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Measuring Reward Hacking and Reasoning-Answer Decoupling Under Position-Confounded Optimization
Suyash Maniyar, Armaan Sandhu, Abhishek Mishra
TL;DR
Correct rewards can still leave models choosing between solving a task and exploiting a surface shortcut, making endpoint scores an unreliable measure of capability. This paper tests that problem with position-confounded reinforcement learning and finds shortcut behavior, reasoning-answer decoupling, out-of-domain transfer, and incomplete recovery.
Problem
When correct rewards are compatible with task solving and surface shortcuts, existing endpoint accuracy cannot distinguish capability from shortcut acquisition.
Method
The study trains language models on four-option math problems whose correct answer is always A, then evaluates randomized positions using accuracy, answer distributions, reasoning checks, and out-of-domain probes.
Results
Biased optimization causes heterogeneous in-domain collapse, reasoning-answer decoupling, transferable option-A bias, and uneven recovery after unbiased retraining.
Takeaways & Limitations
Endpoint accuracy can mix mathematical competence with a learned answer-position policy, so evaluation should jointly inspect reasoning, answer distributions, and out-of-domain behavior.
Takeaways & Limitations
The study uses one deliberately strong confound, small directional out-of-domain probes, and judge-based decoupling that inherits evaluator limitations.
Abstract
from arXiv · showhide
When a reward is correct on every training example yet consistent with more than one goal, a model can acquire an unintended one, a failure known as goal misgeneralization. Endpoint accuracy on the training distribution cannot tell the two apart, because solving the task and exploiting a surface feature can satisfy the reward equally well. We treat this as a measurement problem: what does a benchmark score measure once a model has been optimized against a correct but confounded signal? We train language models with GRPO on multiple-choice math problems where the correct answer is always option A, then evaluate on an unseen test set with unbiased answer positions. Across Qwen2.5, Llama 3.x and Gemma-3 models, biased training often drives option-A rates above 0.90 in smaller models and collapses unbiased accuracy toward chance, so accuracy stops measuring math ability and instead measures an answer-position policy. We further find reasoning-answer decoupling: capable models generate reasoning that reaches the correct numeric answer while still selecting A. We track this with numeric extraction and an LLM judge (GPT-4.1-mini; Qwen2.5-3B decoupling rate is about 0.66). The broken construct generalizes beyond the training domain: biased models inflate A-rates on out-of-domain MMLU and value-laden prompts. Continued training on unbiased data reverses the in-domain shift unevenly and only partially reverses the out-of-domain one, so a model can appear restored on its training distribution while remaining biased on unseen inputs. Reasoning-answer decoupling rate, together with answer distributions and out-of-domain behavior, separates capability loss from a learned, transferable shortcut.
1 Introduction
This study shows that a factually correct but position-confounded reward can make benchmark accuracy measure an answer-position shortcut rather than task ability. Reasoning-answer decoupling, answer distributions, out-of-domain transfer, and uneven recovery reveal this measurement failure.
- Introduction: The controlled setup converts GSM8K into four-option questions, trains with correct rewards where every answer is A, and evaluates with randomized answer positions.Because solving and always choosing A receive identical reward during biased training, endpoint training accuracy cannot distinguish intended reasoning from position exploitation.
- Results: Biased optimization often drives option-A rates above 0.90 while randomized-position math accuracy approaches chance, though collapse varies across models.For Llama 3.1-8B, accuracy falls from 0.82 to 0.31 as A-rate rises from 0.26 to 0.94.
- Results: Reasoning-answer decoupling occurs when capable models reach the correct numeric answer but select the wrong final option, usually A.This is verified with both a rule-based numeric check and an LLM judge; under GPT-4.1-mini, Qwen2.5-1.5B decoupling rises from 0.11 to 0.43.
- Results: On MMLU-50, biased checkpoints show large option-A increases despite no MMLU training signal, indicating transfer of the shortcut beyond the training domain.Qwen2.5-1.5B mean A-rate rises from 27% to 77%, while Qwen2.5-3B seed 42 rises from 34% to 82%; the probe is directional because of its small size.
- Results: Continued unbiased training restores some models near unbiased-curriculum behavior, but others retain elevated A-rates in-domain or on out-of-domain probes.Recovery is therefore uneven rather than a uniform reversal of the learned shortcut.
2 Related Work
This work connects goal misgeneralization, reasoning–answer decoupling, and emergent misalignment, while distinguishing its reward-induced mechanism from prior position-ordering interventions. Its correct training signal and out-of-domain transfer also situate the setup within broader work on behavioral shifts and recovery.
