Tuning Universality in Deep Neural Networks
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911293978443776 |
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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 |