Neural Network Training Supervision via the Correlated Ensemble Solver

Classical gradient-based optimisers receive a loss signal that is agnostic to the correlation structure of the input feature space. As model scale grows, approximation errors in that correlation structure compound, degrading gradient quality and slowing convergence. This paper introduces a training methodology in which the Correlated Ensemble Solver (CES) - a parameter-free solver that computes exact joint exceedance probabilities over arbitrarily large correlated variable sets - acts as a real-time external supervisor during neural network (NN) training. The CES is never embedded in the model; at inference time the network runs without it. Per mini-batch, a singular value decomposition (SVD) of the first-layer weight gradient identifies the dominant signal subspace, and the CES evaluates the joint exceedance probability over that subspace. The resulting scalar modulates the batch loss, providing an exact, parameter-free, epoch-by-epoch measure of gradient coherence that guides the optimiser toward high-confidence regions of the loss landscape. Six experiments across five datasets—Breast Cancer Diagnostic (N =30 features), Digits binary (N =64), and three synthetic benchmarks (N =100, N =200) at varying model scales—consistently demonstrate faster convergence of ∆conv ∈ [+8, +20] epochs relative to the unguided baseline, with identical or marginally improved final accuracy. The method is fully reproducible given access to a deployed CES endpoint, with no additional hyper-parameters beyond the supervision weight α and exceedance threshold τ .