Daily Papers

Despite interdisciplinary research leading to larger and longer-term impact, most work remains confined to single-domain academic silos. Recent AI-based approaches to scientific discovery show promise for interdisciplinary research, but many prioritize rapidly designing experiments and solutions, bypassing the exploratory, collaborative reasoning processes that drive creative interdisciplinary breakthroughs. As a result, prior efforts largely prioritize automating scientific discovery rather than augmenting the reasoning processes that underlie scientific disruption. We present Idea-Catalyst, a novel framework that systematically identifies interdisciplinary insights to support creative reasoning in both humans and large language models. Starting from an abstract research goal, Idea-Catalyst is designed to assist the brainstorming stage, explicitly avoiding premature anchoring on specific solutions. The framework embodies key metacognitive features of interdisciplinary reasoning: (a) defining and assessing research goals, (b) awareness of a domain's opportunities and unresolved challenges, and (c) strategic exploration of interdisciplinary ideas based on impact potential. Concretely, Idea-Catalyst decomposes an abstract goal (e.g., improving human-AI collaboration) into core target-domain research questions that guide the analysis of progress and open challenges within that domain. These challenges are reformulated as domain-agnostic conceptual problems, enabling retrieval from external disciplines (e.g., Psychology, Sociology) that address analogous issues. By synthesizing and recontextualizing insights from these domains back into the target domain, Idea-Catalyst ranks source domains by their interdisciplinary potential. Empirically, this targeted integration improves average novelty by 21% and insightfulness by 16%, while remaining grounded in the original research problem.

The ability to summarize and organize knowledge into abstract concepts is key to learning and reasoning. Many industrial applications rely on the consistent and systematic use of concepts, especially when dealing with decision-critical knowledge. However, we demonstrate that, when methodically questioned, large language models (LLMs) often display and demonstrate significant inconsistencies in their knowledge. Computationally, the basic aspects of the conceptualization of a given domain can be represented as Is-A hierarchies in a knowledge graph (KG) or ontology, together with a few properties or axioms that enable straightforward reasoning. We show that even simple ontologies can be used to reveal conceptual inconsistencies across several LLMs. We also propose strategies that domain experts can use to evaluate and improve the coverage of key domain concepts in LLMs of various sizes. In particular, we have been able to significantly enhance the performance of LLMs of various sizes with openly available weights using simple knowledge-graph (KG) based prompting strategies.

Problem-solving has been a fundamental driver of human progress in numerous domains. With advancements in artificial intelligence, Large Language Models (LLMs) have emerged as powerful tools capable of tackling complex problems across diverse domains. Unlike traditional computational systems, LLMs combine raw computational power with an approximation of human reasoning, allowing them to generate solutions, make inferences, and even leverage external computational tools. However, applying LLMs to real-world problem-solving presents significant challenges, including multi-step reasoning, domain knowledge integration, and result verification. This survey explores the capabilities and limitations of LLMs in complex problem-solving, examining techniques including Chain-of-Thought (CoT) reasoning, knowledge augmentation, and various LLM-based and tool-based verification techniques. Additionally, we highlight domain-specific challenges in various domains, such as software engineering, mathematical reasoning and proving, data analysis and modeling, and scientific research. The paper further discusses the fundamental limitations of the current LLM solutions and the future directions of LLM-based complex problems solving from the perspective of multi-step reasoning, domain knowledge integration and result verification.

The solution methods used to realize artificial general intelligence (AGI) may not contain the formalism needed to adequately model and characterize AGI. In particular, current approaches to learning hold notions of problem domain and problem task as fundamental precepts, but it is hardly apparent that an AGI encountered in the wild will be discernable into a set of domain-task pairings. Nor is it apparent that the outcomes of AGI in a system can be well expressed in terms of domain and task, or as consequences thereof. Thus, there is both a practical and theoretical use for meta-theories of learning which do not express themselves explicitly in terms of solution methods. General systems theory offers such a meta-theory. Herein, Mesarovician abstract systems theory is used as a super-structure for learning. Abstract learning systems are formulated. Subsequent elaboration stratifies the assumptions of learning systems into a hierarchy and considers the hierarchy such stratification projects onto learning theory. The presented Mesarovician abstract learning systems theory calls back to the founding motivations of artificial intelligence research by focusing on the thinking participants directly, in this case, learning systems, in contrast to the contemporary focus on the problems thinking participants solve.

