Large Language Model Reasoning

The proliferation of Large Language Models (LLMs) in medicine has enabled impressive capabilities, yet a critical gap remains in their ability to perform systematic, transparent, and verifiable reasoning, a cornerstone of clinical practice. This has catalyzed a shift from single-step answer generation to the development of LLMs explicitly designed for medical reasoning. This paper provides the first systematic review of this emerging field. We propose a taxonomy of reasoning enhancement techniques, categorized into training-time strategies (e.g., supervised fine-tuning, reinforcement learning) and test-time mechanisms (e.g., prompt engineering, multi-agent systems). We analyze how these techniques are applied across different data modalities (text, image, code) and in key clinical applications such as diagnosis, education, and treatment planning. Furthermore, we survey the evolution of evaluation benchmarks from simple accuracy metrics to sophisticated assessments of reasoning quality and visual interpretability. Based on an analysis of 60 seminal studies from 2022-2025, we conclude by identifying critical challenges, including the faithfulness-plausibility gap and the need for native multimodal reasoning, and outlining future directions toward building efficient, robust, and sociotechnically responsible medical AI.

Large Language Models (LLMs) often produce plausible but poorly-calibrated answers, limiting their reliability on reasoning-intensive tasks. Recent research suggests that Chain-of-Thought (CoT) reasoning paths are inherent in pre-trained LLMs and can be elicited by simply altering the decoding process, where the presence of a CoT path correlates with higher answer confidence. Building on these insights, we present Reinforcement Learning from Self-Feedback (RLSF), a post-training stage that utilises the model's intrinsic confidence as a self-generated reward. By generating multiple CoT decoding beams from a frozen LLM, we compute the confidence of each final answer span and rank the resulting traces accordingly to create synthetic preferences. These preferences are subsequently utilised to fine-tune the policy through standard preference optimisation, requiring no human labels, gold answers, or externally curated rewards. RLSF simultaneously (i) refines the model's probability estimates--restoring well-behaved calibration--and (ii) strengthens step-by-step reasoning, yielding improved performance on arithmetic reasoning and multiple-choice question answering. By converting a model's own uncertainty into structured self-feedback, RLSF affirms reinforcement learning on intrinsic model behaviour as a principled and data-efficient component of the LLM post-training pipeline. Our results demonstrate that leveraging these inherent reasoning capabilities provides a robust path for enhancing model reliability without manual prompt engineering or external supervision.

Long-context reasoning requires accurately identifying relevant information in extensive, noisy input contexts. In this work, we propose PERK (Parameter Efficient Reasoning over Knowledge), a scalable approach for learning to encode long contexts using gradient updates at test time. Specifically, PERK employs two nested optimization loops in a meta-training phase. The inner loop rapidly encodes contexts into a low-rank adapter (LoRA) that serves as a parameter-efficient memory module for the base model. Concurrently, the outer loop learns to use the updated adapter to accurately recall and reason over relevant information from the encoded long context. Our evaluations on several long-context reasoning tasks show that PERK significantly outperforms the standard long-context finetuning, achieving average absolute performance gains of up to 20% for Qwen-2.5 (0.5B & 7B) on synthetic and real-world long-context reasoning. PERK also maintains its advantages across model scales and families. Compared to specialized long-context LLMs, PERK matches or surpasses their performance. Finally, our analyses show PERK is more robust to reasoning complexity, length extrapolation, and the positions of relevant information in contexts. https://perk-long-context.web.app

Recent progress in large-scale reinforcement learning (RL) has notably enhanced the reasoning capabilities of large language models (LLMs), especially in mathematical domains. However, current multimodal LLMs (MLLMs) for mathematical reasoning often rely on one-to-one image-text pairs and single-solution supervision, overlooking the diversity of valid reasoning perspectives and internal reflections. In this work, we introduce MathV-DP, a novel dataset that captures multiple diverse solution trajectories for each image-question pair, fostering richer reasoning supervision. We further propose Qwen-VL-DP, a model built upon Qwen-VL, fine-tuned with supervised learning and enhanced via group relative policy optimization (GRPO), a rule-based RL approach that integrates correctness discrimination and diversity-aware reward functions. Our method emphasizes learning from varied reasoning perspectives and distinguishing between correct yet distinct solutions. Extensive experiments on the MathVista's minitest and Math-V benchmarks demonstrate that Qwen-VL-DP significantly outperforms prior base MLLMs in both accuracy and generative diversity, highlighting the importance of incorporating diverse perspectives and reflective reasoning in multimodal mathematical reasoning.

