arXiv:2608.11520 2026 Memory 1 ideas extracted · analyzed Sep 1, 2026
The paper provides a constructive finite-atomic moment representation: a sequence of power moments has a finite-rank Hankel matrix, whose nullspace yields an annihilating polynomial and therefore the latent nodes and weights. This is an implementable Prony-type compression mechanism, with exact recovery equations rather than generic low-rank approximation. A promising neural-network transfer is to replace long temporal hidden-state histories or selected KV-cache trajectories by a small number of learned exponential modes, using Hankel rank estimation and stability constraints on the recovered nodes.
Approximate a long hidden-state or key/value trajectory by a small sum of exponential modes, storing only the mode nodes and vector weights instead of every timestep. Recover the modes from a Hankel matrix through an annihilating polynomial, then reconstruct the trajectory or a compact recurrent state during inference.