Recent advances in Large Reasoning Models (LRMs) trained with Long Chain-of-Thought (Long CoT) reasoning have demonstrated remarkable cross-domain generalization capabilities. However, the underlying mechanisms supporting such transfer remain poorly understood. We hypothesize that cross-domain generalization arises from shared abstract reasoning prototypes -- fundamental reasoning patterns that capture the essence of problems across domains. These prototypes minimize the nuances of the representation, revealing that seemingly diverse tasks are grounded in shared reasoning structures.Based on this hypothesis, we propose ProtoReasoning, a framework that enhances the reasoning ability of LLMs by leveraging scalable and verifiable prototypical representations (Prolog for logical reasoning, PDDL for planning).ProtoReasoning features: (1) an automated prototype construction pipeline that transforms problems into corresponding prototype representations; (2) a comprehensive verification system providing reliable feedback through Prolog/PDDL interpreters; (3) the scalability to synthesize problems arbitrarily within prototype space while ensuring correctness. Extensive experiments show that ProtoReasoning achieves 4.7% improvement over baseline models on logical reasoning (Enigmata-Eval), 6.3% improvement on planning tasks, 4.0% improvement on general reasoning (MMLU) and 1.0% on mathematics (AIME24). Significantly, our ablation studies confirm that learning in prototype space also demonstrates enhanced generalization to structurally similar problems compared to training solely on natural language representations, validating our hypothesis that reasoning prototypes serve as the foundation for generalizable reasoning in large language models.

Large language models (LLMs) have demonstrated impressive performance on reasoning tasks, including mathematical reasoning. However, the current evaluation mostly focuses on carefully constructed benchmarks and neglects the consideration of real-world reasoning problems that present missing or contradictory conditions, known as ill-defined problems. To further study this problem, we develop a largescale benchmark called Problems with Missing and Contradictory conditions ( PMC) containing over 5,000 validated ill-defined mathematical problems. Our preliminary experiments through PMC reveal two challenges about existing methods: (1) traditional methods exhibit a trade-off between solving accuracy and rejection capabilities, and (2) formal methods struggle with modeling complex problems. To address these challenges, We develop Variable-Constraint Search (VCSEARCH), a trainingfree framework that leverages formal language to detect ill-defined problems, where a variableconstraint pair search strategy is incorporated to improve the modeling capability of formal language. Extensive experiments demonstrate that VCSEARCH improves the accuracy of identifying unsolvable problems by at least 12% across different LLMs, thus achieving stronger robust mathematical reasoning ability.

Large language models (LLMs) have significantly advanced the field of natural language processing (NLP), providing a highly useful, task-agnostic foundation for a wide range of applications. However, directly applying LLMs to solve sophisticated problems in specific domains meets many hurdles, caused by the heterogeneity of domain data, the sophistication of domain knowledge, the uniqueness of domain objectives, and the diversity of the constraints (e.g., various social norms, cultural conformity, religious beliefs, and ethical standards in the domain applications). Domain specification techniques are key to make large language models disruptive in many applications. Specifically, to solve these hurdles, there has been a notable increase in research and practices conducted in recent years on the domain specialization of LLMs. This emerging field of study, with its substantial potential for impact, necessitates a comprehensive and systematic review to better summarize and guide ongoing work in this area. In this article, we present a comprehensive survey on domain specification techniques for large language models, an emerging direction critical for large language model applications. First, we propose a systematic taxonomy that categorizes the LLM domain-specialization techniques based on the accessibility to LLMs and summarizes the framework for all the subcategories as well as their relations and differences to each other. Second, we present an extensive taxonomy of critical application domains that can benefit dramatically from specialized LLMs, discussing their practical significance and open challenges. Last, we offer our insights into the current research status and future trends in this area.

Domain Large Language Models (LLMs) are developed for domain-specific tasks based on general LLMs. But it still requires professional knowledge to facilitate the expertise for some domain-specific tasks. In this paper, we investigate into knowledge-intensive calculation problems. We find that the math problems to be challenging for LLMs, when involving complex domain-specific rules and knowledge documents, rather than simple formulations of terminologies. Therefore, we propose a pipeline to solve the domain-specific calculation problems with Knowledge-Intensive Programs Generator more effectively, named as KIPG. It generates knowledge-intensive programs according to the domain-specific documents. For each query, key variables are extracted, then outcomes which are dependent on domain knowledge are calculated with the programs. By iterative preference alignment, the code generator learns to improve the logic consistency with the domain knowledge. Taking legal domain as an example, we have conducted experiments to prove the effectiveness of our pipeline, and extensive analysis on the modules. We also find that the code generator is also adaptable to other domains, without training on the new knowledge.

We describe a method, based on Jennifer Nado's proposal for classification procedures as targets of conceptual engineering, that implements such procedures by prompting a large language model. We apply this method, using data from the Wikidata knowledge graph, to evaluate stipulative definitions related to two paradigmatic conceptual engineering projects: the International Astronomical Union's redefinition of PLANET and Haslanger's ameliorative analysis of WOMAN. Our results show that classification procedures built using our approach can exhibit good classification performance and, through the generation of rationales for their classifications, can contribute to the identification of issues in either the definitions or the data against which they are being evaluated. We consider objections to this method, and discuss implications of this work for three aspects of theory and practice of conceptual engineering: the definition of its targets, empirical methods for their investigation, and their practical roles. The data and code used for our experiments, together with the experimental results, are available in a Github repository.

