Tuning Universality in Deep Neural Networks

Fuente: arXiv
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Auteur principal: Ghavasieh, Arsham
Format: Preprint
Publié: 2025
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author Ghavasieh, Arsham
author_facet Ghavasieh, Arsham
contents Deep neural networks (DNNs) exhibit crackling-like avalanches whose origin lacks a mechanistic explanation. Here, I derive a stochastic theory of deep information propagation (DIP) by incorporating Central Limit Theorem (CLT)-level fluctuations. Four effective couplings $(r, h, D_1, D_2)$ characterize the dynamics, yielding a Landau description of the static exponents and a Directed Percolation (DP) structure of activity cascades. Tuning the couplings selects between avalanche dynamics generated by a Brownian Motion (BM) in a logarithmic trap and an absorbed free BM, each corresponding to a distinct universality classes. Numerical simulations confirm the theory and demonstrate that activation function design controls the collective dynamics in random DNNs.
format Preprint
id arxiv_https___arxiv_org_abs_2512_00168
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Tuning Universality in Deep Neural Networks
Ghavasieh, Arsham
Disordered Systems and Neural Networks
Statistical Mechanics
Artificial Intelligence
Adaptation and Self-Organizing Systems
Biological Physics
Deep neural networks (DNNs) exhibit crackling-like avalanches whose origin lacks a mechanistic explanation. Here, I derive a stochastic theory of deep information propagation (DIP) by incorporating Central Limit Theorem (CLT)-level fluctuations. Four effective couplings $(r, h, D_1, D_2)$ characterize the dynamics, yielding a Landau description of the static exponents and a Directed Percolation (DP) structure of activity cascades. Tuning the couplings selects between avalanche dynamics generated by a Brownian Motion (BM) in a logarithmic trap and an absorbed free BM, each corresponding to a distinct universality classes. Numerical simulations confirm the theory and demonstrate that activation function design controls the collective dynamics in random DNNs.
title Tuning Universality in Deep Neural Networks
topic Disordered Systems and Neural Networks
Statistical Mechanics
Artificial Intelligence
Adaptation and Self-Organizing Systems
Biological Physics
url https://arxiv.org/abs/2512.00168