Certified Topological Interaction in Neural Representations: Exact Tests and the Statistic They Require
Class disentanglement--the separation of a representation's class-conditional point clouds along depth and over training--is measured by descriptive curves: the sentence such a study wants to write, layer l+1 is more disentangled than layer l, is an eyeball judgement with no null. We supply the inferential layer for a topological measurement of class overlap, the Intersection Euler Characteristic Profile: the Euler characteristic of the overlap of the clouds' ball unions as a function of scale, from one Alpha-complex sweep with no boundary-matrix reduction. Every number carries a test--exact permutation tests in both directions, a guarded separation certificate the invariant requires, and...
| Authors | Sushovan Majhi |
|---|---|
| Primary category | cs.LG |
| Published | 8 September 2026 |
| Last updated at source | 18 September 2026 |
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