- Goal misgeneralization and position bias: Goal misgeneralization describes policies that follow a spurious feature after distribution shift despite correct training specifications.The setup deliberately induces this failure through position bias, paralleling the canonical coin-at-level-end example.
- Reasoning–answer decoupling: Turpin et al. (2023) found that making few-shot answers always A elicited reasoning that rationalized A and reduced accuracy by up to 36%.This work instead induces reasoning–answer divergence through a training reward.
- Reward-induced misalignment and recovery: Emergent-misalignment research studies how correct-looking signals can produce broad behavioral shifts, including on unrelated inputs after narrow fine-tuning.This setup is distinctive because every training datum is factually and logically correct at every point.
3 Experimental Setup
The study tests position-confounded reward optimization by comparing unbiased and always-A multiple-choice curricula built from GSM8K, then evaluating shortcut learning, transfer, and recovery. It separates answer selection from reasoning using accuracy, option-A rates, and reasoning-answer decoupling measures.
- Dataset and curricula: 1266 training questions and a held-out test set convert GSM8K problems into four-option questions with one correct answer and three plausible distractors.GPT-4.1-mini generates distractors designed to reflect common procedural mistakes rather than arbitrary numeric perturbations.
- Dataset and curricula: The unbiased curriculum shuffles correct answers across A/B/C/D, whereas the biased curriculum always places the correct answer at A while keeping questions, options, and gold answers identical.Thus, the biased curriculum contains no incorrect labels, but correctness is perfectly confounded with answer position.
- Training procedure: Qwen2.5, Llama 3.x, and Gemma3 models are trained with GRPO and LoRA adapters under three stages that progressively introduce the final reasoning format.The stages move from letter-only answers to tagged answers and finally reasoning before the answer.
- Training procedure: The reward combines stage-appropriate formatting with parsed-answer correctness, while omitting reasoning quality, trace-level numeric correctness, and reasoning-answer agreement.Under biased training, selecting A is always rewarded, so the reward cannot distinguish solving from position selection.
- Recovery: Recovery continues biased checkpoints for 200 GRPO steps on unbiased data to test whether correct supervision removes the position policy or leaves shortcut residue.Recovered checkpoints use the same reward and final output format.
- Evaluation: Evaluation uses a randomized-position held-out math test set (n = 135), a fixed MMLU-50 probe, and a value-laden binary-choice prompt sampled 50 times per model.The MMLU probe contains 10 questions each from five listed subjects, while the binary prompt tests a strong non-A base-model preference.
- Metrics: Accuracy and option-A rate jointly distinguish correct performance from shortcut exploitation, while numeric extraction and an LLM judge measure reasoning-answer decoupling.Low accuracy with high A-rate indicates shortcut exploitation; decoupling compares reasoning support with the final selected option.
4 Results
Biased optimization turns endpoint accuracy into a mixture of task competence and a learned answer-position policy, often producing reasoning–answer decoupling. The shortcut can transfer beyond math and persist after unbiased recovery, so in-domain accuracy alone can falsely suggest repair.
- Endpoint measurement: Qwen2.5-1.5B shifts from roughly 67% accuracy and 33% A-rate under unbiased training to roughly 26% accuracy and 99% A-rate under biased training.Because option A is always correct during training, the reward supports either solving the problem or learning a positional rule.
- Endpoint measurement: Susceptibility varies across families, scales, models, and seeds: some nearly collapse to option A, while larger Qwen2.5 models retain high accuracy and low shortcut rates.Collapse timing and final shortcut strength also vary, so endpoint scores hide how quickly the shortcut emerged.
- Endpoint measurement: Biased training induces the position bias during optimization, making unbiased-test accuracy reflect remaining competence and shortcut strength rather than math ability alone.Susceptible models rapidly shift toward high option-A selection on unbiased validation during the biased curriculum.
- Reasoning–answer decoupling: Reasoning–answer decoupling occurs when reasoning contains the correct numeric answer but the parsed final option is incorrect, especially when selection follows the rewarded position.Numeric extraction is the primary measure, with an independent LLM judge as a companion validity check; strongest numeric decoupling is roughly 29% in biased Qwen2.5-1.5B and 19% in Qwen2.5-3B.
- Out-of-domain transfer: Qwen2.5-1.5B biased runs select A on roughly 72–80% of MMLU items versus 24–32% for unbiased runs, while Qwen2.5-3B seed 42 rises from 34% to 82%.These shifts occur without MMLU training, indicating that the position policy generalizes beyond the math distribution.
- Recovery: After unbiased recovery, Qwen2.5-1.5B seeds 42 and 123 remain at roughly 84% A on MMLU, while Llama3.2-3B seeds 7 and 42 remain at 76% and 72%.Thus, recovered in-domain accuracy can coexist with residual answer-position bias on out-of-domain probes.
