# Harness-agnostic detection and immunization of reward hacking in self-evolving language models

arXiv: https://arxiv.org/abs/2609.04665 · HTML: https://mlsanity.com/paper/2609.04665/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Reward hacking and misspecification, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 14 of its 23 references that are in the map.
- First posted on arXiv 4 Sep 2026.

## Placed in

- LLM alignment / RLHF / preference optimisation / [Reward hacking and misspecification](https://mlsanity.com/alignment/reward-hacking-and-misspecification/)
- Synthetic data and self-improvement for LLMs / [Safety of self-evolving systems](https://mlsanity.com/synth/safety-of-self-evolving-systems/)

## Builds on (most cited first, 14 of 14)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [DSPy: Compiling Declarative Language Model Calls into Self-Improving Pipelines](https://mlsanity.com/paper/2310.03714/) (2023)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [GEPA: Reflective Prompt Evolution Can Outperform Reinforcement Learning](https://mlsanity.com/paper/2507.19457/) (2025)
- [R-Zero: Self-Evolving Reasoning LLM from Zero Data](https://mlsanity.com/paper/2508.05004/) (2025)
- [A Careful Examination of Large Language Model Performance on Grade School Arithmetic](https://mlsanity.com/paper/2405.00332/) (2024)
- [GSM-Plus: A Comprehensive Benchmark for Evaluating the Robustness of LLMs as Mathematical Problem Solvers](https://mlsanity.com/paper/2402.19255/) (2024)
- [Categorizing Variants of Goodhart's Law](https://mlsanity.com/paper/1803.04585/) (2018)
- [Reward Hacking in the Era of Large Models: Mechanisms, Emergent Misalignment, Challenges](https://mlsanity.com/paper/2604.13602/) (2026)
- [PaCoST: Paired Confidence Significance Testing for Benchmark Contamination Detection in Large Language Models](https://mlsanity.com/paper/2406.18326/) (2024)

## Built on by (most cited first, 3 of 3)

- [Bad Genius: Counterfactual-Guided Harness Evolution Beyond Task-Specific Shortcuts](https://mlsanity.com/paper/2609.18366/) (2026)
- [What Does a Harness Repair? A Preregistered Study of Visibility, Baseline Adequacy and Evaluation Defects](https://mlsanity.com/paper/2610.05533/) (2026)
- [Reflective Prompt Optimization of a Deep-Research Agent: A Topic-Disjoint, Multi-Seed Protocol for Measuring Transferable Gains and Prompt-Level Overfitting](https://mlsanity.com/paper/2610.12601/) (2026)

## Abstract (arXiv)

Self-evolving language models improve by proposing candidate updates and keeping whatever raises a visible score. When that score is an imperfect proxy for the capability one actually wants, sustained selection widens the gap between the two. This is reward hacking. We introduce HackProbe, a monitor that attaches to an arbitrary self-evolving loop through two black-box hooks, with no access to weights or activations. It keeps a secret, distribution-fixed comparison core, whose frozen distribution makes its capability proxy comparable across generations, alongside a rotated fresh layer that hardens the bank against co-adaptation. Four tests built on that proxy cover the level gap, a scale-aligned divergence with online change-point detection, capability stagnation, and a conditional confidently-wrong rate; a Sidak correction turns them into a calibrated family-wise p-value. Diagnosis alone recovers nothing, so a risk-aware immunization layer reselects an honest candidate from the proposal pool using the core together with a purely structural gaming footprint, disclosing at most log2 Pi bits per generation to the host. We prove a detectability bound that converts a target error rate into an explicit probe-size budget, and we delimit what probe rotation does and does not buy. On a controlled prompt-level host with four injected hacking channels and ground-truth labels, HackProbe reaches 0.763 AUROC against 0.663 for the strongest baseline and cuts the false-positive rate from 0.706 to 0.434. Its bandwidth-limited reselection is the only immunization level that returns more true capability under hacking, 5.2 points on average, than it forfeits on clean runs, 4.7; per-channel effects are mostly not individually significant.