Understanding Gradient Calculation in PyTorch: Why You Might See "Gradients Not Calculated"

In deep learning with PyTorch, gradients are crucial for training models. They represent the sensitivity of the loss function (how much the loss changes) with respect to each model parameter (weight or bias). These gradients are used by optimizers like SGD (Stochastic Gradient Descent) to adjust the parameters in a direction that minimizes the loss.

Why Gradients Might Not Be Calculated

Here are common reasons why PyTorch might not calculate gradients for parameters:

1. requires_grad Not Set: PyTorch requires you to explicitly set the requires_grad attribute to True for parameters you want to train (update during backpropagation). If you forget this or set it to False, gradients won't be calculated for those parameters.

   import torch
   
   # Example: Set requires_grad to True for parameters to be trained
   model = torch.nn.Linear(10, 5)
   for param in model.parameters():
       param.requires_grad = True
   

2. Loss Not Backpropagated: You need to call the loss.backward() method on your loss function to trigger the backward pass (backpropagation) that calculates gradients. If you don't call backward(), gradients won't be computed.

   # Example: Backpropagate gradients using loss.backward()
   loss = criterion(output, target)
   loss.backward()
   

Troubleshooting Tips

• Check for requires_grad: Verify that requires_grad is set to True for the parameters you intend to train.
• Ensure loss.backward() Call: Make sure you're calling loss.backward() after calculating the loss to trigger gradient calculation.
• Inspect Parameter Gradients: Use param.grad to check if gradients are indeed being calculated for your parameters. If they're None, there's a problem.

import torch

# Model without requires_grad set (parameters won't be trained)
model = torch.nn.Linear(10, 5)

# Forward pass
input = torch.randn(1, 10)
output = model(input)

# Loss calculation (but gradients won't be computed)
loss = torch.nn.functional.mse_loss(output, torch.ones(1, 5))

# Optimizer won't update parameters because gradients are None
optimizer = torch.optim.SGD(model.parameters(), lr=0.1)
optimizer.zero_grad()
loss.backward()  # Gradients won't be calculated here (because requires_grad is not set)
optimizer.step()

print(model.weight.grad)  # This will likely be None

Scenario 2: Missing loss.backward()

import torch

model = torch.nn.Linear(10, 5)
for param in model.parameters():
    param.requires_grad = True

# Forward pass
input = torch.randn(1, 10)
output = model(input)

# Loss calculation, but backward pass not triggered
loss = torch.nn.functional.mse_loss(output, torch.ones(1, 5))

# Optimizer won't update parameters because gradients are not calculated
optimizer = torch.optim.SGD(model.parameters(), lr=0.1)
optimizer.zero_grad()
# loss.backward() is missing here!
optimizer.step()

print(model.weight.grad)  # This will likely be None

Correct Code (Gradients Calculated):

import torch

model = torch.nn.Linear(10, 5)
for param in model.parameters():
    param.requires_grad = True

# Forward pass
input = torch.randn(1, 10)
output = model(input)

# Loss calculation and backward pass to calculate gradients
loss = torch.nn.functional.mse_loss(output, torch.ones(1, 5))
loss.backward()

# Optimizer can now update parameters using calculated gradients
optimizer = torch.optim.SGD(model.parameters(), lr=0.1)
optimizer.zero_grad()
optimizer.step()

print(model.weight.grad)  # This will now show the calculated gradients

• This involves calculating gradients by hand using mathematical formulas. It's generally less efficient than autograd but can be useful for understanding the underlying concepts or for very simple models. Here's a basic example (not recommended for practical use):

import torch

def mse_loss(y_pred, y_true):
  return 0.5 * (y_pred - y_true) ** 2

def linear_forward(x, w, b):
  return torch.mm(x, w) + b

def linear_backward(y_pred, y_true, x):
  # Manual gradient calculation for linear layer
  dw = torch.mm(x.T, y_pred - y_true)
  db = torch.sum(y_pred - y_true)
  return dw, db

# Example usage
x = torch.randn(1, 2)
w = torch.randn(2, 3)
b = torch.randn(3)

y_pred = linear_forward(x, w, b)
loss = mse_loss(y_pred, torch.ones(1, 3))

dw, db = linear_backward(y_pred, torch.ones(1, 3), x)

# Update weights and bias manually (not using optimizer)
w -= 0.1 * dw
b -= 0.1 * db

Symbolic Differentiation Libraries:

Finite Difference Approximation:

• This approach involves numerically estimating the gradient by calculating the change in loss with respect to a small change in the parameter value. It's less accurate than autograd and can be computationally expensive.

Important Considerations:

• Autograd is generally the preferred method due to its efficiency and ease of use.
• Manual differentiation and symbolic libraries are more for educational purposes or specific use cases where autograd might not be suitable.
• Finite difference approximation should be used cautiously due to its limitations.