Conceptual knowledge is fundamental to human cognition and knowledge bases. However, existing knowledge probing works only focus on evaluating factual knowledge of pre-trained language models (PLMs) and ignore conceptual knowledge. Since conceptual knowledge often appears as implicit commonsense behind texts, designing probes for conceptual knowledge is hard. Inspired by knowledge representation schemata, we comprehensively evaluate conceptual knowledge of PLMs by designing three tasks to probe whether PLMs organize entities by conceptual similarities, learn conceptual properties, and conceptualize entities in contexts, respectively. For the tasks, we collect and annotate 24k data instances covering 393 concepts, which is COPEN, a COnceptual knowledge Probing bENchmark. Extensive experiments on different sizes and types of PLMs show that existing PLMs systematically lack conceptual knowledge and suffer from various spurious correlations. We believe this is a critical bottleneck for realizing human-like cognition in PLMs. COPEN and our codes are publicly released at https://github.com/THU-KEG/COPEN.

The performance of large language models (LLMs) on existing reasoning benchmarks has significantly improved over the past years. In response, we present JEEBench, a considerably more challenging benchmark dataset for evaluating the problem solving abilities of LLMs. We curate 515 challenging pre-engineering mathematics, physics and chemistry problems from the highly competitive IIT JEE-Advanced exam. Long-horizon reasoning on top of deep in-domain knowledge is essential for solving problems in this benchmark. Our evaluation on various open-source and proprietary models reveals that the highest performance, even after using techniques like self-consistency, self-refinement and chain-of-thought prompting, is less than 40%. The typical failure modes of GPT-4, the best model, are errors in algebraic manipulation, difficulty in grounding abstract concepts into mathematical equations accurately and failure in retrieving relevant domain-specific concepts. We also observe that by mere prompting, GPT-4 is unable to assess risk introduced by negative marking for incorrect answers. For this, we develop a post-hoc confidence-thresholding method over self-consistency, which enables effective response selection. We hope that our challenging benchmark will guide future re-search in problem-solving using LLMs.

Mathematical reasoning serves as a cornerstone for assessing the fundamental cognitive capabilities of human intelligence. In recent times, there has been a notable surge in the development of Large Language Models (LLMs) geared towards the automated resolution of mathematical problems. However, the landscape of mathematical problem types is vast and varied, with LLM-oriented techniques undergoing evaluation across diverse datasets and settings. This diversity makes it challenging to discern the true advancements and obstacles within this burgeoning field. This survey endeavors to address four pivotal dimensions: i) a comprehensive exploration of the various mathematical problems and their corresponding datasets that have been investigated; ii) an examination of the spectrum of LLM-oriented techniques that have been proposed for mathematical problem-solving; iii) an overview of factors and concerns affecting LLMs in solving math; and iv) an elucidation of the persisting challenges within this domain. To the best of our knowledge, this survey stands as one of the first extensive examinations of the landscape of LLMs in the realm of mathematics, providing a holistic perspective on the current state, accomplishments, and future challenges in this rapidly evolving field.

Training large language models for complex reasoning is bottlenecked by the scarcity of verifiable, high-quality data. In domains like physics, standard text augmentation often introduces hallucinations, while static benchmarks lack the reasoning traces required for fine-tuning. We introduce the Infinite Problem Generator (IPG), an agentic framework that synthesizes physics problems with guaranteed solvability through a Formula-as-Code paradigm. Unlike probabilistic text generation, IPG constructs solutions as executable Python programs, enforcing strict mathematical consistency. As a proof-of-concept, we release ClassicalMechanicsV1, a high-fidelity corpus of 1,335 classical mechanics problems expanded from 165 expert seeds. The corpus demonstrates high structural diversity, spanning 102 unique physical formulas with an average complexity of 3.05 formulas per problem. Furthermore, we identify a Complexity Blueprint, demonstrating a strong linear correlation (R^2 approx 0.95) between formula count and verification code length. This relationship establishes code complexity as a precise, proxy-free metric for problem difficulty, enabling controllable curriculum generation. We release the full IPG pipeline, the ClassicalMechanicsV1 dataset, and our evaluation report to support reproducible research in reasoning-intensive domains.

The integration of knowledge extracted from diverse models, whether described by domain experts or generated by machine learning algorithms, has historically been challenged by the absence of a suitable framework for specifying and integrating structures, learning processes, data transformations, and data models or rules. In this work, we extend algebraic specification methods to address these challenges within such a framework. In our work, we tackle the challenging task of developing a comprehensive framework for defining and analyzing deep learning architectures. We believe that previous efforts have fallen short by failing to establish a clear connection between the constraints a model must adhere to and its actual implementation. Our methodology employs graphical structures that resemble Ehresmann's sketches, interpreted within a universe of fuzzy sets. This approach offers a unified theory that elegantly encompasses both deterministic and non-deterministic neural network designs. Furthermore, we highlight how this theory naturally incorporates fundamental concepts from computer science and automata theory. Our extended algebraic specification framework, grounded in graphical structures akin to Ehresmann's sketches, offers a promising solution for integrating knowledge across disparate models and domains. By bridging the gap between domain-specific expertise and machine-generated insights, we pave the way for more comprehensive, collaborative, and effective approaches to knowledge integration and modeling.

