Broadcasting Addition - Python Basics for ML

Broadcasting Addition

What you'll build

A function broadcast_add(matrix, vector) that adds a vector to every row of a matrix with a single +, letting broadcasting do the repetition.

Background

This is exactly how a neural network layer adds its bias: x @ W has shape (batch, d_out) and the bias b has shape (d_out,). Broadcasting stretches b across the batch without ever copying it, so the same code works for any batch size.

Formula

result[i, j] = matrix[i, j] + vector[j]      for every row i

Broadcasting rule

NumPy compares shapes from the right. (m, n) and (n,) line up as (m, n) and (1, n); the size-1 dimension is stretched to m, giving (m, n).

Inputs

• matrix: 2D array of shape (m, n)
• vector: 1D array of shape (n,), with 1 <= m, n <= 100. Integer or float entries.

Expected Return Format

A 2D array of shape (m, n): vector added to each row.

Constraints

Use broadcasting; no loops, np.tile or np.repeat.

Follow-up

• How would you add a value to every column instead, with one value per row? (Hint: a vector of shape (m, 1).)
• What error do you get for a (2, 3) matrix plus a (2,) vector, and why?

Input: broadcast_add(np.array([[1, 2, 3], [4, 5, 6]]), np.array([10, 20, 30]))
Output: array([[11, 22, 33],
       [14, 25, 36]])

Input: broadcast_add(np.array([[1, 2], [3, 4]]), np.array([-1, -2]))
Output: array([[0, 0],
       [2, 2]])

import numpy as np

def broadcast_add(matrix: np.ndarray, vector: np.ndarray) -> np.ndarray:
    """
    Add a vector to each row of a matrix using broadcasting.

    Args:
        matrix: 2D array of shape (m, n)
        vector: 1D array of shape (n,)

    Returns:
        Array of shape (m, n) with result[i, j] = matrix[i, j] + vector[j]
    """
    # Your code here
    pass