Broadcasting in Python and Deep Learning

Broadcasting is a powerful feature in NumPy (and many deep learning libraries) that lets you perform operations on arrays of different shapes without writing explicit for loops. This makes your code simpler, faster, and more readable.

---

🍎 Broadcasting Example: Calories Matrix

We have a matrix A of calories from Carbs, Proteins, and Fats in different foods:

         Apples   Beef   Eggs   Potatoes
Carbs     56.0     0.0    4.4     68.0
Protein    1.2   104.0   52.0      8.0
Fat        1.8   135.0   99.0      0.9

Each column is a food. Each row is a macronutrient.

Task:

Calculate the percentage of calories in each food that comes from Carbs, Protein, Fat — without using a loop.

---

✅ Vectorized Solution (No for-loop)

import numpy as np

A = np.array([[56.0,   0.0,  4.4, 68.0],
              [ 1.2, 104.0, 52.0,  8.0],
              [ 1.8, 135.0, 99.0,  0.9]])

cal = A.sum(axis=0)  # Total calories per column (food)
percentage = 100 * A / cal  # Broadcasting divides each column by its total

• axis=0 tells NumPy to sum down the rows for each column (i.e., per food).
• Broadcasting handles the division of a (3,4) matrix by a (1,4) vector — applies elementwise!

---

🤹 General Principle of Broadcasting

NumPy automatically adjusts dimensions during operations. These rules apply:

• (m, n) + (1, n) -> result is (m, n)
• (m, n) * (m, 1) -> result is (m, n)

Scalar Broadcasting Examples:

np.array([[1], [2], [3]]) + 100
# Output: [[101], [102], [103]]

np.array([1, 2, 3]) + 100
# Output: [101, 102, 103]

---

🧠 Why It Matters in Deep Learning

Broadcasting lets us:

• Add biases to all training examples at once.
• Subtract labels from predictions in logistic regression.
• Perform matrix-based calculations for forward and backward propagation without explicit loops.

For example, in logistic regression:

Z = np.dot(w.T, X) + b  # Broadcasting b across all examples

Without broadcasting, you’d need a loop to add b to each column of Z. 😅

---

Summary

Concept	Meaning
Broadcasting	Applying operations across mismatched shapes
axis=0 in sum	Sum over rows (per column)
Avoid for-loops	Vectorized ops are faster and more readable
Used in	Neural nets, regression, backprop, numpy tricks

---

🧪 Challenge

Recreate the example using your own 3x4 matrix — try using different axis values and observe the results.