batchnorm-inference — Databricks case

Databricks-inspired batch inference service has a trained normalization layer whose running statistics are already fixed. You need to apply the inference-time BatchNorm transformation consistently so predictions do not change merely because request batches have different sizes.

Apply the inference-time batch-normalisation transform with fixed running statistics: $y=\gamma {\displaystyle \frac{x-\mu }{\sqrt{{\sigma }^2+\epsilon }}}+\beta y=\backslash gamma\backslash ,\backslash dfrac\{x-\backslash mu\}\{\backslash sqrt\{\backslash sigma^2+\backslash varepsilon\}\}+\backslash beta$ with eps defaulting to ${10}^{-5}10^\{-5\}$. All of mean, var, gamma and beta may be scalars or arrays that broadcast against x.

Implement solve(x, mean, var, gamma, beta, eps=1e-5).

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

Examples

Example 1

Input:

solve([1, 2, 3], [2], [0.25], [2], [0.5])

Output:

[-3.49992, 0.5, 4.49992]

Example 2

Input:

solve([4.0], 2.0, 4.0, 1.0, 0.0, eps=0.0)

Output:

[1.0]