Memory as Resonance: A Biomimetic Architecture for Infinite Context Memory on Ergodic Phonetic Manifolds
Abstract
The memory of contemporary Large Language Models is bound by a physical paradox: as they learn, they fill up. The linear accumulation (O(N)) of Key-Value states treats context as a warehouse of static artifacts, eventually forcing a destructive choice between amnesia and latency. We challenge this discrete orthodoxy, proposing that long-term memory is not the storage of items, but the persistence of a trajectory. We introduce Phonetic Trajectory Memory (PTM), a neuro-symbolic architecture that encodes language not as a sequence of tensors, but as a continuous path on an ergodic manifold governed by irrational rotation matrices. By decoupling the navigation (an invariant O(1) geometric signal) from the reconstruction (a probabilistic generative act), PTM achieves a compression magnitude of greater than 3,000x relative to dense caches. We demonstrate that retrieval becomes a process of resonance: the phonetic trace stabilizes the model against hallucination via "Signal Consensus" mechanism, securing up to approximately 92% factual accuracy. While this aggressive abstraction alters generative texture, it unlocks immediate access latency (approximately 34ms) independent of depth. Our results suggest that infinite context does not require infinite silicon; it requires treating memory not as data to be stored, but as a reconstructive process acting on a conserved, undying physical signal.
Cite
@article{arxiv.2512.20245,
title = {Memory as Resonance: A Biomimetic Architecture for Infinite Context Memory on Ergodic Phonetic Manifolds},
author = {Tarik Houichime and Abdelghani Souhar and Younes El Amrani},
journal= {arXiv preprint arXiv:2512.20245},
year = {2025}
}