Self-Certification of Representation Adequacy: Sequential Certification at Minimum Task Loss

Zijie Huang

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arXiv · 2608.02267

Self-Certification of Representation Adequacy: Sequential Certification at Minimum Task Loss

Zijie Huang

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Abstract

Agents that act on a compressed representation of their history face a structural risk: if the representation aliases histories with different optimal actions, no rule measurable with respect to the representation can avoid an irreducible per-round loss, and the agent may be unable to detect this from its own transcript. This paper develops a four-layer theory of self-certification of representation adequacy. The static layer defines decision-theoretic adequacy through a Bayes-risk grouping identity and prices a one-shot external verification by an exact total-variation threshold. The sequential layer poses certification as an optimal-stopping problem in the currency of task loss: we define an environment-wise certification complexity constant through a covering linear program, prove an information-task-loss lower bound for every delta-correct strategy, and give a Certification Track-and-Stop policy whose cost matches the bound asymptotically. A final boundary layer gives an explicit kernel-switching example and identifies the open theorem needed to cover policy switching or representation repair; it does not claim that the fixed-kernel guarantees extend to representation revision. The proofs of the two main theorems are given in full in the appendices.

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Zijie Huang. 2026-09-12. Self-Certification of Representation Adequacy: Sequential Certification at Minimum Task Loss. https://arxiv.org/abs/2608.02267

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