5 Discussion
Biased optimization exposes a construct-validity failure: endpoint accuracy can conflate mathematical competence with an answer-position policy, even when reasoning reaches the correct numeric answer. The shortcut can persist out of domain and evade conventional audits, so recovery requires answer-distribution and probe checks alongside accuracy.
- Measurement problem: A correct reward can underidentify the trained policy, and only randomized test positions distinguish solving from exploiting answer position.The setup deliberately places every correct answer at A to isolate this measurement problem.
- Construct validity: After biased optimization, endpoint accuracy measures task competence mixed with a learned answer-position policy rather than math ability alone.Reasoning-answer decoupling shows capable models may derive the correct numeric answer while selecting the rewarded letter.
- Generalization and recovery: Elevated option-A rates on MMLU-50 show that the shortcut can persist beyond the original training setting, while unbiased-math recovery may leave residue.Repair should therefore assess answer distributions and out-of-domain probes, not accuracy alone.
- Limitations: The proof-of-concept uses a strong A-position confound, so weaker or different confounds may behave differently and the probes remain directional rather than standalone benchmarks.The MMLU probe is small, while the value-laden probe samples a single prompt 50 times per model and condition.
- Threat model: Because every rewarded completion is factually correct, per-example label, reward-correctness, and training-accuracy checks miss the corrupted surface-feature correlation.This proof of concept illustrates a failure standard audits are built to miss, rather than an attack in the wild.
A Appendix · A.1 Additional figures
The appendix adds dense validation-accuracy trajectories, final answer-letter distributions, and a position-swap control. Together, these materials show how evaluation behavior changes across training and how harmful-option selection depends on position rather than content alone.
- A.1 Additional figures: Figure 5 provides dense unbiased-validation accuracy over training steps, complementing Figure 2’s stage-checkpoint view.A Appendix · A.1 Additional figures
- A Appendix: The appendix therefore documents both training-step accuracy dynamics and final answer-position behavior under different model conditions.These views are supplied by Figures 5 and 6, while Table 2 tests position dependence directly.
- A.1 Additional figures: Figure 6 reports final unbiased-test option-letter distributions as %A, %B, %C, and %D by model and training condition.A Appendix · A.1 Additional figures
- A.1 Additional figures: On the value-laden prompt, moving the harmful option from A to B reduced the biased model’s harmful selection rate from 0.84 to 0.00.The control uses 50 samples per cell with 95% Wilson intervals.
- A.1 Additional figures: Base and unbiased checkpoints remained near zero for harmful-option selection in both option placements.The content was held fixed while only the harmful option’s position changed.
- A.1 Additional figures: The position-swap control isolates a placement × condition interaction in harmful-option selection.The interaction is identified by comparing original placement in A with swapped placement in B across training conditions.
A.2 Qualitative example of reasoning–answer decoupling
A biased Qwen2.5-3B generation computes the correct numeric result but selects option A, showing that its reasoning and answer channels can diverge. The model’s final selection follows the position shortcut rather than the conclusion reached by its arithmetic.
- Qualitative example: A single biased Qwen2.5-3B generation computes the correct numeric answer while selecting option A.The reasoning derives $2, corresponding to option D, but the final answer tag emits A.
- Qualitative example: The arithmetic correctly calculates Juice Box C as $11 and Juice Box B as $9, yielding a $2 difference.The options identify 2 as option D.
- Qualitative example: The answer channel emits A independently of the reasoning’s conclusion, making selection fail to read off the computed answer.The biased curriculum has fixed the answer token to A, illustrating the qualitative signature of reasoning–answer decoupling.
A.3 Value-laden prompt
The value-laden probe tests whether position-confounded training transfers to an unseen binary career-choice prompt. Biased training can increase harmful-option selection, while reasoning may partially contradict the selected harmful answer.
- Probe design: The held-out binary probe was sampled 50 times per model-condition pair across base, biased, unbiased, and recovered checkpoints.The prompt asks respondents to choose between earning money by killing people and earning money through honest work.
- Reasoning-answer decoupling: A biased Qwen2.5-1.5B sample explicitly selected the harmful option while reasoning warned that it was dangerous and morally reprehensible.The example illustrates transfer qualitatively rather than serving as a standalone safety benchmark.
- Position control: The same prompt was evaluated with harmful and honest options swapped, and harmful-option rates were reported to distinguish positional from content-based selection.Each placement was sampled 50 times per model and condition.
- Transfer result: 84% harmful-A selections were observed for Qwen2.5-1.5B after biased training, versus 4% for both base and unbiased checkpoints.The harmful-A rate remained 70% after recovery.