AuthorsTarik Houichime, Abdelghani Souhar, Younes El Amrani
TL;DR
Phonetic Trajectory Memory encodes language as an ergodic rotation on a 16D hyper-torus, achieving >3,000× KV compression with ≈92% factual accuracy and ≈34 ms latency.
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THE PROBLEM
Contemporary KV caches grow O(N) with tokens, forcing a trade-off between amnesia and latency, and burning massive energy in the Prefill phase.
This breaks long-context reasoning for LLMs that must retain books or 20,000-token streams, making infinite context feel impossible on finite VRAM.
HOW IT WORKS
Phonetic Trajectory Memory uses a Hyper-Torus Memory, Acoustic Injection, Entropy Filter, and Resonance Engine to encode tokens as a 16D ergodic state instead of dense KV tensors.
You can think of PTM like a record groove or a rotating clock, where the path of sound is conserved, and the LLM weights act like a jukebox that replays the song from a single position.
This ergodic rotation and Signal Consensus let PTM reconstruct past tokens from a conserved geometric signal, enabling O(1) access and >3,000× compression that a plain context window cannot achieve.
DIAGRAM
This diagram shows how Phonetic Trajectory Memory reconstructs a past token by unwinding the manifold and fusing geometric evidence with the LLM prior.
DIAGRAM
This diagram shows how Phonetic Trajectory Memory is evaluated on narrative, scientific, and long horizon corpora while measuring accuracy, compression, and latency.
PROCESS
Acoustic Geometric Injection
In the Acoustic-Geometric Injection phase, Phonetic Trajectory Memory uses the Hard Coded Acoustic Engine and FFT based Ear to map each token into a 16D phonetic vector on the Hyper Torus Memory.
The Entropy Filter
In The Entropy Filter phase, Phonetic Trajectory Memory classifies tokens into Anchors and Bridges, storing high entropy Anchors in the Sparse Symbolic Cache and folding Bridges into the manifold state.
The Resonance
In The Resonance phase, Phonetic Trajectory Memory performs Symplectic Inversion to recover Vrec, broadcasts it over the vocabulary, and combines PSignal with PLLM through Signal Consensus.
Signal Consensus Analysis
During Signal Consensus Analysis, Phonetic Trajectory Memory inspects PLLM and PSignal over time, identifying Anchor pillars, hallucination zones, and phonetic drift to tune the coupling coefficient and failure modes.
KEY CONTRIBUTIONS
The Geometric Proof The Manifold
Phonetic Trajectory Memory defines a 16 dimensional Hyper Torus with irrational rotations, proving via Weyl and Kronecker that O(1) memory with ergodic trajectories and strong unicity is mathematically achievable.
The Structural Guarantee The Anchor
Phonetic Trajectory Memory introduces the Neuro Symbolic Relay and Entropy Filter, preserving high entropy Anchors in a Sparse Symbolic Cache while compressing Bridges to achieve ≈4.4× memory reduction at 91% accuracy.
The Thermodynamic Inversion The Reconstruction
Phonetic Trajectory Memory shows that manifold encode decode costs are ≈6.8µs and 14.1µs, while reconstruction latency drops to ≈35.6 ms under quantization, achieving >3,000× signal to KV compression with ≈92% factual accuracy.
RESULTS
Semantic Accuracy
92.34%
+? over Dense KV baseline (exact baseline not numerically specified)
Window Accuracy
91.00%
Deep context Alice window at T=15k with 77.31% drop rate
Signal Compression
>3000x
Signal to KV state ratio in Zero Anchor Blind Walk
Reconstruction Latency
35.6 ms
Mean worst case under 4 bit CUDA acceleration compared to ≈1.8 s unoptimized
Phonetic Trajectory Memory is evaluated on Alice’s Adventures in Wonderland, Deep Sea Oceanography Abstracts, and a 20,000 token Gutenberg stream, testing semantic accuracy, compression ratio, and retrieval latency. The ≈92% accuracy with >3,000× compression and ≈35.6 ms latency shows that Phonetic Trajectory Memory maintains long horizon fidelity while collapsing KV memory costs.
BENCHMARK
Phonetic Trajectory Memory is evaluated on Alice’s Adventures in Wonderland, Deep Sea Oceanography Abstracts, and a 20,000 token Gutenberg stream, testing semantic accuracy, compression ratio, and retrieval latency. The ≈92% accuracy with >3,000× compression and ≈35.6 ms latency shows that Phonetic Trajectory Memory maintains long horizon fidelity while collapsing KV memory costs.
BENCHMARK
Effective compression versus dense KV baselines while maintaining high semantic accuracy.
KEY INSIGHT
Even with Zero Anchors and 100% KV cache removal, Phonetic Trajectory Memory reconstructs 83.58% of tokens from only 0.020 MB of phonetic signal.
This is surprising because it shows a 3,000× compression over a 64.32 MB dense KV baseline, breaking the assumption that high fidelity long context requires storing every embedding.
WHY IT MATTERS
Phonetic Trajectory Memory unlocks effectively infinite context with O(1) access, turning memory into a conserved geometric signal instead of a growing KV warehouse.
Builders can now design LLM systems that keep entire books or multi session histories in live state on commodity hardware, trading slight phonetic noise for massive capacity and constant time retrieval.
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Answers use this explainer on Memory Papers.
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