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Minimal Recurrent Behavioral Memory for Imitation under Partial Observability

arXiv · AI, language, vision and robotics · article · Sep 22, 2026 · UTC

What is the least recurrent memory needed to reproduce a specified expert under partial observability? The instantaneous requirement is the conditional entropy of the expert's behavioral quotient, but recurrence must also preserve distinctions that future observations will not restore before use. We characterize this minimal recurrent behavioral memory by a compatibility relation: under transitivity its classes attain the exact minimum, while the general case is an entropy minimization over closed compatible state assignments, with exact certificates on finite instances. A sole-carrier measure

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