Vacoal Hippocampal Memory

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name: vacoal-hippocampal-memory
description: "VaCoAl algebro-deterministic hippocampal memory architecture. Bridges silicon and hippocampus by connecting Vector-HaSH, TEM, and hyperdimensional computing. Use when: hippocampal memory modeling, grid-cell scaffolds, episodic memory replay, sharp-wave ripples, Vector-HaSH, Tolman-Eichenbaum Machine, hyperdimensional computing, Galois-field LFSRs, multi-hop memory replay, memory fidelity decay, STDP-like path selection, EC-CA3 pathways, dentate gyrus, compositional memory, hippocampal-entorhinal circuit."
---

# VaCoAl: Algebro-Deterministic Hippocampal Memory Architecture

## Paper Reference

- **Title**: Bridging Silicon and the Hippocampus: Algebro-Deterministic Memory "VaCoAl" as a Substrate for Vector-HaSH and TEM
- **arXiv**: 2605.15652
- **Authors**: Hiroyuki Chuma, Kanji Otsuka, Yoichi Sato
- **Date**: 2026-05-19
- **Category**: cs.NE (Neural and Evolutionary Computing)

## Core Innovation

VaCoAl provides a shared algebraic object connecting three parallel research literatures:
1. **Vector-HaSH**: Hippocampal-entorhinal circuit factorizes content from grid-cell scaffold
2. **TEM (Tolman-Eichenbaum Machine)**: Compositional memory via ripple-mediated replay
3. **Human iEEG findings**: Sharp-wave ripples gate episodic recall; multi-hop replay fidelity decays multiplicatively

## Key Components

### 1. Galois-Field Diffusion Substrate

- Deterministic Galois-field LFSRs provide quasi-orthogonal vectors
- Replaces Vector-HaSH's random scaffold-to-hippocampus projection
- **Advantages**: Matched second-moment statistics, stronger avalanche behavior, bit-exact reproducibility
- **Architecture**: Built from Linear Feedback Shift Registers over GF(2)

### 2. Confidence Ratio (CR) Model for Multi-Hop Replay

- **CR1**: Per-step confidence ratio for single-hop reactivation
- **CR2**: Path-integral = product of CR1 values along n-hop chain
- Models observed multiplicative decay in multi-hop replay fidelity
- First algebraically tractable model under conditional independence assumption

### 3. STDP-like Path Selection

Emerges from architectural demands:
- Similarity preservation
- Compositional reversibility
- Bounded-frontier search

### 4. Hippocampal Pathway Correspondences

VaCoAl operating regimes share architectural commitments with:
- **EC → CA3**: Direct entorhinal-to-CA3 pathway
- **EC → DG → CA3**: Dentate gyrus-mediated pathway
- Conserved across >520 Myr of evolution

## Testable Predictions

1. Multiplicative fidelity decay follows CR1^n form in iEEG recordings
2. Ripple-locked cortical reactivation patterns match VaCoAl replay sequences
3. DG elaboration in primates reflects capacity-plasticity tradeoff predicted by VaCoAl

## Activation Keywords

hippocampal memory, VaCoAl, Vector-HaSH, Tolman-Eichenbaum Machine, grid cells, episodic memory, sharp-wave ripples, hyperdimensional computing, Galois field, LFSR, multi-hop replay, STDP, entorhinal cortex, CA3, dentate gyrus, compositional memory, memory fidelity decay