The paper details a new approach to large language model (LLM) decoding, addressing limitations in existing Sequential Monte Carlo (SMC) methods. Current equal-weight resampling techniques can aggressively prune diverse reasoning paths, reducing the genealogical diversity of the search space. Chopthin-Consensus Power Sampling (CCPS) introduces a targeted intervention to mitigate this. The method utilizes the Chopthin resampler, enforcing an upper bound on the ratio between the largest and smallest weights within the SMC population. This maintains the weighted SMC approximation’s conditional expectation while preserving a richer set of distinct reasoning paths and guaranteeing a lower bound on the effective sample size.
To fully leverage the enriched population, the research employs a semantic-majority selection mechanism. This mechanism merges token-identical final trajectories, clusters semantically equivalent answers, and returns the answer supported by the largest number of distinct trajectories. The evaluation involved three open-weight models and five reasoning benchmarks. Results indicate that CCPS increases oracle coverage in 13 of 15 settings. When combined with the semantic-majority selection, CCPS achieves accuracy comparable to or exceeding the Power-SMC baseline in 14 of 15 settings, with absolute gains of up to 10.6 percentage points.
These findings demonstrate the complementary benefits of diversity-preserving resampling and diversity-aware selection for training-free LLM reasoning. The research suggests that maintaining a broader range of reasoning paths, combined with a mechanism to prioritize the most coherent answers, can significantly improve LLM performance without requiring retraining.
The code for the CCPS method is available for public use. The research was accepted at the COLM 2026 Workshop on Efficient Reasoning.
Source: https://arxiv.org/abs/2609.12243
