VaCoAl: New algebro-deterministic memory model bridges hippocampal replay and silicon

A new paper from researchers Hiroyuki Chuma, Kanji Otsuka, and Yoichi Sato proposes VaCoAl, an algebro-deterministic hyperdimensional memory architecture that bridges silicon hardware and hippocampal memory processing. VaCoAl uses Galois-field linear feedback shift registers (LFSRs) to generate deterministic, quasi-orthogonal vectors, replacing the random projection matrices used by the Vector-HaSH model of hippocampal-entorhinal computation. This substrate-level alternative satisfies the same quasi-orthogonality requirements but offers bit-exact reproducibility, stronger avalanche behavior, and matched second-moment statistics. The authors formally show that VaCoAl provides the missing algebraic object unifying Vector-HaSH grid-cell factorisation and the Tolman-Eichenbaum Machine (TEM).

VaCoAl also provides the first algebraic model of multi-hop replay fidelity decay observed in human iEEG studies. The path-integral Confidence Ratio CR2, defined as the product of per-step confidence ratios along an n-hop chain, naturally fits the multiplicative decay pattern reported for ripple-locked cortical reactivations. The architecture’s STDP-like path selection emerges from requirements for similarity preservation, compositional reversibility, and bounded-frontier search—requirements that also constrain hippocampal computation. The authors argue VaCoAl’s operating regimes parallel EC-CA3 and EC-DG-CA3 pathways, offering an energy-capacity-plasticity explanation for why both pathways are conserved across 520+ million years of evolution. The paper derives explicit, testable iEEG predictions, bridging computational neuroscience and hyperdimensional engineering for the first time.