Rodrigo Carmo Terin

Rodrigo Carmo Terin

We extend our gauge-covariant stochastic neural-field framework by promoting architecture-level parameters to slow stochastic variables evolving in function space. Our effective theory is formulated in terms of classical commuting fields and provides symmetry-constrained diagnostics of marginality and finite-width effects through the maximal Lyapunov exponent, the amplification factor, and dressed spectral kernels. On top of this dynamics, we introduce a Markovian evolutionary scheme compatible with the local $U(1)$ structure of the effective model. By using a minimal implementation, the genotype is reduced to the weight-variance parameter $σ_w^2$, and the fitness functional combines spectral agreement, marginal stability, and a symmetry-constrained critical anchor. Comparing three evolutionary models, we find that only the fully symmetry-constrained Ginibre $U(1)$ version robustly approaches a narrow near-marginal regime and reproduces the predicted low-frequency finite-width spectral behavior. These results support the use of symmetry-guided effective stability diagnostics as practical principles for stochastic architecture search in controlled settings.

Rodrigo Carmo Terin

Neural networks with positively homogeneous activations exhibit an exact continuous reparametrization symmetry: neuron-wise rescalings generate parameter-space orbits along which the input--output function is invariant. We interpret this symmetry as a gauge redundancy and introduce gauge-adapted coordinates that separate invariant and scale-imbalance directions. Inspired by gauge fixing in field theory, we introduce a soft orbit-selection (norm-balancing) functional acting only on redundant scale coordinates. We show analytically that it induces dissipative relaxation of imbalance modes to preserve the realized function. In controlled experiments, this orbit-selection penalty expands the stable learning-rate regime and suppresses scale drift without changing expressivity. These results establish a structural link between gauge-orbit geometry and optimization conditioning, providing a concrete connection between gauge-theoretic concepts and machine learning.

Rodrigo Carmo Terin

Physics-informed neural networks (PINNs) are employed to solve the Dyson--Schwinger equations of quantum electrodynamics (QED) in Euclidean space, with a focus on the non-perturbative generation of the fermion's dynamical mass function in the Landau gauge. By inserting the integral equation directly into the loss function, our PINN framework enables a single neural network to learn a continuous and differentiable representation of the mass function over a spectrum of momenta. Also, we benchmark our approach against a traditional numerical algorithm showing the main differences among them. Our novel strategy, which is expected to be extended to other quantum field theories, is the first step towards forefront applications of machine learning in high-level theoretical physics.

Rodrigo Carmo Terin

The development of a Euclidean stochastic field-theoretic approach that maps deep neural networks (DNNs) to quantum electrodynamics (QED) with local U(1) symmetry is presented. Neural activations and weights are represented by fermionic matter and gauge fields, with a fictitious Langevin time enabling covariant gauge fixing. This mapping identifies the gauge parameter with kernel design choices in wide DNNs, relating stability thresholds to gauge-dependent amplification factors. Finite-width fluctuations correspond to loop corrections in QED. As a proof of concept, we validate the theoretical predictions through numerical simulations of standard multilayer perceptrons and, in parallel, propose a gauge-invariant neural network (GINN) implementation using magnitude--phase parameterization of weights. Finally, a double-copy replica approach is shown to unify the computation of the largest Lyapunov exponent in stochastic QED and wide DNNs.

Rodrigo Carmo Terin

A Minkowskian physics-informed neural network approach (M--PINN) is formulated to solve the Dyson--Schwinger integral equations (DSE) of quantum electrodynamics (QED) directly in Minkowski spacetime. Our novel strategy merges two complementary approaches: (i) a dispersive solver based on Lehmann representations and subtracted dispersion relations, and (ii) a M--PINN that learns the fermion mass function $B(p^2)$, under the same truncation and renormalization configuration (quenched, rainbow, Landau gauge) with the loss integrating the DSE residual with multi--scale regularization, and monotonicity/smoothing penalties in the spacelike branch in the same way as in our previous work in Euclidean space. The benchmarks show quantitative agreement from the infrared (IR) to the ultraviolet (UV) scales in both on-shell and momentum-subtraction schemes. In this controlled setting, our M--PINN reproduces the dispersive solution whilst remaining computationally compact and differentiable, paving the way for extensions with realistic vertices, unquenching effects, and uncertainty-aware variants.