More Correct Mass, Worse Answers: Why Power Sampling Can Fail and How to Fix It

Abstract:Power Sampling sharpens a language model's distribution over complete generation trajectories, offering a verifier-free way to improve reasoning at inference time. It also has the potential to serve as a general-purpose front end for a broad range of downstream sampling methods. However, we uncover a striking paradox: Power Sampling can drive more probability mass toward correct trajectories while degrading the downstream inference it is intended to enhance. Using self-consistency as a representative case, we observe accuracy drops of up to 18.5 percentage points across models and reasoning benchmarks. We trace this paradox to two mismatches. Dose mismatch arises because a fixed exponent induces drastically different amounts of distributional change across problems. Coverage mismatch arises because global sharpening concentrates mass on a narrow set of dominant paths: high pass@k, often interpreted as evidence of preserved diversity, can therefore coexist with the loss of broad reasoning-path support required for downstream aggregation, search, and selection. Guided by this diagnosis, we replace uniform trajectory exponentiation with a deformation-controlled, support-preserving Power target that calibrates sharpening across problems while limiting the suppression of moderate-probability paths. In a same-budget instantiation with weighted self-consistency, the repaired sampler reverses the losses caused by global Power and outperforms standard multi-sample inference across reasoning benchmarks.

16 pages, 8 figures, 1 table. Haohui Yang and Jiaxing Sun contributed equally. Xiujun Ma is the corresponding author

Machine Learning (cs.LG)

arXiv:2608.14420 [cs.LG]

(or arXiv:2608.14420v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2608.14420 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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