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Certified Topological Interaction in Neural Representations: Exact Tests and the Statistic They Require — arXiv:2609.08561

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.08561
License (as archived): CC0-1.0
Archived: 2026-10-16T13:58:17.595Z
SHA-256 of the archived text: bdf01ecc9093465f0c98e4daebacd2dbafd227f40e17606850a55a9511df28e0
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Certified Topological Interaction in Neural Representations: Exact Tests and the Statistic They Require — arXiv:2609.08561 — arXiv (en), https://arxiv.org/abs/2609.08561 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ce43bb5106ea (Metraipolis archive dc_ce43bb5106ea, sha256 bdf01ecc9093465f0c98e4daebacd2dbafd227f40e17606850a55a9511df28e0)

BibTeX

@misc{dcce43bb5106ea,
  title = {Certified Topological Interaction in Neural Representations: Exact Tests and the Statistic They Require — arXiv:2609.08561},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.08561},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ce43bb5106ea; sha256 bdf01ecc9093465f0c98e4daebacd2dbafd227f40e17606850a55a9511df28e0},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.08561. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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 a paired sign-flip test for comparative claims. Building that test taught a lesson outliving this invariant: its statistic must be scale-free. On the raw profile mass, which has units of feature length, 12,375 paired tests return 5,633 significant steps of which every one at the first epoch points the wrong way, certifying feature-norm dynamics as disentanglement; the dimensionless statistic returns 2,707, with 2,026 decreases. Across 111 networks and 52,650 measurements, disentanglement is depth-graded and early, and interaction quotients rank class pairs by confusability (rho=0.83), on par with cheap separability statistics. In a 96-model factorial, augmentation is the one training choice that separates classes relative to chance; weight decay compresses the overlap without separating. Only a k-fold statistic can pose the structural question: the joint entanglement of a class triple sits below its strongest pair in 97% of triple-layer cells and 99.5% of deep cells, at median ratios far below a measured null floor, in vision encoders and frozen language models--a regularity, not a law. The unnormalized mass predicts test accuracy (R^2=0.94), the quotient does not, and neither beats a linear probe.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-09 in cs.LG).
Categorie arXiv: Machine Learning (cs.LG) ; Algebraic Topology (math.AT).
Pagina del lavoro: https://arxiv.org/abs/2609.08561 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T13:39:43.046Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-09-09?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).