# Signed Compression Progress on a Sealed Audit is Goodhart-Resistant

arXiv: https://arxiv.org/abs/2606.11417 · HTML: https://mlsanity.com/paper/2606.11417/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 17 references that are in the map.
- First posted on arXiv 9 Jun 2026.

## Builds on (most cited first, 11 of 11)

- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)
- [Exploration by Random Network Distillation](https://mlsanity.com/paper/1810.12894/) (2018)
- [The Effects of Reward Misspecification: Mapping and Mitigating Misaligned Models](https://mlsanity.com/paper/2201.03544/) (2022)
- [Defining and Characterizing Reward Hacking](https://mlsanity.com/paper/2209.13085/) (2022)
- [Categorizing Variants of Goodhart's Law](https://mlsanity.com/paper/1803.04585/) (2018)
- [Generalization in Adaptive Data Analysis and Holdout Reuse](https://mlsanity.com/paper/1506.02629/) (2015)
- [The Surprising Creativity of Digital Evolution: A Collection of Anecdotes from the Evolutionary Computation and Artificial Life Research Communities](https://mlsanity.com/paper/1803.03453/) (2018)
- [The Ladder: A Reliable Leaderboard for Machine Learning Competitions](https://mlsanity.com/paper/1502.04585/) (2015)
- [ARC-TGI: Human-Validated Task Generators with Reasoning Chain Templates for ARC-AGI](https://mlsanity.com/paper/2603.05099/) (2026)

## Built on by (most cited first, 1 of 1)

- [Which Self-Improvements Should We Trust? Reliable Self-Improvement When Agents Reuse Their Benchmarks](https://mlsanity.com/paper/2609.33180/) (2026)

## Abstract (arXiv)

Compression progress is a long-standing proposal for intrinsic motivation: reward an agent when its world model becomes better at predicting or compressing experience. The folk claim is that this reward is "credible" because it is paid only for learning. We make this precise and prove it. If intrinsic reward is the signed decrease of a fixed sealed-audit loss, r_t = E(theta_{t-1}) - E(theta_t), then cumulative reward telescopes exactly to endpoint audit improvement, so no policy can push reward up indefinitely while true audit performance stagnates or degrades. For finite audit panels the same result holds with a sharp false-positive budget: cumulative empirical reward is at most true audit improvement plus 2 Delta_n(F, delta), the uniform audit deviation of the model class. This is horizon-free: adaptivity over time costs nothing once the sealed panel uniformly controls the class. The theorem also identifies the failure modes: the guarantee disappears if progress is clipped, scored on the agent's own stream, exposed to a high-capacity model on a reusable panel, or applied to a neural class that makes Delta_n vacuous. We give a Lean 4 mechanization of the structural core (telescoping, the finite-audit bound, finite Gibbs, and the entropy floor) and an experiment suite on ARC-TGI grid-transformation generators with adaptive holdout attacks. Experiments confirm the theory: finite-audit deviation scales as n^{-0.527}; signed progress resists clip-farming, stream leakage, and noisy-TV curiosity; naive reusable audits are exploitable by black-box scalar feedback, while standard release defenses keep the attack below the 2 Delta_n threshold. Signed compression progress on a sealed audit is an accounting signal of genuine improvement.