A hand-worked batch norm example shows exactly what gets normalized and why
ProfTomYeh · x · 2026-07-21
A hand-worked walkthrough of batch normalization
This post walks through batch normalization step by step using a small example by hand.
What it explains
- Batch norm is applied after a linear layer, so it normalizes features, not inputs, weights, or biases.
- The example computes batch statistics feature by feature across four training examples.
- It then shows the two core normalization steps: subtracting the mean and dividing by the standard deviation.
- Finally, it explains the trainable scale and shift parameters, and contrasts batch norm with layer norm.
Takeaway
The author emphasizes that the statistics are not trainable, while the affine scale/shift is. The walkthrough is meant to make the mechanics of batch norm intuitive rather than mysterious.
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