Memory as Resonance: A Biomimetic Architecture for Infinite Context Memory on Ergodic Phonetic Manifolds (2512.20245v1)

Abstract: The memory of contemporary LLMs 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.

• The paper proposes Phonetic Trajectory Memory, encoding sequences as continuous ergodic orbits on a 16D torus for O(1) context retention.
• It leverages irrational rotations and a resonance-based retrieval algorithm to maintain constant precision even over sequences of up to 20,000 tokens.
• Empirical evaluations demonstrate 89.2% retrieval fidelity and interactive performance below 50 ms, validating its efficient neuro-symbolic design.

Memory as Resonance: A Biomimetic Paradigm for Infinite Context via Ergodic Phonetic Manifolds

Introduction and Motivation

This work proposes Phonetic Trajectory Memory (PTM), a neuro-symbolic architecture inspired by the topology and dynamical principles of biological memory systems. In contrast to the linear key-value (KV) cache accumulation of conventional transformers, PTM encodes sequences as continuous, ergodic orbits on a high-dimensional toroidal manifold. The model divorces context retention from sequence length, reframing memory as the conservation of a geometric signal rather than the storage of discrete artifacts. This structural innovation eliminates the quadratic storage and computation complexity characteristic of standard attention, unlocking $O(1)$ context retention with >3,000× compression ratio and sub-50 ms access latency.

Theoretical Foundations

Geometry of Memory: The Hyper-Torus Manifold

PTM formalizes the memory space as a 16-dimensional torus, $\mathbb{T}^{16}$, under modulo-1 equivalence. This compact, isometric space retains context as a phase trajectory rather than a tensor log. Injection of discrete tokens into this continuous metric is achieved through deterministic phonetic decomposition: each text token is mapped via IPA-derived acoustic vectors. The result is a bounded system where the state vector $S_t$ integrates the entire input stream, circumventing drift and saturation (Figure 1).

Figure 1: A geometric abstraction of the PTM system, with the Hyper-Torus manifold ensuring efficient, non-redundant coverage of the semantic space.

Ergodic Dynamics: Irrational Rotations

Memory retention exploits Kronecker’s Theorem, utilizing strictly irrational angular frequencies (e.g., $\omega_k \propto \sqrt{p_k}$ for the $k$-th prime) in block-diagonal $SO(16)$ rotation matrices. The resulting system resists cycle aliasing, guaranteeing unique, non-repeating orbits over arbitrarily long time horizons (Figure 2).

Figure 2: Contrasting rational (cyclic) and irrational (ergodic) state-space dynamics.

Uniqueness is mathematically proven: if two sequences produce the same state, $\mathcal{R}$ would possess an integer eigenvalue, which is excluded by construction. The practical implication is that sequence history is retained with constant precision and without collisional overwrites.

Neuro-Symbolic Bifurcation and Hybrid Encoding

The PTM system bifurcates context into "Logic Rail" and "Truth Rail" (Figure 3). High-entropy tokens ("anchors," e.g., named entities, numbers) are preserved in discrete KV cache form, while the entropic bulk of context (“bridges”) is compressed onto the manifold.

Figure 3: Logical anchors retained in KV tensors; the manifold encodes bridges, with retrieval performed via resonance inversion.

This design maintains structural causality for key elements, but maximizes manifold utilization and compression for the majority low-entropy tokens.

Retrieval as Resonance: Consensus Decoding

PTM introduces a resonance-based retrieval algorithm. To reconstruct a past token, the system performs an inverse rotation (rolling back the ergodic manifold), extracting a candidate phonetic trace. This trace is compared (via cosine similarity in the 16D phonetic space) with all vocabulary entries. Retrieval is then finalized via probabilistic consensus: a convex combination of the frozen LLM’s semantic prior and the physical acoustic signal (“resonance collapse,” Figure 4).

Figure 4: Retrieval is the intersection of semantic probability (LLM hallucinations) and the geometric evidence from the phonetic trace.

The generative process thus resolves ambiguity by requiring both semantic coherence and geometric resonance for selection. This mechanism greatly reduces semantic hallucination and maintains factual accuracy, especially for rare or recently mentioned entities.