Recent work by (Richardson and Kuhn, 2017a,b; Richardson et al., 2018) looks at semantic parser induction and question answering in the domain of source code libraries and APIs. In this brief note, we formalize the representations being learned in these studies and introduce a simple domain specific language and a systematic translation from this language to first-order logic. By recasting the target representations in terms of classical logic, we aim to broaden the applicability of existing code datasets for investigating more complex natural language understanding and reasoning problems in the software domain.

Integer sequences are of central importance to the modeling of concepts admitting complete finitary descriptions. We introduce a novel view on the learning of such concepts and lay down a set of benchmarking tasks aimed at conceptual understanding by machine learning models. These tasks indirectly assess model ability to abstract, and challenge them to reason both interpolatively and extrapolatively from the knowledge gained by observing representative examples. To further aid research in knowledge representation and reasoning, we present FACT, the Finitary Abstraction Comprehension Toolkit. The toolkit surrounds a large dataset of integer sequences comprising both organic and synthetic entries, a library for data pre-processing and generation, a set of model performance evaluation tools, and a collection of baseline model implementations, enabling the making of the future advancements with ease.

Large language model (LLM) performance on reasoning problems typically does not generalize out of distribution. Previous work has claimed that this can be mitigated by modifying prompts to include examples with chains of thought--demonstrations of solution procedures--with the intuition that it is possible to in-context teach an LLM an algorithm for solving the problem. This paper presents a case study of chain of thought on problems from Blocksworld, a classical planning domain, and examine the performance of two state-of-the-art LLMs across two axes: generality of examples given in prompt, and complexity of problems queried with each prompt. While our problems are very simple, we only find meaningful performance improvements from chain of thought prompts when those prompts are exceedingly specific to their problem class, and that those improvements quickly deteriorate as the size n of the query-specified stack grows past the size of stacks shown in the examples. Our results hint that, contrary to previous claims in the literature, CoT's performance improvements do not stem from the model learning general algorithmic procedures via demonstrations and depend on carefully engineering highly problem specific prompts. This spotlights drawbacks of chain of thought, especially because of the sharp tradeoff between possible performance gains and the amount of human labor necessary to generate examples with correct reasoning traces.

There is growing interest in utilizing large language models (LLMs) as co-pilots for combinatorial optimization and constraint programming tasks across various problems. This paper aims to advance this line of research by introducing Text2Zinc}, a cross-domain dataset for capturing optimization and satisfaction problems specified in natural language text. Our work is distinguished from previous attempts by integrating both satisfaction and optimization problems within a unified dataset using a solver-agnostic modeling language. To achieve this, we leverage MiniZinc's solver-and-paradigm-agnostic modeling capabilities to formulate these problems. Using the Text2Zinc dataset, we conduct comprehensive baseline experiments to compare execution and solution accuracy across several methods, including off-the-shelf prompting strategies, chain-of-thought reasoning, and a compositional approach. Additionally, we explore the effectiveness of intermediary representations, specifically knowledge graphs. Our findings indicate that LLMs are not yet a push-button technology to model combinatorial problems from text. We hope that Text2Zinc serves as a valuable resource for researchers and practitioners to advance the field further.

Understanding Rebus Puzzles (Rebus Puzzles use pictures, symbols, and letters to represent words or phrases creatively) requires a variety of skills such as image recognition, cognitive skills, commonsense reasoning, multi-step reasoning, image-based wordplay, etc., making this a challenging task for even current Vision-Language Models. In this paper, we present left|,circlearrowright,text{BUS},right|, a large and diverse benchmark of 1,333 English Rebus Puzzles containing different artistic styles and levels of difficulty, spread across 18 categories such as food, idioms, sports, finance, entertainment, etc. We also propose RebusDescProgICE, a model-agnostic framework which uses a combination of an unstructured description and code-based, structured reasoning, along with better, reasoning-based in-context example selection, improving the performance of Vision-Language Models on left|,circlearrowright,text{BUS},right| by 2.1-4.1% and 20-30% using closed-source and open-source models respectively compared to Chain-of-Thought Reasoning.

Human reasoning relies on constructing and manipulating mental models-simplified internal representations of situations that we use to understand and solve problems. Conceptual diagrams (for example, sketches drawn by humans to aid reasoning) externalize these mental models, abstracting irrelevant details to efficiently capture relational and spatial information. In contrast, Large Language Models (LLMs) and Large Multimodal Models (LMMs) predominantly reason through textual representations, limiting their effectiveness in complex multi-step combinatorial and planning tasks. In this paper, we propose a zero-shot fully automatic framework that enables LMMs to reason through multiple chains of self-generated intermediate conceptual diagrams, significantly enhancing their combinatorial planning capabilities. Our approach does not require any human initialization beyond a natural language description of the task. It integrates both textual and diagrammatic reasoning within an optimized graph-of-thought inference framework, enhanced by beam search and depth-wise backtracking. Evaluated on multiple challenging PDDL planning domains, our method substantially improves GPT-4o's performance (for example, from 35.5% to 90.2% in Blocksworld). On more difficult planning domains with solution depths up to 40, our approach outperforms even the o1-preview reasoning model (for example, over 13% improvement in Parking). These results highlight the value of conceptual diagrams as a complementary reasoning medium in LMMs.

