# Detecting and Suppressing Reward Hacking with Gradient Fingerprints

arXiv: https://arxiv.org/abs/2604.16242 · HTML: https://mlsanity.com/paper/2604.16242/

## Key facts

- Cited by 5 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 56 of its 76 references that are in the map.
- First posted on arXiv 17 Apr 2026.

## Placed in

- LLM alignment / RLHF / preference optimisation / [Reward hacking and misspecification](https://mlsanity.com/alignment/reward-hacking-and-misspecification/)

## Builds on (most cited first, 30 of 56)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Measuring Coding Challenge Competence With APPS](https://mlsanity.com/paper/2105.09938/) (2021)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [Towards Faithfully Interpretable NLP Systems: How should we define and evaluate faithfulness?](https://mlsanity.com/paper/2004.03685/) (2020)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [Beyond neural scaling laws: beating power law scaling via data pruning](https://mlsanity.com/paper/2206.14486/) (2022)
- [Fooling LIME and SHAP: Adversarial Attacks on Post hoc Explanation Methods](https://mlsanity.com/paper/1911.02508/) (2019)
- [Reasoning Models Don't Always Say What They Think](https://mlsanity.com/paper/2505.05410/) (2025)
- [ReTool: Reinforcement Learning for Strategic Tool Use in LLMs](https://mlsanity.com/paper/2504.11536/) (2025)
- [Monitoring Reasoning Models for Misbehavior and the Risks of Promoting Obfuscation](https://mlsanity.com/paper/2503.11926/) (2025)
- [A Long Way to Go: Investigating Length Correlations in RLHF](https://mlsanity.com/paper/2310.03716/) (2023)
- [Faithful Chain-of-Thought Reasoning](https://mlsanity.com/paper/2301.13379/) (2023)
- [GRAD-MATCH: Gradient Matching based Data Subset Selection for Efficient Deep Model Training](https://mlsanity.com/paper/2103.00123/) (2021)
- [Prioritized Training on Points that are Learnable, Worth Learning, and Not Yet Learnt](https://mlsanity.com/paper/2206.07137/) (2022)
- [Let's Think Dot by Dot: Hidden Computation in Transformer Language Models](https://mlsanity.com/paper/2404.15758/) (2024)
- [Sycophancy to Subterfuge: Investigating Reward-Tampering in Large Language Models](https://mlsanity.com/paper/2406.10162/) (2024)
- [Chain-of-Thought Reasoning In The Wild Is Not Always Faithful](https://mlsanity.com/paper/2503.08679/) (2025)
- [The Unreliability of Explanations in Few-shot Prompting for Textual Reasoning](https://mlsanity.com/paper/2205.03401/) (2022)
- [WARM: On the Benefits of Weight Averaged Reward Models](https://mlsanity.com/paper/2401.12187/) (2024)
- [Implicit Gradient Regularization](https://mlsanity.com/paper/2009.11162/) (2020)
- [Natural Emergent Misalignment from Reward Hacking in Production RL](https://mlsanity.com/paper/2511.18397/) (2025)
- [Language Models Learn to Mislead Humans via RLHF](https://mlsanity.com/paper/2409.12822/) (2024)
- [Learning to Deceive with Attention-Based Explanations](https://mlsanity.com/paper/1909.07913/) (2019)
- [Making Reasoning Matter: Measuring and Improving Faithfulness of Chain-of-Thought Reasoning](https://mlsanity.com/paper/2402.13950/) (2024)
- [Big-Math: A Large-Scale, High-Quality Math Dataset for Reinforcement Learning in Language Models](https://mlsanity.com/paper/2502.17387/) (2025)
- [Question Decomposition Improves the Faithfulness of Model-Generated Reasoning](https://mlsanity.com/paper/2307.11768/) (2023)
- [MATES: Model-Aware Data Selection for Efficient Pretraining with Data Influence Models](https://mlsanity.com/paper/2406.06046/) (2024)

## Built on by (most cited first, 5 of 5)

- [Do Androids Dream of Breaking the Game? Systematically Auditing AI Agent Benchmarks with BenchJack](https://mlsanity.com/paper/2605.12673/) (2026)
- [When Confidence Rises Too Early: Detecting Shortcut Reasoning via Premature Answer Commitment](https://mlsanity.com/paper/2609.35074/) (2026)
- [Verifier Errors in RLVR: Reward Hacking, Limits of Feedback, and Selective Control](https://mlsanity.com/paper/2609.35677/) (2026)
- [CATCH: A Controllable Analysis Testbed for Reward Hacking in Coding RL](https://mlsanity.com/paper/2609.39533/) (2026)
- [A Near-Zero Monitor Readout Is Not Evidence of Behavioral Control](https://mlsanity.com/paper/2610.03458/) (2026)

## Abstract (arXiv)

Reinforcement learning with verifiable rewards (RLVR) typically optimizes for outcome rewards without imposing constraints on intermediate reasoning. This leaves training susceptible to reward hacking, where models exploit loopholes (e.g., spurious patterns in training data) in the reward function to achieve high scores without solving the intended task. These reward-hacking behaviors are often implicit, as the intermediate chain-of-thought (CoT) may appear plausible on the surface, limiting the effectiveness of purely text-based monitoring. We propose Gradient Fingerprint (GRIFT), a method for detecting reward hacking using models' internal computations. Given a prompt and a model-generated CoT, GRIFT computes gradients of the CoT conditioned on the prompt and compresses them into a compact representation, which is then used to assess whether the CoT reflects reward hacking behavior. Across verifiable reasoning benchmarks spanning math, code, and logical reasoning, GRIFT substantially outperforms strong baselines, including CoT Monitor and TRACE, achieving over 25% relative improvement in detecting reward hacking behavior. Moreover, integrating GRIFT into the rejection fine-tuning pipeline for reasoning tasks reduces reward hacking and improves performance on the true task objective. Our results highlight a promising direction of leveraging gradient level representations for assessing the quality of CoT reasoning traces. Our code is available at: https://github.com/songtao-x/reward_hack.