Inference-time power sampling via Sequential Monte Carlo (SMC) can substantially improve large language model (LLM) reasoning without requiring post-training. However, many existing SMC approaches rely on equal-weight resampling, which can aggressively prune low-weight trajectories, discarding potentially correct reasoning paths and degrading the genealogical diversity of the search space. To address this, we introduce Chopthin-Consensus Power Sampling (CCPS). Our method 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, we employ 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-weight models and five reasoning benchmarks, we show that Chopthin increases oracle coverage in 13 of 15 settings. Combined with semantic-majority selection, CCPS matches or exceeds the final-answer accuracy of the Power-SMC baseline 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. Code is available at github.com/MinooAhmadii/chopthin-consensus-power-sampling.
Large language models (LLMs) can achieve strong reasoning performance through chain-of-thought (CoT) reasoning, yet they often generate unnecessarily long reasoning paths that incur high inference cost. Self-consistency-based approaches push accuracy higher still, but they require sampling and aggregating multiple reasoning trajectories, leading to substantial computational overhead. In this paper, we introduce a confidence-aware selective sampling framework that, at inference time, analyzes a single reasoning trajectory to adaptively determine whether to rely on that trajectory alone or trigger multi-path sampling. The framework uses trajectory-level numeric features and sentence-level linguistic features extracted from reasoning states to guide selective multi-path reasoning. We train it on MedQA and evaluate it in-domain on MedQA and under calibration-only transfer on MathQA, MedMCQA, and MMLU, without further fine-tuning. Experimental results show that the proposed framework maintains comparable performance to full and efficient multi-path reasoning baselines, with accuracy changes of −0.41±0.58 and −0.31±0.58 percentage points, respectively, while reducing token usage by 71.7±5.0 and 36.6±9.1. These findings demonstrate that reasoning trajectories contain rich signals for uncertainty estimation, enabling a simple, transferable mechanism to balance accuracy and efficiency in LLM reasoning.
Generating diverse responses is crucial for test-time scaling of large language models (LLMs), yet standard stochastic sampling mostly yields surface-level lexical variation, limiting semantic exploration. In this paper, we propose Exploratory Sampling (ESamp), a decoding approach that explicitly encourages semantic diversity during generation. ESamp is motivated by the well-known observation that neural networks tend to make lower-error predictions on inputs similar to those encountered before, and incur higher prediction error on novel ones. Building on this property, we train a lightweight Distiller at test time to predict deep-layer hidden representations of the LLM from its shallow-layer representations to model the LLM's depth-wise representation transitions. During decoding, the Distiller continuously adapts to the mappings induced by the current generation context. ESamp uses the prediction error as a novelty signal to reweight candidate token extensions conditioned on the current prefix, thereby biasing decoding toward less-explored semantic patterns. ESamp is implemented with an asynchronous training--inference pipeline, with less than 5% worst case overhead (1.2% in the optimized release). Empirical results show that ESamp significantly boosts the Pass@k efficiency of reasoning models, showing superior or comparable performance to strong stochastic and heuristic baselines. Notably, ESamp achieves robust generalization across mathematics, science, and code generation benchmarks and breaks the trade-off between diversity and coherence in creative writing. Our code has released at: https://github.com/LinesHogan/tLLM.
A central question in LLM reasoning is whether reinforcement learning (RL) instills genuinely new capabilities or merely reshapes how existing knowledge is expressed during inference. Building on the distribution-sharpening hypothesis, which holds that RL reallocates probability mass toward high-reward trajectories already latent in base models, we ask: can we unlock those latent paths without costly RL fine-tuning? We present Decision-Flow Sampling (DF-Sample), a training-free, data-free inference-time framework that constructs a hierarchical reasoning tree, scores terminal nodes for quality, and back-propagates utilities to inform each intermediate branching decision. Unlike conventional sampling strategies that make purely local step-wise choices, DF-Sample performs explicit global trajectory evaluation before committing to a path, recovering high-quality but low-probability reasoning chains that standard decoding overlooks. On GPQA, DF-Sample achieves 45.6% accuracy, surpassing power sampling (38.9%) and GRPO (39.9%), showing that a training-free method can outperform a trained one. Across three models and four benchmarks, DF-Sample consistently outperforms baselines, indicating substantial latent reasoning potential in pretrained base models.