Training-Time Batch Normalization Reshapes Local Partition Geometry in Piecewise-Affine Networks
Batch normalization (BN) is central to modern deep networks, but its effect on the realized function during training remains less understood than its optimization benefits. We study training-time BN in continuous piecewise-affine (CPA) networks through the geometry of switching hyperplanes and the induced affine-region partition. Conditioned on a mini-batch, we show that BN defines for each neuron a reference hyperplane through the batch centroid, and that breakpoint-switching hyperplanes are parallel translates whose offsets are expressed in batch-standardized coordinates and are independent of the raw bias. This yields an exact criterion for when a switching hyperplane intersects a loca...
| Authors | Xuan Qi, Yi Wei, Fanqi Yu et al. |
|---|---|
| Primary category | cs.LG |
| Published | 6 May 2026 |
| Last updated at source | 12 May 2026 |
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