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This paper critically examines power sampling for LLM test-time sharpening, revealing that MCMC and SMC samplers often fail to converge to the target $\pi_\alpha$ under practical compute constraints, with gains largely attributable to Best-of-$N$ selection. Direct fine-tuning to match $\pi_\alpha$ also produces noisy and model-specific improvements, suggesting the utility of power sampling stems from selecting high-probability sequences rather than faithfully approximating the distribution. The key finding is that the observed benefits of power sampling are primarily driven by extracting likely outputs from the base model, not by the theoretical properties of the power distribution itself.
LLM test-time sharpening via power sampling doesn't actually target the intended power distribution; its gains come from simple sequence selection.
Reinforcement learning with verifiable rewards (RLVR) has substantially improved LLM reasoning, yet growing evidence suggests it mainly performs distribution sharpening: concentrating probability mass on reasoning paths the base model already produces. Recent work therefore seeks RLVR's gains without needing reward signals, by sampling from the power distribution $\pi_\alpha \propto \pi_{\text{base}}^\alpha$ via Markov chain Monte Carlo or sequential Monte Carlo. We show that these samplers fail to converge to $\pi_\alpha$ under realistic compute budgets, and that their gains are largely recreated via simple Best-of-$N$ with appropriate grading . This suggests they succeed by selecting high-probability sequences, not by approximating $\pi_\alpha$, raising a natural question: is the power distribution itself a worthwhile target? We test this hypothesis directly by fine-tuning the base model to match $\pi_\alpha$, sidestepping sampler convergence issues entirely. Despite approximating the target far more faithfully than existing samplers, this strategy yields gains that are noisy and specific to certain models and sampling tasks. Together, our results suggest that the value of power sampling lies not in faithfully targeting $\pi_\alpha$, but in the simpler goal of extracting sequences the base model already deems likely.
