Memory as Resonance: A Biomimetic Architecture for Infinite Context Memory on Ergodic Phonetic Manifolds

TL;DR

The paper tackles the Memory Wall in large language models by reframing memory as a reconstructive, trajectory-based process on a conserved ergodic manifold. It introduces Phonetic Trajectory Memory (PTM), which encodes text as a low-dimensional phonetic signal that evolves on a Hyper-Torus under strictly irrational rotations, enabling infinite context with constant-time access. Retrieval is achieved via a Signal Consensus between a semantic prior and a geometric phonetic trace, yielding compression >$3{,}000\times$ and factual accuracy near $92\%$, with latency around $34$ ms. While offering dramatic efficiency gains, PTM introduces a precision trade-off (structural agnosia for some punctuation/verbs) and relies on anchor-based entropy filtering to preserve critical tokens, marking a shift from storage-centric to perception-centric long-context AI design. Overall, the work demonstrates that infinite context can be achieved with finite silicon by transforming memory into a dynamical, resonant process rather than a static archive, with practical implications for scalable reasoning and real-time applications.

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.

Figures (11)

• Figure 1: A geometric abstraction of the proposed PTM system. The central structure represents the Hyper-Torus Memory, a bounded, continuous state-space where compressed phonetic vectors are stored. Unlike discrete KV blocks, the signal trajectory (visualized as the organic lattice) traverses this manifold ergodically, efficiently covering the semantic space with zero redundancy.
• Figure 2: Top: A geometric contrast between rational and irrational dynamics. Under rational rotation ($\theta \in \mathbb{Q}\pi$, left), the trajectory collapses into a closed loop ($S_{t+N} \equiv S_t$), enforcing a hard "Memory Wall" via self-intersection. Conversely, irrational rotation ($\theta \notin \mathbb{Q}\pi$, right) generates an open spiral that physically realizes Weyl's Equidistribution Theorem, densely filling the manifold without repetition to fold infinite context into finite dimensions. Middle: The memory manifold is realized as 8 independent planar rotors, each spinning at a distinct irrational velocity ($\omega_i \propto \sqrt{p_i}$). Because the frequencies are incommensurable over $\mathbb{Q}$, the system never returns to a previous configuration, ensuring every timestep $t$ possesses a unique geometric phase signature. Bottom: A recursive stress test ($T=100,000$ steps) confirms that unlike autoregressive caches where noise accumulates quadratically, the manifold exhibits bounded error variance. The maximum reconstruction error saturates at the floating-point floor ($1.79 \times 10^{-7}$), proving that the memory limit is defined by precision, not capacity.
• Figure 3: The system bifurcates the input stream into two orthogonal realities: (1) The Logic Rail (Top): High-entropy syntactic pivots ("Anchors") are retained in standard discrete KV tensors to preserve structural causality. (2) The Truth Rail (Bottom): The bulk of the context is projected onto the Ergodic Manifold, compressing the infinite sequence into a fixed-size continuous orbit. The Retrieval: The "Resonance Engine" executes the symplectic inverse rotation ($\mathbf{R}^{-(T-t)}$) to unwind time. It fuses the recovered physical signal with the semantic intelligence of the frozen LLM, reconstructing the complete context window in strictly constant $O(1)$ time.
• Figure 4: Reconstruction is visualized not as a search, but as the intersection of two orthogonal fields. (Top) The Semantic Field (Logic): The LLM hallucinates contextually plausible futures (e.g., Shore, Beach), generating the prior $P_{\theta}$. It knows what should happen. (Bottom) The Acoustic Trace (Memory): The Manifold defines a rigid locus of phonetically valid candidates (e.g., Post, Toast, Ghost), generating the likelihood $P_{\phi}$. It knows what did happen. The Collapse: The system recovers the true token "Coast" by finding the unique topological point where these two realities intersect. The PTM acts as a high-pass filter, suppressing semantic hallucinations (which sound wrong) and phonetic noise (which means nothing).
• Figure 5: Evaluation of retrieval fidelity across increasing context depths ($N=20,000$). The system exhibits monotonic stability, defying the standard inverse-scaling law of attention mechanisms (where accuracy typically plummets for distant tokens). Aside from a singular "Transient Turbulence" event at $t \approx 9,500$ (attributed to localized manifold resonance interference), the accuracy stabilizes around a global mean of $89.2\%$. This plateau effect empirically validates the ergodic property of the encoding: the state vector $S_t$ does not saturate, preserving distinguishing features for deep context retrieval regardless of sequence length.