Chopthin-Consensus Power Sampling: A Diversity-Preserving Approach to LLM Decoding

Inference-time power sampling via Sequential Monte Carlo (SMC) can substantially improve large language model (LLM) reasoning without requiring post-training. However, most current SMC approaches rely on equal-weight resampling, which aggressively prunes low-weight trajectories, discarding potentially correct reasoning paths and degrading the genealogical diversity of the search space. To resolve this, we introduce Chopthin-Consensus Power Sampling (CCPS). CCPS applies the Chopthin resampler to LLM decoding: rather than equalizing weights and forcing unnecessary particle duplication, it enforces an upper bound on the ratio between the largest and smallest weights and carries the unequal weights forward. This targeted intervention preserves a richer set of distinct reasoning paths, keeps the weighted SMC approximation unchanged in conditional expectation, and guarantees a lower bound on the post-resampling effective sample size (ESS). To fully exploit this enriched population, CCPS employs a semantic-majority selection mechanism that merges token-identical final trajectories, clusters semantically equivalent answers, and returns the answer supported by the largest number of distinct trajectories. Evaluating across three open models and five reasoning benchmarks, we show that Chopthin increases observed oracle coverage in 13 of 15 settings. Combined with semantic-majority selection, CCPS matches or exceeds the final-answer accuracy of the baseline Power-SMC approach in 14 of 15 settings, delivering absolute gains of up to 10.6 percentage points. These findings demonstrate that diversity-preserving resampling and diversity-aware selection are complementary mechanisms for training-free LLM reasoning.