# Tuning Universality in Deep Neural Networks

arXiv: https://arxiv.org/abs/2512.00168 · HTML: https://mlsanity.com/paper/2512.00168/

## Key facts

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- First posted on arXiv 28 Nov 2025.

## Abstract (arXiv)

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, D1, D2) 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.