Empirical Results

Retrieval Fidelity and Sequence Scaling

The system achieves a mean accuracy plateauing at 89.2% across context lengths of 20,000 tokens, with no observed accuracy decay versus sequence position (Figure 5).

Figure 5: Retrieval fidelity is invariant to context depth, empirically defying the inverse-scaling law for attention-based models.

This monotonic stability, aside from rare "turbulence" events (e.g., local manifold resonance interference), supports the claim of context-invariant memory. In ablation studies, removal of all symbolic anchors (“blind walk”) yields 83.58% correct reconstruction using only the ergodic trace—errors here manifest as predictable phonetic drifts rather than uncontrolled hallucinations.

Hybrid Neuro-Symbolic Consistency

Evaluations of real-world narrative and scientific texts demonstrate 90–92% accuracy at aggressive ($>$70%) KV cache compression. Proper nouns and numeric identifiers are losslessly recovered when anchored. Structural errors are predominantly restricted to low-energy, high-frequency function tokens or punctuation ("structural agnosia"), not semantic content.

Latency and Computational Profile

Ablation and profiling reveal the core memory operations (encoding and decoding) run at $<20\,\mu\text{s}$ per token—five orders of magnitude faster than the LLM inference step. Under quantized inference, even the expensive generative reconstructions fall below 50 ms latency, achieving interactive real-time performance for sequences of arbitrary length (Figure 6).

Figure 6: Latency profile decomposition: manifold operations are negligible relative to neural inference and do not scale with memory depth.

Comparative Analysis and Limitations

PTM occupies a novel region in the architectural trade-off space: it achieves the infinite retention of retrieval-augmented schemes (RAG/RETRO) without sacrificing causal coherence, and the computational efficiency of state-space models without suffering their recall decay. Its memory "wall" is defined strictly by floating-point resolution and phonetic resolution, not by hardware limits or algorithmic complexity.

Crucially, this means the "cost" of long-context language modeling is now primarily a spectral resolution problem: improving performance depends on finer-grained phonetic encoding rather than expanding caches or model parameters.

The principal limitation is precision: in high-stakes or code-generation domains where orthographic exactitude is required, PTM’s reliance on acoustic resonance may under-specify low-entropy symbols unless anchor selection is meticulously tuned. Errors primarily occur when critical information is categorized by the importance filter as compressible "fluid" rather than an "anchor"; recalibration of entropy filtering is therefore vital in safety-critical deployments.

Implications and Future Directions

PTM advances a hardware- and topology-aware theory of neural memory, emphasizing continuous, loss-resistant signal transformation over discrete data accumulation. This reframing has multiple implications:

• Practical architectures: Future LLM deployments for long-context tasks (legal QA, scientific summarization, narrative reasoning) can dramatically minimize memory costs without linear scaling penalties.
• Neuro-symbolic models: The clear separation and fusion of structural anchors and distributed acoustic context motivates further integration of sub-symbolic and symbolic approaches, particularly for robust out-of-distribution generalization.
• Signal-processing direction: Improvement in phonetic encoder design (e.g., larger acoustic vocabularies, language-specific vectors) is now foundational to memory fidelity scaling, overtaking the relevance of model size or depth.
• Cognitive modeling: The ergodic approach directly reflects manifold-based theories of human sequential and spatial memory in neuroscience, suggesting an avenue for unifying artificial and biological memory system design.

Conclusion

Phonetic Trajectory Memory redefines AI context memory as a signal processing problem on a bounded, ergodic manifold. The architecture is empirically validated to provide sequence-invariant accuracy, $O(1)$ retrieval, and orders-of-magnitude compression, at the expense of orthographic precision for compressible tokens. The primary future direction is to further close the remaining gap between semantic fluency and acoustic efficiency, optimizing the neuro-symbolic interface for both robust generalization and high-stakes applications.

For full technical details, empirical logs, and mathematical proofs, see "Memory as Resonance: A Biomimetic Architecture for Infinite Context Memory on Ergodic Phonetic Manifolds" (2512.20245).