Vacoal Algebro Deterministic Memory

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name: vacoal-algebro-deterministic-memory
description: "Algebro-deterministic hippocampal memory architecture (VaCoAl) built from Galois-field LFSRs. Provides substrate-level alternative to random scaffold-to-hippocampus projections, algebraically tractable model of multi-hop replay-fidelity decay, and STDP-like path selection. Based on Chuma, Otsuka & Sato (arXiv: 2605.15652). Use when designing brain-inspired memory systems, implementing hippocampal replay mechanisms, building hippocampus-silicon bridge architectures, or modeling memory consolidation with algebraic methods."
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# VaCoAl: Algebro-Deterministic Hippocampal Memory

Algebro-deterministic hyperdimensional memory architecture bridging silicon and hippocampal memory. Based on Chuma, Otsuka & Sato (arXiv: 2605.15652).

## Core Architecture

- Built from Galois-field Linear Feedback Shift Registers (LFSRs)
- Connects Vector-HaSH and Tolman-Eichenbaum Machine (TEM) frameworks
- Deterministic Galois-field diffusion replaces random scaffold-to-hippocampus projections
- Path-integral Confidence Ratio: first algebraically tractable model of multi-hop replay-fidelity decay
- STDP-like path selection emerges from architectural demands

## Key Components

### Galois-Field Diffusion
Deterministic alternative to random projections. LFSRs generate structured, reproducible hyperdimensional vectors with provable algebraic properties.

### Confidence Ratio
Path-integral-based metric for multi-hop replay fidelity decay. Algebraically tractable — enables analytical prediction of memory retrieval quality.

### STDP-like Path Selection
Emerges from requirements of similarity preservation and compositional reversibility. No explicit learning rule needed; selection follows from architecture.

## When to Use

- Designing brain-inspired memory systems with hippocampal replay
- Implementing Vector-HaSH or TEM with substrate-level memory
- Building silicon-hippocampus bridge architectures
- Modeling memory consolidation with algebraic/deterministic methods
- Multi-hop memory retrieval with fidelity guarantees

## Related Concepts

- Vector-HaSH (Vector-based Hippocampal Sequence encoding)
- Tolman-Eichenbaum Machine (TEM)
- Hyperdimensional Computing
- Galois Fields / LFSRs
- STDP (Spike-Timing-Dependent Plasticity)

**Activation**: vacoal, algebro-deterministic memory, hippocampal memory, galois-field LFSR, vector-hash, tolman-eichenbaum, replay fidelity, brain-inspired memory, arXiv:2605.15652