Batch-of-Thought: Cross-Instance Learning for Enhanced LLM Reasoning

Recent work on test-time scaling for large language model (LLM) reasoning typically assumes that allocating more inference-time computation uniformly improves correctness. However, prior studies show that reasoning uncertainty is highly localized: a small subset of low-confidence tokens disproportionately contributes to reasoning errors and unnecessary output expansion. Motivated by this observation, we propose Thinking by Subtraction, a confidence-driven contrastive decoding approach that improves reasoning reliability through targeted token-level intervention. Our method, Confidence-Driven Contrastive Decoding, detects low-confidence tokens during decoding and intervenes selectively at these positions. It constructs a contrastive reference by replacing high-confidence tokens with minimal placeholders, and refines predictions by subtracting this reference distribution at low-confidence locations. Experiments show that CCD significantly improves accuracy across mathematical reasoning benchmarks while substantially reducing output length, with minimal KV-cache overhead. As a training-free method, CCD enhances reasoning reliability through targeted low-confidence intervention without computational redundancy. Our code will be made available at: https://github.com/bolo-web/CCD.

Large Language Models (LLMs) often exhibit strong linguistic abilities while remaining unreliable on multi-step reasoning tasks, particularly when deployed without additional training or fine-tuning. In this work, we study inference-time techniques to improve the reasoning accuracy of LLMs. We systematically evaluate three classes of inference-time strategies: (i) self-consistency via stochastic decoding, where the model is sampled multiple times using controlled temperature and nucleus sampling and the most frequent final answer is selected; (ii) dual-model reasoning agreement, where outputs from two independent models are compared and only consistent reasoning traces are trusted; and (iii) self-reflection, where the model critiques and revises its own reasoning. Across all evaluated methods, we employ Chain-of-Thought (CoT) [1] prompting to elicit explicit intermediate reasoning steps before generating final answers. In this work, we provide a controlled comparative evaluation across three inference-time strategies under identical prompting and verification settings. Our experiments on LLM [2] show that self-consistency with nucleus sampling and controlled temperature value yields the substantial gains, achieving a 9% to 15% absolute improvement in accuracy over greedy single-pass decoding, well-suited for low-risk domains, offering meaningful gains with minimal overhead. The dual-model approach provides additional confirmation for model reasoning steps thus more appropriate for moderate-risk domains, where higher reliability justifies additional compute. Self-reflection offers only marginal improvements, suggesting limited effectiveness for smaller non-reasoning models at inference time.

Large Language Models (LLMs) often fail to utilize their latent reasoning capabilities due to a distributional mismatch between ambiguous human inquiries and the structured logic required for machine activation. Existing alignment methods either incur prohibitive $O(N)$ costs by fine-tuning each model individually or rely on static prompts that fail to resolve query-level structural complexity. In this paper, we propose ReQueR (Reinforcement Query Refinement), a modular framework that treats reasoning elicitation as an inference-time alignment task. We train a specialized Refiner policy via Reinforcement Learning to rewrite raw queries into explicit logical decompositions, treating frozen LLMs as the environment. Rooted in the classical Zone of Proximal Development from educational psychology, we introduce the Adaptive Solver Hierarchy, a curriculum mechanism that stabilizes training by dynamically aligning environmental difficulty with the Refiner's evolving competence. ReQueR yields consistent absolute gains of 1.7%--7.2% across diverse architectures and benchmarks, outperforming strong baselines by 2.1% on average. Crucially, it provides a promising paradigm for one-to-many inference-time reasoning elicitation, enabling a single Refiner trained on a small set of models to effectively unlock reasoning in diverse unseen models. Code is available at https://github.com/newera-xiao/ReQueR.