Layer normalization with scalar gain and offset

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The implementation subtracts the vector’s mean, divides by √(population variance+EPSILON_PHI), then applies scalar gain γ and offset β. This controls the scale of a feature vector while preserving relative centered differences. The code uses one gain and one offset for the whole vector rather than separately learned values per component.

Terms & definitions

How it works

Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.

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Original context

		}
	}

	return output
}

// LayerNorm computes layer normalization
// y = (x - μ) / σ · γ + β
func LayerNorm(x []float64, gamma, beta float64) []float64 {
	n := len(x)
	if n == 0 {
		return x
	}

	// Compute mean
	mean := 0.0
	for _, v := range x {
		mean += v

y = (x - μ) / σ · γ + β

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