A common approach for teaching large language models (LLMs) to reason is to train on chain-of-thought (CoT) traces of in-distribution reasoning problems, but such annotated data is costly to obtain for every problem of interest. We want reasoning models to generalize beyond their training distribution, and ideally to generalize compositionally: combine atomic reasoning skills to solve harder, unseen reasoning tasks. We take a step towards compositional generalization of reasoning skills when addressing a target compositional task that has no labeled CoT data. We find that simply training models on CoT data of atomic tasks leads to limited generalization, but minimally modifying CoT formats of constituent atomic tasks to be composable can lead to improvements. We can train "atomic CoT" models on the atomic tasks with Composable CoT data and combine them with multitask learning or model merging for better zero-shot performance on the target compositional task. Such a combined model can be further bootstrapped on a small amount of compositional data using rejection sampling fine-tuning (RFT). Results on string operations and natural language skill compositions show that training LLMs on Composable CoT outperforms multitask learning and continued fine-tuning baselines within a given training data budget.

Large Language Models (LLMs) excel at complex reasoning through search algorithms, yet current strategies often suffer from massive token consumption due to redundant exploration of semantically equivalent steps. Existing semantic similarity methods struggle to accurately identify such equivalence in domain-specific contexts like mathematical reasoning. To address this, we propose EquivPruner, a simple yet effective approach that identifies and prunes semantically equivalent actions during LLM reasoning search. We also introduce MathEquiv, the first dataset we created for mathematical statement equivalence, which enables the training of a lightweight equivalence detector. Extensive experiments across various models and tasks demonstrate that EquivPruner significantly reduces token consumption, improving searching efficiency and often bolstering reasoning accuracy. For instance, when applied to Qwen2.5-Math-7B-Instruct on GSM8K, EquivPruner reduced token consumption by 48.1% while also improving accuracy. Our code is available at https://github.com/Lolo1222/EquivPruner.

Large language models (LLMs) struggle with formal domains that require rigorous logical deduction and symbolic reasoning, such as mathematical proof generation. We propose a neuro-symbolic approach centered on the hypothesis that structurally analogous problems often admit similar proofs. As a proof-of-concept, we focus on SAT-level geometry problems. Our approach is two-fold: (1) We retrieve analogous problems and use their proofs to guide the LLM, and (2) a formal verifier evaluates the generated proofs and provides feedback, helping the model fix incorrect proofs. Our complete pipeline substantially improves proof accuracy across model families, achieving 68%-96% accuracy compared with 10%-44% for LLM-only baselines that use neither analogy retrieval nor verifier feedback. When comparing against models with the same verifier feedback and inference budget, analogical guidance improves accuracy from 88% to 96% for GPT-5, 78% to 86% for Claude Sonnet 4.6, 72% to 86% for Gemini-Flash-2.5, and 52% to 80% for OpenAI o1. More broadly, shifting to LLMs that generate provably correct conclusions has the potential to dramatically improve their reliability, accuracy and consistency, unlocking complex tasks and critical real-world applications that require trustworthiness.

Recent advancements in Large Language Models (LLMs) have significantly enhanced their ability to perform complex reasoning tasks, transitioning from fast and intuitive thinking (System 1) to slow and deep reasoning (System 2). While System 2 reasoning improves task accuracy, it often incurs substantial computational costs due to its slow thinking nature and inefficient or unnecessary reasoning behaviors. In contrast, System 1 reasoning is computationally efficient but leads to suboptimal performance. Consequently, it is critical to balance the trade-off between performance (benefits) and computational costs (budgets), giving rise to the concept of reasoning economy. In this survey, we provide a comprehensive analysis of reasoning economy in both the post-training and test-time inference stages of LLMs, encompassing i) the cause of reasoning inefficiency, ii) behavior analysis of different reasoning patterns, and iii) potential solutions to achieve reasoning economy. By offering actionable insights and highlighting open challenges, we aim to shed light on strategies for improving the reasoning economy of LLMs, thereby serving as a valuable resource for advancing research in this evolving area. We also provide a public repository to continually track developments in this fast-evolving field.

