Layer Normalization

Apply layer normalisation to a 2-D batch X: for each row compute the mean and population variance across its features, normalise with $\sqrt{\text{var}+\epsilon }\backslash sqrt\{\backslash text\{var\}+\backslash varepsilon\}$, then apply the per-feature scale gamma and shift beta. eps defaults to ${10}^{-5}10^\{-5\}$.

Implement solve(X, gamma, beta, eps=1e-5).

Returns. Return a float NumPy array with the shape of X.

Examples

Example 1

Input:

solve([[1, 3], [2, 6]], [1, 2], [0, 1], eps=0)

Output:

[[-1.0, 3.0], [-1.0, 3.0]]

Example 2

Input:

solve([[2, 2]], [3, 4], [1, -1])

Output:

[[1.0, -1.0]]