Neuro-evolutionary stochastic architectures in gauge-covariant neural fields

Competitive artificial-life systems can rank trained controllers differently under training and ecological evaluation. We present Neuroevolution Arena, a GPU-accelerated spatial ecology of independently parameterized neural-network cells, and an audit-tracked nested evaluation protocol. Three implementation-specific update-and-inheritance regimes (EvoEvo, EvoRL, and RLRL) are crossed with two neural architectures for 50,000 generations in three independent training runs per condition. One saved elite-controller artifact from each of the 18 runs enters an aligned-run frozen-evaluation design comprising 198 computational jobs. Pairwise effects average three seed-defined ecological contexts (two cooperation-permitting and one attack-permitting) within each aligned training-run block; the independent level remains n = 3 runs per condition. RL-enabled regimes attain higher recorded training fitness than EvoEvo, whereas pairwise outcomes show architecture-conditioned majority patterns and substantial artifact dependence. Six-way winners vary across artifacts and contexts, and the prespecified survival endpoint has a complete floor. We contribute a nested protocol that separates training-run artifacts from evaluation contexts and exposes, rather than conceals, their different sources of variation.

Uncertainty quantification in neural networks prediction is a main issue for usual applications. Our approach seeks at reducing computation costs by directly evaluating uncertainty using PDE's information on the asymptotic variance, rather than the deep ensemble method which may be seen as a Monte Carlo estimation of the prediction, requiring the training of multiple networks. We thus study the law of the limiting process describing the random fluctuations around the mean-field limit of wide two-layer neural networks trained by stochastic gradient descent in a weak-noise regime. Building on a recent trajectorial central limit theorem, in which this limit is characterized as the weak solution of a linear stochastic evolution equation, we identify its law explicitly. More precisely, we show that it is a centered Gaussian process in the dual of a weighted Sobolev space, and we derive a closed covariance representation for the finite-dimensional distributions obtained by testing it against smooth functions. This covariance is expressed through the solution of a backward transport equation with a nonlocal source term, whose coefficients are driven by the mean-field trajectory. As a consequence, by testing against the activation function at a fixed input, we obtain an expression for the limiting variance of the corresponding network-output fluctuations. We illustrate this result numerically on a one-dimensional regression example.

Neuroevolution is a representative neural architecture search paradigm that evolves both network topology and weights through evolutionary algorithms. In this paper, we propose Seq103, a unified NEAT-style neuroevolution framework for compact sequence architecture discovery. Seq103 consists of a shared evolutionary backbone and an optional recurrent extension. The shared backbone includes an elementary node-and-connection representation, per-class RMSE-based evaluation, mutation-based evolution with class-wise recombination, and elitism. The optional hidden-state mechanism extends the search space with hidden-state nodes and hidden connections, enabling temporal memory when step-wise recurrent inference is required. With this design, Seq103 applies the same core search pipeline to both step-wise recurrent and sample-wise feedforward sequence classification. In recurrent tasks, the hidden-state extension is enabled to provide temporal memory; in feedforward tasks, it is disabled while the shared evolutionary backbone remains unchanged. We evaluate Seq103 on 8 text classification datasets and the full UCRArchive2018 benchmark with 128 univariate time-series datasets. On step-wise tasks, Seq103 retains 86.96% of the best-baseline accuracy on average while using 34.6x to 3218.0x fewer parameters. On sample-wise tasks over the full UCRArchive2018 benchmark, Seq103 retains 81.95% of the best-baseline accuracy on average while using 11.8x to 160,601.0x fewer parameters.