Large language models (LLMs) have shown remarkable capabilities in natural language processing. However, in knowledge graph question answering tasks (KGQA), there remains the issue of answering questions that require multi-hop reasoning. Existing methods rely on entity vector matching, but the purpose of the question is abstract and difficult to match with specific entities. As a result, it is difficult to establish reasoning paths to the purpose, which leads to information loss and redundancy. To address this issue, inspired by human reverse thinking, we propose Ontology-Guided Reverse Thinking (ORT), a novel framework that constructs reasoning paths from purposes back to conditions. ORT operates in three key phases: (1) using LLM to extract purpose labels and condition labels, (2) constructing label reasoning paths based on the KG ontology, and (3) using the label reasoning paths to guide knowledge retrieval. Experiments on the WebQSP and CWQ datasets show that ORT achieves state-of-the-art performance and significantly enhances the capability of LLMs for KGQA.

Large language models (LLMs) have developed rapidly, and their reasoning capabilities have become a hot research topic. However, there is still limited exploration of abductive reasoning. The multi-perspective and multi-level of causes is one of the core challenges of abductive reasoning, which cannot be solved well by existing methods. We construct a specialized dataset named DeepAbduction, which is designed for tracing the causes of pollution and disease, addressing the lack of datasets in this field. We propose \textsc{Inverse-Forward Abductive Reasoning} (IFAR) framework for LLMs multi-perspective and multi-level abductive reasoning. IFAR is zero-shot and combines generalized backward reasoning with relation-by-relation forward verification. Experimental results show that IFAR achieves an improvement of approximately 40% in the F1 score compared to other methods under mainstream LLMs, while maintaining a balance between recall and precision. Furthermore, IFAR enhances the performance of non-reasoning LLMs to surpass LLMs which have been trained for reasoning, and remains effective when applied to the latter. Code will be released after the acceptance of our work.

Modern language models (LMs) can learn to perform new tasks in different ways: in instruction following, the target task is described explicitly in natural language; in few-shot prompting, the task is specified implicitly with a small number of examples; in instruction inference, LMs are presented with in-context examples and are then prompted to generate a natural language task description before making predictions. Each of these procedures may be thought of as invoking a different form of reasoning: instruction following involves deductive reasoning, few-shot prompting involves inductive reasoning, and instruction inference involves abductive reasoning. How do these different capabilities relate? Across four LMs (from the gpt and llama families) and two learning problems (involving arithmetic functions and machine translation) we find a strong dissociation between the different types of reasoning: LMs can sometimes learn effectively from few-shot prompts even when they are unable to explain their own prediction rules; conversely, they sometimes infer useful task descriptions while completely failing to learn from human-generated descriptions of the same task. Our results highlight the non-systematic nature of reasoning even in some of today's largest LMs, and underscore the fact that very different learning mechanisms may be invoked by seemingly similar prompting procedures.

Autoregressive large language models (LLMs) compress knowledge from their training data through next-token conditional distributions. This limits tractable querying of this knowledge to start-to-end autoregressive sampling. However, many tasks of interest -- including sequence continuation, infilling, and other forms of constrained generation -- involve sampling from intractable posterior distributions. We address this limitation by using amortized Bayesian inference to sample from these intractable posteriors. Such amortization is algorithmically achieved by fine-tuning LLMs via diversity-seeking reinforcement learning algorithms: generative flow networks (GFlowNets). We empirically demonstrate that this distribution-matching paradigm of LLM fine-tuning can serve as an effective alternative to maximum-likelihood training and reward-maximizing policy optimization. As an important application, we interpret chain-of-thought reasoning as a latent variable modeling problem and demonstrate that our approach enables data-efficient adaptation of LLMs to tasks that require multi-step rationalization and tool use.

Industrial B2B applications (e.g., construction site risk prediction, material procurement) face extreme data sparsity yet feature rich textual interactions. In such environments, traditional ID-based collaborative filtering fails lacking co-occurrence signals, while fine-tuning standard Large Language Models (LLMs) incurs high operational costs and struggles with frequent data drift. We propose LLMAR (LLM-Annotated Recommendation), a tuning-free framework. Moving beyond simple embeddings, LLMAR systematically integrates LLM reasoning to capture user "latent motives" without any training process. We introduce three core contributions: (1) Inference-Driven Annotation: uses LLMs to transform behavioral history into structured semantic motives, enabling reasoning-based matching unattainable by ID-based methods; (2) Reflection Loop: a self-correction mechanism that refines generated queries to mitigate hallucinations and resolve "context competition" between past history and current instructions; and (3) Cost-Effective Architecture: relies on tuning-free components and asynchronous batch processing to minimize maintenance costs. Evaluations on public benchmarks (MovieLens-1M, Amazon Prime Pantry) and a sparse industrial dataset (construction risk prediction) demonstrate that LLMAR outperforms state-of-the-art learning-based models (SASRecF), achieving up to a 54.6% nDCG@10 improvement on the industrial dataset. Inference costs remain highly practical (~$1 per 1,000 users). For B2B domains where strict real-time latency is not critical, combining LLM reasoning with self-verification offers a superior alternative to training-based approaches across accuracy, explainability, and operational cost.

