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

arXiv: https://arxiv.org/abs/2608.02267 · HTML: https://mlsanity.com/paper/2608.02267/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 61 references that are in the map.
- First posted on arXiv 3 Aug 2026.

## Builds on (most cited first, 6 of 6)

- [Optimal Best Arm Identification with Fixed Confidence](https://mlsanity.com/paper/1602.04589/) (2016)
- [Pure Exploration with Multiple Correct Answers](https://mlsanity.com/paper/1902.03475/) (2019)
- [Cost Aware Best Arm Identification](https://mlsanity.com/paper/2402.16710/) (2024)
- [Monitored Markov Decision Processes](https://mlsanity.com/paper/2402.06819/) (2024)
- [Bayes-Sufficient Representations in Supervised Learning](https://mlsanity.com/paper/2606.04045/) (2026)
- [Testing Sufficiency for Transfer Learning](https://mlsanity.com/paper/2304.05636/) (2023)

## Abstract (arXiv)

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.