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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2508.18948 |
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| _version_ | 1866911613484793856 |
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| author | Terin, Rodrigo Carmo |
| author_facet | Terin, Rodrigo Carmo |
| contents | We develop a gauge-covariant stochastic effective field theory for stability and finite-width effects in deep neural systems. The model uses classical commuting fields: a complex matter field, a real Abelian connection field, and a fictitious stochastic depth variable. Using the Martin--Siggia--Rose--Janssen--de~Dominicis formalism, we derive its functional representation and a two-replica linear-response construction defining the maximal Lyapunov exponent and the amplification factor for the edge of chaos. Finite-width effects appear as perturbative corrections to dressed kernels, and the marginality condition remains unchanged at the order considered for fixed kernel geometry. Numerically, finite-width multilayer perceptrons follow the mean-field instability threshold, and a linear stochastic effective sector reproduces the predicted low-frequency spectral deformation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_18948 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gauge-covariant stochastic neural fields: Stability and finite-width effects Terin, Rodrigo Carmo High Energy Physics - Theory Disordered Systems and Neural Networks Machine Learning We develop a gauge-covariant stochastic effective field theory for stability and finite-width effects in deep neural systems. The model uses classical commuting fields: a complex matter field, a real Abelian connection field, and a fictitious stochastic depth variable. Using the Martin--Siggia--Rose--Janssen--de~Dominicis formalism, we derive its functional representation and a two-replica linear-response construction defining the maximal Lyapunov exponent and the amplification factor for the edge of chaos. Finite-width effects appear as perturbative corrections to dressed kernels, and the marginality condition remains unchanged at the order considered for fixed kernel geometry. Numerically, finite-width multilayer perceptrons follow the mean-field instability threshold, and a linear stochastic effective sector reproduces the predicted low-frequency spectral deformation. |
| title | Gauge-covariant stochastic neural fields: Stability and finite-width effects |
| topic | High Energy Physics - Theory Disordered Systems and Neural Networks Machine Learning |
| url | https://arxiv.org/abs/2508.18948 |