Bridging Silicon and the Hippocampus: Algebro-Deterministic Memory "VaCoAl" as a Substrate for Vector-HaSH and TEM

2026-05-22 · Source: cs.NE updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences, Robotics & Autonomous Systems · Depth: Expert, extended

Summary

The paper introduces VaCoAl, an algebro-deterministic hyperdimensional memory architecture built from Galois-field linear-feedback shift registers (LFSRs). It bridges computational neuroscience, hippocampal electrophysiology, and hyperdimensional computing by showing VaCoAl supplies a shared algebraic object for Vector Hippocampal Scaffolded Heteroassociative Memory (Vector-HaSH) and the Tolman–Eichenbaum Machine (TEM). Specifically, VaCoAl's deterministic Galois-field diffusion offers a substrate-level alternative to Vector-HaSH's random scaffold projection, satisfying quasi-orthogonality with matched second-moment statistics and bit-exact reproducibility. Furthermore, VaCoAl's path-integral Confidence Ratio CR2 provides the first algebraically tractable model for empirically reported multiplicative decay of multi-hop replay fidelity in human intracranial electrophysiology (iEEG). The architecture also explains STDP-like path selection and rationalizes the conservation of two hippocampal orthogonalizing pathways across >520 Myr of vertebrate evolution.

Key takeaway

For AI Engineers designing memory-based reasoning systems, this work suggests adopting VaCoAl's algebro-deterministic diffusion to achieve reproducible, auditable, and energy-efficient hyperdimensional computing. You should consider implementing its path-integral Confidence Ratio (CR2) for built-in explainability and robust multi-hop inference, especially in neuro-symbolic AI applications. This approach offers a principled way to balance capacity, energy, and plasticity, mirroring biological hippocampal strategies.

Key insights

VaCoAl offers a deterministic, algebraic substrate for hippocampal memory, unifying computational models and empirical replay dynamics.

Principles

• Deterministic Galois-field diffusion achieves quasi-orthogonality.
• Multi-hop replay fidelity decays multiplicatively.
• STDP-like path selection arises from architectural demands.

Method

VaCoAl uses Galois-field diffusion via LFSRs for quasi-orthogonal addressing, block-wise algebraic majority voting for retrieval, and path-integral Confidence Ratios (CR1/CR2) for multi-hop sequence evaluation.

In practice

• Substitute Galois-field diffusion for random projection in HDC.
• Use CR2 for auditable, explainable multi-hop reasoning.
• Implement dual orthogonalizers for energy-capacity trade-offs.

Topics

• Hyperdimensional Computing
• Galois Fields
• Hippocampal Memory
• Sharp-Wave Ripples
• Vector-HaSH
• Neuro-symbolic AI

Best for: AI Scientist, Research Scientist, AI Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.NE updates on arXiv.org.