTorch?

easy

A. loss.backwards()

B. loss.backward()

C. loss.backwarded()

D. loss.backward_pass()

Solution

1. Step 1: Recall PyTorch syntax for backward pass

   The correct method to compute gradients is loss.backward().

2. Step 2: Identify incorrect method names

   Other options are invalid method names and will cause errors.

3. Final Answer:

   loss.backward() -> Option B

4. Quick Check:

   Correct method name = backward() [OK]

Hint: Use exact method name: backward() with no extra letters [OK]

Common Mistakes:

• Adding extra letters or suffixes to backward
• Using plural form backwards
• Confusing method name with optimizer step

3. Consider the following PyTorch code snippet:

import torch
x = torch.tensor(2.0, requires_grad=True)
y = x ** 3
loss = y
loss.backward()
print(x.grad)

What will be the output of print(x.grad)?

medium

A. tensor(0.)

B. tensor(8.)

C. tensor(6.)

D. tensor(12.)

Solution

1. Step 1: Compute the derivative of y = x^3 at x=2

   The derivative dy/dx = 3 * x^2. At x=2, this is 3 * 4 = 12.

2. Step 2: Understand backward() computes this gradient

   Calling loss.backward() computes and stores this gradient in x.grad.

3. Final Answer:

   tensor(12.) -> Option D

4. Quick Check:

   Derivative of x^3 at 2 = 12 [OK]

Hint: Derivative of x^3 is 3x^2; plug in x=2 [OK]

Common Mistakes:

• Calculating derivative incorrectly as 8 or 6
• Forgetting to set requires_grad=True
• Not calling loss.backward() before accessing grad

4. What is the error in the following PyTorch code snippet?

import torch
x = torch.tensor(3.0, requires_grad=True)
y = x * 2
loss = y
# Missing backward call
print(x.grad)

medium

A. x.grad will be zero tensor automatically.

B. SyntaxError because backward() is missing.

C. x.grad will be None because backward() was not called.

D. RuntimeError because loss is not scalar.

Solution

1. Step 1: Identify missing backward() call

   The code does not call loss.backward(), so gradients are not computed.

2. Step 2: Understand gradient attribute behavior

   Without backward(), x.grad remains None, not zero or error.

3. Final Answer:

   x.grad will be None because backward() was not called. -> Option C

4. Quick Check:

   No backward() means no gradients [OK]

Hint: Always call loss.backward() before checking .grad [OK]

Common Mistakes:

• Expecting zero tensor instead of None
• Thinking missing backward() causes syntax error
• Assuming RuntimeError for non-scalar loss here

5. You have a model with parameters and a loss computed. You call loss.backward() twice in a row without zeroing gradients in between. What will happen to the gradients stored in the parameters?

hard

A. Gradients will accumulate, doubling the values from one backward call.

B. Gradients will reset to zero before the second backward call.

C. An error will be raised because backward() cannot be called twice.

D. Gradients will be overwritten by the second backward call.

Solution

1. Step 1: Understand gradient accumulation in PyTorch

   By default, gradients accumulate in the .grad attribute when backward() is called multiple times.

2. Step 2: Effect of calling backward() twice without zeroing

   Calling backward() twice adds gradients twice, effectively doubling them.

3. Final Answer:

   Gradients will accumulate, doubling the values from one backward call. -> Option A

4. Quick Check:

   Multiple backward calls add gradients [OK]

Hint: Call optimizer.zero_grad() to reset gradients before backward() [OK]

Common Mistakes:

• Assuming gradients reset automatically
• Expecting an error on second backward call
• Thinking gradients overwrite instead of accumulate