On (fake) Stationarity in Stochastic Volterra Equations with Affine Drift and Regular Kernels

What the math gives to ML

The paper gives a constructive recipe for combining causal Volterra memory, affine mean reversion, and a stabilizing diffusion amplitude so that marginal statistics remain approximately stationary despite long-range dependence. This can transfer to recurrent or state-space neural layers as a power-law memory block that preserves information over long contexts without the uncontrolled variance drift common in unconstrained recurrences. The most practical implementation is a discretized exponential-fractional convolution with learned drift targets and batch-estimated innovation scaling. The key experiment is whether this produces longer useful memory and more stable activations than GRUs or standard diagonal state-space models at comparable compute.