A Held-Out Transition-Pair Falsifier for Long-Horizon Non-Abelian State Tracking

• URL: http://arxiv.org/abs/2606.07254v1
• Date: Fri, 05 Jun 2026 13:26:41 GMT
• Title: A Held-Out Transition-Pair Falsifier for Long-Horizon Non-Abelian State Tracking
• Abstract summary: We introduce a held-out transition-pair falsifier for finite non-Abelian group tracking.<n>In a controlled $S_3 times S_3$ benchmark, a projected recurrent state model trained only on length-8 sequences produces error-free final-state predictions.
• Score: 0.5076419064097734
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: State tracking exposes a sharp limitation of sequence models: the relevant signal is often not a summary of observed tokens, but an ordered latent state that evolves through non-commutative transformations. We introduce a held-out transition-pair falsifier for finite non-Abelian group tracking. The protocol forbids selected ordered generator pairs during training and requires the same local patterns during evaluation, blocking one direct local-transition memorization pathway. In a controlled $S_3 \times S_3$ benchmark, a projected recurrent state model trained only on length-8 sequences produces error-free final-state predictions (perfect 250/250 per horizon) through evaluation horizons up to 1,048,576 tokens across five seeds. Matched native-readout baselines, including bag, GRU, and a single-configuration structured state-space model, remain near floor under the same protocol. Projection-matched GRU, structured SSM, and bag baselines equipped with analogous finite-group prototype readouts also remain near chance under the same split. Mechanism diagnostics show that hard projection coincides with low homomorphism error, low state-consistency drift, and non-trivial commutator separation, while softened projection collapses final-state accuracy. Clean-split audits verify zero verbatim reduced-word overlap and zero structural-template overlap between training and evaluation partitions. The evidence is scoped to this controlled finite-group falsifier rather than to a general architecture ranking. Within that regime, explicit projected non-commutative state composition acts as a useful inductive bias for long-horizon hidden-state tracking.

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