Contemporary large language models (LLMs) have demonstrated remarkable reasoning capabilities, particularly in specialized domains like mathematics and physics. However, their ability to generalize these reasoning skills to more general and broader contexts--often termed general reasoning--remains under-explored. Unlike domain-specific reasoning, general reasoning relies less on expert knowledge but still presents formidable reasoning challenges, such as complex constraints, nested logical branches, and semantic interference. To address this gap, we introduce General365, a benchmark specifically designed to assess general reasoning in LLMs. By restricting background knowledge to a K-12 level, General365 explicitly decouples reasoning from specialized expertise. The benchmark comprises 365 seed problems and 1,095 variant problems across eight categories, ensuring both high difficulty and diversity. Evaluations across 26 leading LLMs reveal that even the top-performing model achieves only 62.8% accuracy, in stark contrast to the near-perfect performances of LLMs in math and physics benchmarks. These results suggest that the reasoning abilities of current LLMs are heavily domain-dependent, leaving significant room for improvement in broader applications. We envision General365 as a catalyst for advancing LLM reasoning beyond domain-specific tasks toward robust, general-purpose real-world scenarios. Code, Dataset, and Leaderboard: https://general365.github.io

Large language models (LLMs) have attracted considerable attention in various fields for their cost-effective solutions to diverse challenges, especially with advancements in instruction tuning and quantization. E-commerce, with its complex tasks and extensive product-user interactions, presents a promising application area for LLMs. However, the domain-specific concepts and knowledge inherent in e-commerce pose significant challenges for adapting general LLMs. To address this issue, we developed EC-Guide https://github.com/fzp0424/EC-Guide-KDDUP-2024, a comprehensive e-commerce guide for instruction tuning and quantization of LLMs. We also heuristically integrated Chain-of-Thought (CoT) during inference to enhance arithmetic performance. Our approach achieved the 2nd place in Track 2 and 5th place in Track 5 at the Amazon KDD Cup'24 https://www.aicrowd.com/challenges/amazon-kdd-cup-2024-multi-task-online-shopping-challenge-for-llms. Additionally, our solution is model-agnostic, enabling effective scalability across larger systems.

Multi-constraint planning involves identifying, evaluating, and refining candidate plans while satisfying multiple, potentially conflicting constraints. Existing large language model (LLM) approaches face fundamental limitations in this domain. Pure reasoning paradigms, which rely on long natural language chains, are prone to inconsistency, error accumulation, and prohibitive cost as constraints compound. Conversely, LLMs combined with coding- or solver-based strategies lack flexibility: they often generate problem-specific code from scratch or depend on fixed solvers, failing to capture generalizable logic across diverse problems. To address these challenges, we introduce the Scalable COde Planning Engine (SCOPE), a framework that disentangles query-specific reasoning from generic code execution. By separating reasoning from execution, SCOPE produces solver functions that are consistent, deterministic, and reusable across queries while requiring only minimal changes to input parameters. SCOPE achieves state-of-the-art performance while lowering cost and latency. For example, with GPT-4o, it reaches 93.1% success on TravelPlanner, a 61.6% gain over the best baseline (CoT) while cutting inference cost by 1.4x and time by ~4.67x. Code is available at https://github.com/DerrickGXD/SCOPE.

This paper investigates the mathematical reasoning capabilities of large language models (LLMs) using 50 newly constructed high-school-level word problems. Unlike prior studies that focus solely on answer correctness, we rigorously analyze both final answers and solution steps to identify reasoning failures. Evaluating eight state-of-the-art models - including Mixtral, Llama, Gemini, GPT-4o, and OpenAI's o1 variants - we find that while newer models (e.g., o3-mini, deepseek-r1) achieve higher accuracy, all models exhibit errors in spatial reasoning, strategic planning, and arithmetic, sometimes producing correct answers through flawed logic. Common failure modes include unwarranted assumptions, over-reliance on numerical patterns, and difficulty translating physical intuition into mathematical steps. Manual analysis reveals that models struggle with problems requiring multi-step deduction or real-world knowledge, despite possessing broad mathematical knowledge. Our results underscore the importance of evaluating reasoning processes, not just answers, and caution against overestimating LLMs' problem-solving proficiency. The study highlights persistent gaps in LLMs' generalization abilities, emphasizing the need for targeted improvements in structured reasoning and constraint handling.

