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

Abstract

VaCoAl (Python: PyVaCoAl) attacks the Binding Problem algebraically rather than statistically: an SRAM/DRAM-CAM organised end-to-end around one primitive, XOR-and-shift over GF(2) via primitive-polynomial LFSRs. Rooted in Kanerva's Sparse Distributed Memory, it retrieves in a million-dimensional binary space by Galois-field diffusion; Binding and Unbinding are exactly reversible at O(L), giving compositional generalisation with post-hoc auditability. Unexpectedly, a path-dependent semantic selection mechanism emerges undesigned, functionally equivalent to Spike-Timing-Dependent Plasticity (STDP) and predictable a priori from a closed form matching measurement on tens of millions of records. It is the Don't Care (collision-tolerance) rule: not a defect to engineer away, but the source of its ability to rank paths by quality. Capability: reversible binding plus tolerated collisions yields a path-integral confidence measure (CR2) ranking candidates by accumulated reliability, absent from hash-based search. Necessity: repair the collisions fully and the ranking vanishes; a memory that never fails has no record of which paths were difficult. Position: we do not surpass large language models; the substrate is orthogonal, supplying the auditable path-ranking layer they lack. A mentor-student ontology of ~470,000 WIKIDATA scholars, traversed backwards from all 64 Fields Medalists to depth 57 and >25.5M paths, stress-tests multi-hop reasoning over a large DAG. Ablation shows Don't Care imposing a depth-dependent exponential penalty that prunes circuitous routes and preserves direct ones: an Occam's razor. Per-generation CR1 stays within 0.995-0.999, yet cumulative CR2 decays monotonically to ~0.905 by generation 56, matching the closed form 0.997^56 = 0.846 within observed variation. All measurements are from PyVaCoAl, a software DRAM-CAM; speed and power figures are projections.

58 pages, 4 figure, 19 tables