Reproducing, Analyzing, and Detecting Reward Hacking in Rubric-Based Reinforcement Learning

Rubric-based reinforcement learning (RL) uses an LLM-as-a-Judge (LaaJ) to score model outputs according to rubrics as rewards. However, policy models may exploit latent biases in the judge, leading to reward hacking and ineffective or unsafe training outcomes. In real-world rubric-based RL, such hacking behaviors are often subtle and entangled with multiple judge biases, making them difficult to analyze, detect, and mitigate. In this paper, we introduce CHERRL, a controllable hacking environment for rubric-based RL. By injecting known biases into LaaJ, CHERRL enables stable reproduction of reward hacking, explicit observation of reward divergence, and precise identification of hacking onset. This provides a clean experimental testbed for studying the mechanisms and mitigations of reward hacking in rubric-based RL. To demonstrate its utility, we analyze different judge biases from the perspectives of discoverability and exploitability, and explore an agent-based system for automatically detecting reward hacking onset from training logs. The code and environment are publicly available at https://github.com/THUAIS-Lab/CHERRL.

Echoes as Anchors: Probabilistic Costs and Attention Refocusing in LLM Reasoning

Test-time compute allocation in large reasoning models (LRMs) is widely used and has applications in mathematical problem solving, code synthesis, and planning. Recent work has addressed this problem by scaling self-consistency and parallel thinking, adding generic ``thinking tokens'' and prompting models to re-read the question before answering. Unfortunately, these approaches either inject task-agnostic tokens or mandate heuristics that do not explain -- and often ignore -- the \emph{spontaneous} repetition that many LRMs exhibit at the head of their internal chains. In contrast, we analyze and harness the model's tendency to restate the question, which we term the \emph{Echo of Prompt (EOP)}, as a front-loaded, compute-shaping mechanism. We formalize its probabilistic cost by casting echo removal as rejection-based conditioning and defining the \emph{Echo Likelihood Gap} $Δ\mathcal{L}$ as a computable proxy. This provides the missing theoretical link that links early repetition to likelihood gains and downstream accuracy. However, it does not by itself specify how to exploit EOP. Consequently, we develop \emph{Echo-Distilled SFT (ED-SFT)} to instill an ``echo-then-reason'' pattern through supervised finetuning, and \emph{Echoic Prompting (EP)} to re-ground the model mid-trace without training. While promising, quantifying benefits beyond verbosity is non-trivial. Therefore, we conduct length and suffix-controlled likelihood analyses together with layer-wise attention studies, showing that EOP increases answer to answer-prefix attention in middle layers, consistent with an \emph{attention refocusing} mechanism. We evaluate on GSM8K, MathQA, Hendrycks-MATH, AIME24, and MATH-500 under identical decoding settings and budgets, and find consistent gains over baselines. Code is available at https://github.com/hhh2210/echoes-as-anchors.