{"ID":2835661,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.00168","arxiv_id":"2512.00168","title":"Tuning Universality in Deep Neural Networks","abstract":"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.","short_abstract":"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, yie...","url_abs":"https://arxiv.org/abs/2512.00168","url_pdf":"https://arxiv.org/pdf/2512.00168v1","authors":"[\"Arsham Ghavasieh\"]","published":"2025-11-28T19:14:57Z","proceeding":"cond-mat.dis-nn","tasks":"[\"cond-mat.dis-nn\",\"cond-mat.stat-mech\",\"cs.AI\",\"nlin.AO\",\"physics.bio-ph\"]","methods":"[]","has_code":false}