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A Class of Rényi-based Concentration Metrics for Kolmogorov-Arnold Geometry in Multilayer Perceptrons — arXiv:2610.23267

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.23267
License (as archived): CC0-1.0
Archived: 2026-10-19T09:37:31.880Z
SHA-256 of the archived text: 81980337cf5d6a9308de7ccbb28fc083e43f8d216b419d94a6f70a72d3bbefcd
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How to cite

A Class of Rényi-based Concentration Metrics for Kolmogorov-Arnold Geometry in Multilayer Perceptrons — arXiv:2610.23267 — arXiv (en), https://arxiv.org/abs/2610.23267 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_3ac2e4aef00a (Metraipolis archive dc_3ac2e4aef00a, sha256 81980337cf5d6a9308de7ccbb28fc083e43f8d216b419d94a6f70a72d3bbefcd)

BibTeX

@misc{dc3ac2e4aef00a,
  title = {A Class of Rényi-based Concentration Metrics for Kolmogorov-Arnold Geometry in Multilayer Perceptrons — arXiv:2610.23267},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.23267},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_3ac2e4aef00a; sha256 81980337cf5d6a9308de7ccbb28fc083e43f8d216b419d94a6f70a72d3bbefcd},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.23267. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The interpretability of artificial intelligence models has become a central concern, especially for black-box models such as multilayer perceptrons (MLPs). Kolmogorov-Arnold Geometry has recently emerged as a framework for analysing the internal representations of these networks, by examining how the hidden layer locally responds to changes in the input through the minors of its Jacobian. The degree to which a few of these minors dominate the rest, known as their concentration, has so far been measured with the Participation Ratio. Although this metric has useful properties, its maximum value depends on the size of the network, so a given value cannot be read as high or low concentration without reference to the architecture. To overcome this limitation, in this paper we propose the $\alpha$-RC metrics, a family of Rényi-based concentration measures that compare the normalized magnitudes of the minors with the uniform distribution through the Rényi divergence of order $\alpha$. All the metrics in the family are bounded between 0 and 1 regardless of the architecture, with 0 indicating that the magnitude is evenly spread over the minors and 1 that it is carried by a single one. Moreover, the metrics are non-decreasing in $\alpha$, and for $\alpha$ = 2 they reduce to an explicit transformation of the Participation Ratio. Computational experiments with single-hidden-layer MLPs trained on a synthetic dataset show the benefits of our proposal.

Tema degli esploratori: statistica e scienza dei dati (elenco arXiv stat.ML, nuovi lavori del giorno).
Categorie arXiv: Information Theory (cs.IT) ; Machine Learning (stat.ML).
Pagina del lavoro: https://arxiv.org/abs/2610.23267 — 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 2026-10-19T09:32:44.738Z dalla pagina https://arxiv.org/list/stat.ML/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).