Medium

Batch Normalization Forward

Medium

~15 min

code completion

Batch Normalization

Batch normalization normalizes each feature across the batch dimension, stabilizing training and allowing higher learning rates.

For a mini-batch of activations $X$ of shape (m, d):

μ_{j} = \frac{1}{m} i \sum X_{ij}, σ_{j} = \frac{1}{m} i \sum (X_{ij} - μ_{j})^{2}

\hat{X}_{ij} = \frac{X _{ij} - μ _{j}}{σ _{j} + ϵ}

Each column (feature) is independently normalized to zero mean and unit variance. The $ϵ$ prevents division by zero.

Note: In the full layer, $\hat{X}$ is then scaled and shifted by learned parameters $γ$ and $β$ — we skip that here.

Your task:

Implement batch_normalize(X, eps) that normalizes each feature column.

Example Tests

Sum of normalized output is 0 (all columns are zero-mean)

Input: {"X":[[1,10],[2,20],[3,30]],"eps":0}

Expected: 0

Each column has unit std (check element value)

Input: {"X":[[1,2],[3,4],[5,6]],"eps":0}

Expected: [[-1.22474,-1.22474],[0,0],[1.22474,1.22474]]

Output shape preserved

Input: {"X":[[1,2,3],[4,5,6]],"eps":1e-8}

Expected: [2,3]

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