What is autograd in PyTorch and how does it compute gradients?

PyTorch's autograd engine implements automatic differentiation. When you perform operations on tensors with requires_grad=True, PyTorch records every operation in a dynamic computation graph. Calling .backward() on a scalar loss traverses this graph in reverse using the chain rule, accumulating gradients in each tensor's .grad attribute.

import torch

# requires_grad=True tells PyTorch to track this tensor
x = torch.tensor([2.0, 3.0], requires_grad=True)

# Forward pass — operations are recorded
y = x ** 2           # y = [4.0, 9.0]
z = y.sum()          # z = 13.0  (scalar)

# Backward pass — computes dz/dx using chain rule
z.backward()
print(x.grad)        # tensor([4., 6.])  dz/dx = 2x

# Verify: dz/d(x[0]) = d(x[0]^2)/d(x[0]) = 2*x[0] = 4 ✓

# Gradients ACCUMULATE — always zero before next backward!
x.grad.zero_()   # or optimizer.zero_grad()

# Non-leaf tensors (created by ops) have grad_fn
a = torch.tensor(3.0, requires_grad=True)
b = a * 2
print(b.grad_fn)       # <MulBackward0 object>
print(b.requires_grad) # True — inherited from a

# Detach: stop tracking a tensor
c = b.detach()         # c shares data with b but no grad history
print(c.requires_grad) # False

# torch.no_grad(): context manager to disable gradient tracking
with torch.no_grad():
    inference = a * 2   # faster, no graph built
    print(inference.requires_grad)  # False

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