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CODING CHALLENGE · N°09

Layer Normalization

Easy AI EngineeringTransformersDeep Learning

The stabilizer wrapped around every Transformer sub-layer: re-center and re-scale a vector to mean 0 and variance 1, then let two learned parameters stretch and shift it back. Keeps activations well-behaved so deep nets actually train. No numpy — just the math.

The problem

Implement layer normalization over a single vector x. Compute the mean and (population) variance of x, normalize each element to zero mean and unit variance, then apply a per-element scale gamma and shift beta: y[i] = gamma[i] · (x[i] − mean) / √(var + eps) + beta[i]. Use eps = 1e-5 for numerical stability (so a constant input does not divide by zero). Return the list y.

EXAMPLE 1
Input x=[1,2,3,4], gamma=[1,1,1,1], beta=[0,0,0,0]
Output ≈[-1.34, -0.45, 0.45, 1.34]
mean 0, variance 1 — the raw normalize
EXAMPLE 2
Input x=[0,10], gamma=[1,1], beta=[0,0]
Output ≈[-1.0, 1.0]
two elements → symmetric ±1
EXAMPLE 3
Input x=[7,7,7], gamma=[1,1,1], beta=[0,0,0]
Output [0.0, 0.0, 0.0]
constant input → eps keeps it finite
CONSTRAINTS
  • Use the population variance: mean((x − mean)²), dividing by n (not n−1).
  • Add eps = 1e-5 inside the square root before dividing.
  • gamma and beta are per-element (same length as x) — scale then shift each normalized value.
  • Pyodide has no numpy — use the math stdlib and plain lists only.
SOLVE IT YOURSELF

Your turn — write it

Edit the stub, hit Run (or ⌘/Ctrl + Enter), and watch the hidden tests. Stuck? the hints are right above and Reveal solution is one click away.

YOUR TASK

Implement layer_norm(x, gamma, beta, eps=1e-5). Center and scale x to mean 0 / variance 1, then apply the per-element scale gamma and shift beta.

HINTS — 4 IDEAS
  1. mean = sum(x) / n; var = sum((xi - mean)**2 for xi in x) / n (divide by n).
  2. The denominator is sqrt(var + eps) — the eps is what saves you when var is 0.
  3. Normalize each element: (x[i] - mean) / denom.
  4. Then scale and shift: gamma[i] * normalized + beta[i].
CPython · WebAssembly

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LLM Engineering