How does broadcasting work in PyTorch and what are the rules?

Broadcasting allows PyTorch to perform arithmetic between tensors of different shapes without explicit copying. PyTorch follows the same broadcasting rules as NumPy. Understanding broadcasting is essential to avoid subtle shape bugs.

import torch

# Rule: align shapes from the RIGHT, expand dims of size 1
a = torch.ones(3, 4)     # shape (3, 4)
b = torch.ones(4)        # shape    (4) → treated as (1, 4) → broadcast to (3, 4)
c = a + b                # works! c.shape = (3, 4)

# Adding a bias vector to a batch of activations
batch = torch.randn(32, 128)   # (batch=32, features=128)
bias  = torch.randn(128)       # (128,) broadcasts across the batch dim
out   = batch + bias           # (32, 128) ✓

# Adding column and row vectors → 2D result
col = torch.arange(3).reshape(3, 1)  # (3, 1)
row = torch.arange(4).reshape(1, 4)  # (1, 4)
grid = col + row                      # (3, 4) — outer-sum
print(grid)
# tensor([[0, 1, 2, 3],
#         [1, 2, 3, 4],
#         [2, 3, 4, 5]])

# Common broadcasting errors:
# a = torch.ones(3, 4)
# b = torch.ones(3)        # (3,) aligns to (1, 3) NOT (3, 1)
# a + b  → ERROR: size 4 != size 3 in dimension 1
# Fix: b.reshape(3, 1) to make it (3, 1)

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