Why Power Sampling Fails Reasoning Tasks

Summary & Methodology Analysis

Power Sampling is an inference technique used to adjust the probability distribution of model outputs. The authors demonstrate that while this technique successfully increases the probability mass of correct trajectories, it paradoxically harms performance during multi-trajectory aggregation. This degradation occurs due to coverage and dose mismatches, where the distribution of selected outputs does not align well with the requirements for effective consensus. This issue was observed across multiple environments, including BigCodeBench, LiveAoPSBench, and PHYSICS, using models such as NVIDIA-Nemotron-3-Nano-4B-BF16, Qwen3.5-9B, and Ministral-3-8B-Reasoning-2512. The documented accuracy drops reach as high as 18.5 percentage points, indicating a significant risk when applying simple Power Sampling to production reasoning pipelines. To address these failures, the authors propose an alternative approach that involves sampling trajectories from the base model, calculating the relative within-problem rank for each, and applying a Relative-Rank SoftSat function to generate reweighting multipliers. These multipliers are then used to perform a consensus readout of the trajectories. This method aims to balance the selection process by considering the relative ranking of trajectories rather than relying on a fixed-exponent power adjustment. Despite this, the paper notes that SoftSat does not uniformly outperform uniform consensus and showed regressions in certain test settings. The researchers emphasize that their finite-sample check of weighted realizations is not a claim of universal equivalence or a test of asymptotic convergence, meaning the technique should be validated for specific use cases rather than assumed to be a universal improvement over standard aggregation methods.