Twenty-seven years ago, E. Freuder highlighted that "Constraint programming represents one of the closest approaches computer science has yet made to the Holy Grail of programming: the user states the problem, the computer solves it". Nowadays, CP users have great modeling tools available (like Minizinc and CPMpy), allowing them to formulate the problem and then let a solver do the rest of the job, getting closer to the stated goal. However, this still requires the CP user to know the formalism and respect it. Another significant challenge lies in the expertise required to effectively model combinatorial problems. All this limits the wider adoption of CP. In this position paper, we investigate a possible approach to leverage pre-trained Large Language Models to extract models from textual problem descriptions. More specifically, we take inspiration from the Natural Language Processing for Optimization (NL4OPT) challenge and present early results with a decomposition-based prompting approach to GPT Models.

Large Language Models (LLMs) are widely applied to downstream domains. However, current LLMs for high-stakes domain tasks, such as financial investment and legal QA, typically generate brief answers without reasoning processes and explanations. This limits users' confidence in making decisions based on their responses. While original CoT shows promise, it lacks self-correction mechanisms during reasoning. This work introduces Domaino1s, which enhances LLMs' reasoning capabilities on domain tasks through supervised fine-tuning and tree search. We construct CoT-stock-2k and CoT-legal-2k datasets for fine-tuning models that activate domain-specific reasoning steps based on their judgment. Additionally, we propose Selective Tree Exploration to spontaneously explore solution spaces and sample optimal reasoning paths to improve performance. We also introduce PROOF-Score, a new metric for evaluating domain models' explainability, complementing traditional accuracy metrics with richer assessment dimensions. Extensive experiments on stock investment recommendation and legal reasoning QA tasks demonstrate Domaino1s's leading performance and explainability. Our code is available at https://anonymous.4open.science/r/Domaino1s-006F/.

Large Language Models (LLMs) have demonstrated remarkable performance on various quantitative reasoning and knowledge benchmarks. However, many of these benchmarks are losing utility as LLMs get increasingly high scores, despite not yet reaching expert performance in these domains. We introduce ARB, a novel benchmark composed of advanced reasoning problems in multiple fields. ARB presents a more challenging test than prior benchmarks, featuring problems in mathematics, physics, biology, chemistry, and law. As a subset of ARB, we introduce a challenging set of math and physics problems which require advanced symbolic reasoning and domain knowledge. We evaluate recent models such as GPT-4 and Claude on ARB and demonstrate that current models score well below 50% on more demanding tasks. In order to improve both automatic and assisted evaluation capabilities, we introduce a rubric-based evaluation approach, allowing GPT-4 to score its own intermediate reasoning steps. Further, we conduct a human evaluation of the symbolic subset of ARB, finding promising agreement between annotators and GPT-4 rubric evaluation scores.

Domain-independent heuristics have long been a cornerstone of AI planning, offering general solutions applicable across a wide range of tasks without requiring domain-specific engineering. However, the advent of large language models (LLMs) presents an opportunity to generate heuristics tailored to specific planning problems, potentially challenging the necessity of domain independence as a strict design principle. In this paper, we explore the use of LLMs to automatically derive planning heuristics from task descriptions represented as successor generators and goal tests written in general purpose programming language. We investigate the trade-offs between domain-specific LLM-generated heuristics and traditional domain-independent methods in terms of computational efficiency and explainability. Our experiments demonstrate that LLMs can create heuristics that achieve state-of-the-art performance on some standard IPC domains, as well as their ability to solve problems that lack an adequate Planning Domain Definition Language ({\sc pddl}) representation. We discuss whether these results signify a paradigm shift and how they can complement existing approaches.

This research introduces a novel evaluation framework designed to assess large language models' (LLMs) ability to acknowledge uncertainty on 675 fundamentally unsolvable problems. Using a curated dataset of graduate-level grand challenge questions with intentionally unknowable answers, we evaluated twelve state-of-the-art LLMs, including both open and closed-source models, on their propensity to admit ignorance rather than generate plausible but incorrect responses. The best models scored in 62-68% accuracy ranges for admitting the problem solution was unknown in fields ranging from biology to philosophy and mathematics. We observed an inverse relationship between problem difficulty and model accuracy, with GPT-4 demonstrating higher rates of uncertainty acknowledgment on more challenging problems (35.8%) compared to simpler ones (20.0%). This pattern indicates that models may be more prone to generate speculative answers when problems appear more tractable. The study also revealed significant variations across problem categories, with models showing difficulty in acknowledging uncertainty in invention and NP-hard problems while performing relatively better on philosophical and psychological challenges. These results contribute to the growing body of research on artificial general intelligence (AGI) assessment by highlighting the importance of uncertainty recognition as a critical component of future machine intelligence evaluation. This impossibility test thus extends previous theoretical frameworks for universal intelligence testing by providing empirical evidence of current limitations in LLMs' ability to recognize their own knowledge boundaries, suggesting new directions for improving model training architectures and evaluation approaches.

