Current Large Language Model reasoning systems process queries independently, discarding valuable cross-instance signals such as shared reasoning patterns and consistency constraints. We introduce Batch-of-Thought (BoT), a training-free method that processes related queries jointly to enable cross-instance learning. By performing comparative analysis across queries, BoT identifies high-quality reasoning templates, detects errors through consistency checks, and amortizes computational costs. We instantiate BoT within a multi-agent reflection architecture (BoT-R), where a Reflector performs joint evaluation to unlock mutual information gain unavailable in isolated processing. Experiments across three model families and six benchmarks demonstrate that BoT-R consistently improves accuracy and confidence calibration while reducing inference costs by up to 61%. Our theoretical and experimental analysis reveals when and why batch-aware reasoning benefits LLM systems.

Large language models (LLMs) excel on multiple-choice clinical diagnosis benchmarks, yet it is unclear how much of this performance reflects underlying probabilistic reasoning. We study this through questions from MedQA that ask for the most likely diagnosis. We introduce Frequency-Based Probabilistic Ranker (FBPR), a lightweight method that scores options with a smoothed Naïve Bayes over concept-diagnosis co-occurrence statistics from a large corpus. When co-occurrence statistics are sourced from Dolma, the pretraining corpus for OLMo, and RedPajama, an open reproduction of the LLaMA pretraining-data recipe, FBPR achieves comparable performance to the corresponding LLMs. Furthermore, direct LLM inference and FBPR exhibit complementary strengths, correctly answering largely different subsets of questions with overlap barely above chance. Combining them with a simple hybrid method yields a notable gain over either method alone. These findings show that explicit probabilistic baselines can account for a substantial portion of the benchmark performance on diagnosis questions, while serving as historically grounded reference points and complementary signals for hybridization.