Easy

Layer Normalization

Easy

~12 min

code completion

Layer normalization is similar to batch normalization but normalizes across features within each sample, instead of across the batch.

For a single sample vector $x$ of shape (d,):

μ = \frac{1}{d} j \sum x_{j}, σ = \frac{1}{d} j \sum (x_{j} - μ)^{2}

\overset{x}{^}_{j} = \frac{x _{j} - μ}{σ + ϵ}

This makes it batch-size independent — crucial for Transformers, where sequence lengths vary and batch sizes may be small.

Your task:

Implement layer_normalize(x, eps) for a single 1D input vector.

Example Tests

Sum of output is 0 (zero mean)

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

Expected: 0

Known normalized values

Input: {"x":[1,3,5],"eps":0}

Expected: [-1.22474,0,1.22474]

Constant input: zero after normalization (with eps)

Input: {"x":[7,7,7],"eps":1}

Expected: [0,0,0]

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