Solving math story problems is a complex task for students and NLP models alike, requiring them to understand the world as described in the story and reason over it to compute an answer. Recent years have seen impressive performance on automatically solving these problems with large pre-trained language models and innovative techniques to prompt them. However, it remains unclear if these models possess accurate representations of mathematical concepts. This leads to lack of interpretability and trustworthiness which impedes their usefulness in various applications. In this paper, we consolidate previous work on categorizing and representing math story problems and develop MathWorld, which is a graph-based semantic formalism specific for the domain of math story problems. With MathWorld, we can assign world models to math story problems which represent the situations and actions introduced in the text and their mathematical relationships. We combine math story problems from several existing datasets and annotate a corpus of 1,019 problems and 3,204 logical forms with MathWorld. Using this data, we demonstrate the following use cases of MathWorld: (1) prompting language models with synthetically generated question-answer pairs to probe their reasoning and world modeling abilities, and (2) generating new problems by using the world models as a design space.

AGI has become the Holly Grail of AI with the promise of level intelligence and the major Tech companies around the world are investing unprecedented amounts of resources in its pursuit. Yet, there does not exist a single formal definition and only some empirical AGI benchmarking frameworks currently exist. The main purpose of this paper is to develop a general, algebraic and category theoretic framework for describing, comparing and analysing different possible AGI architectures. Thus, this Category theoretic formalization would also allow to compare different possible candidate AGI architectures, such as, RL, Universal AI, Active Inference, CRL, Schema based Learning, etc. It will allow to unambiguously expose their commonalities and differences, and what is even more important, expose areas for future research. From the applied Category theoretic point of view, we take as inspiration Machines in a Category to provide a modern view of AGI Architectures in a Category. More specifically, this first position paper provides, on one hand, a first exercise on RL, Causal RL and SBL Architectures in a Category, and on the other hand, it is a first step on a broader research program that seeks to provide a unified formal foundation for AGI systems, integrating architectural structure, informational organization, agent realization, agent and environment interaction, behavioural development over time, and the empirical evaluation of properties. This framework is also intended to support the definition of architectural properties, both syntactic and informational, as well as semantic properties of agents and their assessment in environments with explicitly characterized features. We claim that Category Theory and AGI will have a very symbiotic relation.

Recently, a large amount of work has focused on improving large language models' (LLMs') performance on reasoning benchmarks such as math and logic. However, past work has largely assumed that tasks are well-defined. In the real world, queries to LLMs are often underspecified, only solvable through acquiring missing information. We formalize this as a constraint satisfaction problem (CSP) with missing variable assignments. Using a special case of this formalism where only one necessary variable assignment is missing, we can rigorously evaluate an LLM's ability to identify the minimal necessary question to ask and quantify axes of difficulty levels for each problem. We present QuestBench, a set of underspecified reasoning tasks solvable by asking at most one question, which includes: (1) Logic-Q: Logical reasoning tasks with one missing proposition, (2) Planning-Q: PDDL planning problems with initial states that are partially-observed, (3) GSM-Q: Human-annotated grade school math problems with one missing variable assignment, and (4) GSME-Q: a version of GSM-Q where word problems are translated into equations by human annotators. The LLM is tasked with selecting the correct clarification question(s) from a list of options. While state-of-the-art models excel at GSM-Q and GSME-Q, their accuracy is only 40-50% on Logic-Q and Planning-Q. Analysis demonstrates that the ability to solve well-specified reasoning problems may not be sufficient for success on our benchmark: models have difficulty identifying the right question to ask, even when they can solve the fully specified version of the problem. Furthermore, in the Planning-Q domain, LLMs tend not to hedge, even when explicitly presented with the option to predict ``not sure.'' This highlights the need for deeper investigation into models' information acquisition capabilities.

In this paper, we present a new theoretical approach for enabling domain knowledge acquisition by intelligent systems. We introduce a hybrid model that starts with minimal input knowledge in the form of an upper ontology of concepts, stores and reasons over this knowledge through a knowledge graph database and learns new information through a Logic Neural Network. We study the behavior of this architecture when handling new data and show that the final system is capable of enriching its current knowledge as well as extending it to new domains.

This paper introduces a novel method for merging open-domain terminological knowledge. It takes advantage of the Region Connection Calculus (RCC5), a formalism used to represent regions in a topological space and to reason about their set-theoretic relationships. To this end, we first propose a faithful translation of terminological knowledge provided by several and potentially conflicting sources into region spaces. The merging is then performed on these spaces, and the result is translated back into the underlying language of the input sources. Our approach allows us to benefit from the expressivity and the flexibility of RCC5 while dealing with conflicting knowledge in a principled way.

Recent large language models (LLMs) have shown indications of mathematical reasoning ability. However it has not been clear how they would fare on more challenging competition-level problems. And while self-generated verbalizations of intermediate reasoning steps (i.e., chain-of-thought prompting) have been shown to be helpful, whether LLMs can make use of helpful side information such as problem-specific hints has not been investigated before. In this paper, we propose a challenging benchmark dataset for enabling such analyses. The Concept and Hint-Annotated Math Problems (CHAMP) consists of high school math competition problems, annotated with concepts, or general math facts, and hints, or problem-specific tricks. These annotations allow us to explore the effects of additional information, such as relevant hints, misleading concepts, or related problems. This benchmark is difficult, with the best model only scoring 58.1% in standard settings. With concepts and hints, performance sometimes improves, indicating that some models can make use of such side information. We further annotate model-generated solutions for their correctness. Using this corpus, we find that models often arrive at the correct final answer through wrong reasoning steps. In addition, we test whether models are able to verify these solutions, and find that most models struggle. The dataset and code are available on the project website.

