Beyond LLMs, Sparse Distributed Memory, and Neuromorphics <A Hyper-Dimensional SRAM-CAM "VaCoAl" for Ultra-High Speed, Ultra-Low Power, and Low Cost>

Original Abstract

This paper reports an unexpected finding: in a deterministic hyperdimensional computing (HDC) architecture based on Galois-field algebra, a path-dependent semantic selection mechanism emerges, equivalent to spike-timing-dependent plasticity (STDP), with magnitude predictable a priori by a closed-form expression matching large-scale measurements. This addresses limitations of modern AI including catastrophic forgetting, learning stagnation, and the Binding Problem at an algebraic level. We propose VaCoAl (Vague Coincident Algorithm) and its Python implementation PyVaCoAl, combining ultra-high-dimensional memory with deterministic logic. Rooted in Sparse Distributed Memory, it resolves orthogonalisation and retrieval in high-dimensional binary spaces via Galois-field diffusion, enabling low-load deployment. VaCoAl is a memory-centric architecture prioritising retrieval and association, enabling reversible composition while preserving element independence and supporting compositional generalisation with a transparent reliability metric (CR score). We evaluated multi-hop reasoning on about 470k mentor-student relations from Wikidata, tracing up to 57 generations (over 25.5M paths). Using HDC bundling and unbinding with CR-based denoising, we quantify concept propagation over DAGs. Results show a reinterpretation of the Newton-Leibniz dispute and a phase transition from sparse convergence to a post-Leibniz "superhighway", from which structural indicators emerge supporting a Kuhnian paradigm shift. Collision-tolerance mechanisms further induce path-based pruning that favors direct paths, yielding emergent semantic selection equivalent to STDP. VaCoAl thus defines a third paradigm, HDC-AI, complementing LLMs with reversible multi-hop reasoning.