# Gauge-covariant stochastic neural fields: Stability and finite-width effects

arXiv: https://arxiv.org/abs/2508.18948 · HTML: https://mlsanity.com/paper/2508.18948/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 52 references that are in the map.
- First posted on arXiv 26 Aug 2025.

## Builds on (most cited first, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Deep Speech: Scaling up end-to-end speech recognition](https://mlsanity.com/paper/1412.5567/) (2014)
- [Exponential expressivity in deep neural networks through transient chaos](https://mlsanity.com/paper/1606.05340/) (2016)
- [The Principles of Deep Learning Theory](https://mlsanity.com/paper/2106.10165/) (2021)
- [Non-Gaussian processes and neural networks at finite widths](https://mlsanity.com/paper/1910.00019/) (2019)
- [Asymptotics of Wide Networks from Feynman Diagrams](https://mlsanity.com/paper/1909.11304/) (2019)
- [Neural Networks and Quantum Field Theory](https://mlsanity.com/paper/2008.08601/) (2020)
- [Symmetry-via-Duality: Invariant Neural Network Densities from Parameter-Space Correlators](https://mlsanity.com/paper/2106.00694/) (2021)
- [Nonperturbative renormalization for the neural network-QFT correspondence](https://mlsanity.com/paper/2108.01403/) (2021)
- [The edge of chaos: quantum field theory and deep neural networks](https://mlsanity.com/paper/2109.13247/) (2021)
- [Gauge Equivariant Neural Networks for 2+1D U(1) Gauge Theory Simulations in Hamiltonian Formulation](https://mlsanity.com/paper/2211.03198/) (2022)
- [Conformal Fields from Neural Networks](https://mlsanity.com/paper/2409.12222/) (2024)
- [The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learning](https://mlsanity.com/paper/2103.04913/) (2021)
- [Why is AI hard and Physics simple?](https://mlsanity.com/paper/2104.00008/) (2021)
- [Quantum Mechanics and Neural Networks](https://mlsanity.com/paper/2504.05462/) (2025)

## Built on by (most cited first, 3 of 3)

- [Scale redundancy and soft gauge fixing in positively homogeneous neural networks](https://mlsanity.com/paper/2602.14729/) (2026)
- [Spectral functions in Minkowski quantum electrodynamics from neural reconstruction](https://mlsanity.com/paper/2510.24728/) (2025)
- [Spinning Conformal Correlators from Neural Networks](https://mlsanity.com/paper/2608.15001/) (2026)

## Abstract (arXiv)

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.