Meta Integration-Enhanced Optimizer

A single integral order only filters a bounded range of sharp minima. MIEO stacks several integral orders to reshape the loss surface more aggressively and accumulates gradient history, with per-order coefficients updated online by a hypergradient controller whose direction is synthesised to suppress stale information.

Internal ablations cover coefficient-update rules (momentum smoothing versus moment normalisation), the choice of integral order, two-dimensional loss-landscape simulations, and loss-landscape reconstruction on ResNet, together with image classification, self-supervised learning and causal language modelling.