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New paper models affine region growth in piecewise-linear neural networks

By PulseAugur Editorial · [2 sources] ·

Researchers have published a paper on arXiv detailing a mathematical model for the growth of affine regions in deep piecewise-linear neural networks. The study uses a random compositional model based on perturbations of the tent map to analyze the number of affine pieces after multiple layers. The findings establish exponential bounds for the tails of the growth rate and introduce a defect process to derive lower bounds, suggesting eventual exclusion of certain tail behaviors. AI

IMPACT Provides theoretical insights into the structure and growth of neural network architectures.

RANK_REASON The cluster contains an academic paper published on arXiv detailing mathematical research.

Read on arXiv stat.ML →

AI-generated summary · Google Gemini · from 2 sources. How we write summaries →

New paper models affine region growth in piecewise-linear neural networks

COVERAGE [2]

  1. arXiv stat.ML TIER_1 English(EN) · Recep \"Ozkan, Christian Hirsch ·

    Local large deviations for linear-region growth in random piecewise-linear networks

    arXiv:2607.07014v1 Announce Type: cross Abstract: We study a random compositional model for the growth of affine regions in deep piecewise-linear networks. The model is generated by i.i.d.\ perturbations of the symmetric height-one tent map, and the main observable is the number …

  2. arXiv stat.ML TIER_1 English(EN) · Christian Hirsch ·

    Local large deviations for linear-region growth in random piecewise-linear networks

    We study a random compositional model for the growth of affine regions in deep piecewise-linear networks. The model is generated by i.i.d.\ perturbations of the symmetric height-one tent map, and the main observable is the number \(N_n\) of affine pieces after \(n\) layers. We pr…

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