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Backpropagation Simplified with `torch.autograd.backward()` in PyTorch

Last updated: December 14, 2024

In the realm of neural networks, backpropagation is the essential algorithm for training neural networks via gradient descent. It efficiently computes the gradient of the loss function with respect to the weights of the network. PyTorch, a popular machine learning library, provides an elegant and comprehensive tool for this task called torch.autograd.backward().

PyTorch's autograd, short for automatic differentiation, is a system to compute gradients - a crucial component for training neural networks. It records operations performed on tensors to create a computational graph which allows for easy gradient calculation. In this article, we'll delve into backpropagation using torch.autograd.backward(), making it simpler to understand and apply.

The Basics of Backpropagation

Before diving into code, let's recap the backpropagation process. It involves three critical steps:

  1. Forward Pass: Compute the output of the network and the loss value.
  2. Backward Pass: Compute gradients (partial derivatives of the loss concerning each parameter) using the chain rule.
  3. Parameter Update: Adjust the network's parameters by a small amount in the direction that reduces the loss.

Setting Up PyTorch

First, ensure you have PyTorch installed. You can install it using pip:

pip install torch

Computing Gradients with torch.autograd

Let's walk through a simple example demonstrating the use of torch.autograd.backward(). Consider a single-layer neural network that models a simple linear equation: y = x * w + b, where x is the input, w is the weight, and b is the bias.

import torch
torch.manual_seed(0)

# Inputs and True outputs
x = torch.tensor([1.0, 2.0, 3.0], requires_grad=False)
true_y = torch.tensor([2.0, 4.0, 6.0], requires_grad=False)

# Parameters: initially random values
w = torch.tensor(0.0, requires_grad=True)
b = torch.tensor(0.0, requires_grad=True)

# Learning rate
lr = 0.01

Perform a forward pass to compute the predicted value and loss with a simple mean squared error:

# Forward pass: compute predicted y and the loss
def forward(x, w, b):
    return x * w + b

y_pred = forward(x, w, b)

# Loss calculation
loss = ((y_pred - true_y) ** 2).mean()
print(f'Initial loss: {loss.item()}')  # Prints the initial loss

Next, execute the backward pass using torch.autograd.backward() to compute gradients:

# Compute gradients using backpropagation
loss.backward()

# Print the gradients
print(f'Gradient of w: {w.grad}')
print(f'Gradient of b: {b.grad}')

Finally, update parameters using the computed gradients and repeat the forward and backward passes over multiple epochs:

# Training loop
for epoch in range(100):
    # Forward pass
    y_pred = forward(x, w, b)
    loss = ((y_pred - true_y) ** 2).mean()

    # Backward pass
    loss.backward()

    # Update parameters
    with torch.no_grad():
        w -= lr * w.grad
        b -= lr * b.grad
        # Manually zero the gradients after updating
        w.grad.zero_()
        b.grad.zero_()

    if epoch % 10 == 0:
        print(f'Epoch {epoch} loss: {loss.item()}')

Here, torch.no_grad() is used to prevent gradient tracking during the update phase. Each parameter is updated according to its respective gradient, adjusted by the learning rate.

Key Takeaways

The function torch.autograd.backward() is an extremely useful tool that makes calculating the backpropagation gradients straightforward. PyTorch abstracts many of the manual calculations involved with backpropagation, thereby helping developers focus more on model architecture and less on the intricate details of gradient computation.

By simplifying the calculations required to update model weights, PyTorch accelerates the process of building and training neural networks, supporting developers from initial research experiments to deploying sophisticated deep learning models. Understanding the basics shown here will enable you to dive into more advanced deep learning setups confidently.

Next Article: A Guide to Checking CUDA Availability with `torch.cuda.is_available()` in PyTorch

Previous Article: An Introduction to Automatic Differentiation with `torch.autograd.grad()` in PyTorch

Series: Working with Tensors in PyTorch

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