Verbalized confidence, in which LLMs report a numerical certainty score, is widely used to estimate uncertainty in black-box settings, yet the confidence scale itself (typically 0--100) is rarely examined. We show that this design choice is not neutral. Across six LLMs and three datasets, verbalized confidence is heavily discretized, with more than 78% of responses concentrating on just three round-number values. To investigate this phenomenon, we systematically manipulate confidence scales along three dimensions: granularity, boundary placement, and range regularity, and evaluate metacognitive sensitivity using $meta\text{-}d'$. We find that a 0--20 scale consistently improves metacognitive efficiency over the standard 0--100 format, while boundary compression degrades performance and round-number preferences persist even under irregular ranges. These results demonstrate that confidence scale design directly affects the quality of verbalized uncertainty and should be treated as a first-class experimental variable in LLM evaluation.

Semantic reasoning aims to infer new knowledge from existing knowledge, with OWL ontologies serving as a standardized framework for organizing information. A key challenge in semantic reasoning is verifying ontology consistency. However, state-of-the-art reasoners are computationally expensive, and their efficiency decreases as ontology sizes grow. While classical machine learning models have been explored for consistency checking of A-Box axioms, considering T-Boxes remains unaddressed. Large language models (LLMs) have shown promising results for natural language inference but perform poorly on logical reasoning. The recently introduced Graph Language Model (GLM) offers a way to simultaneously process graph-structured data and text. This paper proposes GLaMoR (Graph Language Model for Reasoning), a reasoning pipeline that transforms OWL ontologies into graph-structured data and adapts the GLM architecture for consistency checking. We evaluate GLaMoR on ontologies from the NCBO BioPortal repository, converting them into triples suitable for model input. Our results show that the GLM outperforms all baseline models, achieving $95\%$ accuracy, and is $20$ times faster than classical reasoners.

We present $\textbf{Korean SimpleQA (KoSimpleQA)}$, a benchmark for evaluating factuality in large language models (LLMs) with a focus on Korean cultural knowledge. KoSimpleQA is designed to be challenging yet easy to grade, consisting of 938 short, fact-seeking questions with unambiguous answers. We conduct a comprehensive evaluation across a diverse set of open-source LLMs of varying sizes that support Korean, and find that even the strongest model generates correct answer only 31.6% of the time, underscoring the challenging nature of KoSimpleQA. Notably, performance rankings on KoSimpleQA differ substantially from those on the English SimpleQA, highlighting the unique value of our dataset. Furthermore, we observe that reasoning helps mitigate the cross-lingual knowledge gap in LLMs, which refers to disparities in their ability to manifest knowledge across languages. KoSimpleQA can be found at https://github.com/naver-ai/KoSimpleQA.

Large reasoning models (LRMs) produce reasoning traces with non-linear structures, such as backtracking and self-correction, that complicate the evaluation and monitoring of the reasoning process. We introduce ReasoningFlow, a framework that captures the discourse structures of LRM reasoning traces into fine-grained directed acyclic graphs (DAGs). We develop and validate our annotation schema through careful manual annotation of 31 traces (2.1k steps), achieving high inter-annotator agreement, then scale to automatic annotation of 1,260 traces (247.7k steps) spanning three tasks (math, science, argumentation) and five models (Qwen2.5-32B-Inst, QwQ-32B, DeepSeek-V3, DeepSeek-R1, GPT-oss-120B). By analyzing ReasoningFlow graphs, we find: (1) LRMs exhibit structurally similar traces, despite being trained from different base models and potentially non-overlapping post-training data. (2) ReasoningFlow reveals diverse fine-grained reasoning behaviors (e.g., local verification, self-reflection, and assumptions) that can be used for better reasoning trace monitorability. (3) In LRMs, most of the erroneous steps are not used to derive final answers. (4) Mechanistic causal dependencies between steps do not reflect the language-level discourse structure. We release the dataset and code in: https://github.com/jinulee-v/reasoningflow.