Signed-XOR Error and Sparse Coding in a Dale-Complaint Substrate for Sequence Memorization

Abstract

How much machinery does a network need to memorize and recall discrete sequences when constrained to a biologically plausible substrate? We address this question using 50 short monophonic melodies in 4/4, used only as a controlled sequence-memory benchmark. Each beat is encoded with two clean one-hot populations - a 12-way pitch code and a separate 2-way {onset, sustain} code - and the decoder emits the same 14-dimensional code, so the autoregressive loop closes in a single neural format. The model obeys Dales law: latent units are excitatory or inhibitory, synaptic weights are non-negative, the decoder is implemented as explicit multi-contact bundles, and the encoder is a frozen sparse random projection wired at cortical ([~]10%) density. On this substrate, a local ENGRAMMER signed-XOR read-out rule combined with a sparse k-winner-take-all code stores the training corpus exactly. With a modest latent expansion (L = 512), the model reaches 100% teacher-forced and autoregressive pitch accuracy, recognizes all training melodies, and separates all held-out melodies as novel with zero overlap. Ablations show that the signed error, sparse code, explicit E/I routing, and multi-contact synapses are the main load-bearing ingredients, whereas learning the encoder is strongly detrimental and dense input wiring does not help. Capacity sweeps show that Dales law mainly increases the capacity required for stable autoregressive recall: teacher-forced storage saturates between L = 128 and L = 256, while free-running recall becomes perfect by L = 512. A matched random corpus reaches the same final fidelity and is recalled at least as well at every capacity, indicating that musical structure does not improve recall on this benchmark and that final fidelity is set by capacity rather than by structure. The result is a Dale-compliant, gradient-free sparse associative memory rather than a general sequence learner.