While large language models (LLMs) have shown strong performance in math and logic reasoning, their ability to handle combinatorial optimization (CO) -- searching high-dimensional solution spaces under hard constraints -- remains underexplored. To bridge the gap, we introduce NLCO, a Natural Language Combinatorial Optimization benchmark that evaluates LLMs on end-to-end CO reasoning: given a language-described decision-making scenario, the model must output a discrete solution without writing code or calling external solvers. NLCO covers 43 CO problems and is organized using a four-layer taxonomy of variable types, constraint families, global patterns, and objective classes, enabling fine-grained evaluation. We provide solver-annotated solutions and comprehensively evaluate LLMs by feasibility, solution optimality, and reasoning efficiency. Experiments across a wide range of modern LLMs show that high-performing models achieve strong feasibility and solution quality on small instances, but both degrade as instance size grows, even if more tokens are used for reasoning. We also observe systematic effects across the taxonomy: set-based tasks are relatively easy, whereas graph-structured problems and bottleneck objectives lead to more frequent failures.

Recent methods have demonstrated that Large Language Models (LLMs) can solve reasoning tasks better when they are encouraged to solve subtasks of the main task first. In this paper we devise a similar strategy that breaks down reasoning tasks into a problem decomposition phase and a problem solving phase and show that the strategy is able to outperform a single stage solution. Further, we hypothesize that the decomposition should be easier to distill into a smaller model compared to the problem solving because the latter requires large amounts of domain knowledge while the former only requires learning general problem solving strategies. We propose methods to distill these two capabilities and evaluate their impact on reasoning outcomes and inference cost. We find that we can distill the problem decomposition phase and at the same time achieve good generalization across tasks, datasets, and models. However, it is harder to distill the problem solving capability without losing performance and the resulting distilled model struggles with generalization. These results indicate that by using smaller, distilled problem decomposition models in combination with problem solving LLMs we can achieve reasoning with cost-efficient inference and local adaptation.

Among the hardest tasks for humans are those found in competitive programming where problems require sophisticated algorithmic thinking, puzzle solving, and the creation of effective code. As a domain to assess language models (LMs), it has not received enough attention, though. This study presents the ICPC benchmark, which consists of 254 international collegiate programming contest (ICPC) tasks. Each problem includes official analysis, reference code, and sample, high-quality unit, and hidden tests. We are able to develop and evaluate a variety of LM inference techniques for competitive programming with these resources. With zero-shot chain-of-thought prompting, we find that o1 only achieves a 19.1\% pass@1 solve rate. With our best inference technique, which combines multi-turn self-judge with reflection and retrieval over episodic information, raises this to 42.2\%. Furthermore, we conduct a new human-in-the-loop investigation to gain a deeper understanding of the remaining difficulties. Surprisingly, we discover that o1 can solve 17 out of 18 problems that were previously unsolvable by any model or technique with just a few specific instructions. A footstep toward LMs with grounded, imaginative, and algorithmic thinking is provided by our quantitative findings and qualitative research. We open-source our code and data at https://github.com/kraritt/zolve.

We introduce Vibe Reasoning, a human-AI collaborative paradigm for solving complex mathematical problems. Our key insight is that frontier AI models already possess the knowledge required to solve challenging problems -- they simply do not know how, what, or when to apply it. Vibe Reasoning transforms AI's latent potential into manifested capability through generic meta-prompts, agentic grounding, and model orchestration. We demonstrate this paradigm through IMO 2025 Problem 6, a combinatorial optimization problem where autonomous AI systems publicly reported failures. Our solution combined GPT-5's exploratory capabilities with Gemini 3 Pro's proof strengths, leveraging agentic workflows with Python code execution and file-based memory, to derive both the correct answer (2112) and a rigorous mathematical proof. Through iterative refinement across multiple attempts, we discovered the necessity of agentic grounding and model orchestration, while human prompts evolved from problem-specific hints to generic, transferable meta-prompts. We analyze why capable AI fails autonomously, how each component addresses specific failure modes, and extract principles for effective vibe reasoning. Our findings suggest that lightweight human guidance can unlock frontier models' mathematical reasoning potential. This is ongoing work; we are developing automated frameworks and conducting broader evaluations to further validate Vibe Reasoning's generality and effectiveness.

Concepts serve as fundamental abstractions that support human reasoning and categorization. However, it remains unclear whether large language models truly capture such conceptual structures or primarily rely on surface-level pattern memorization. Existing benchmarks are largely static and fact oriented, which limits their ability to probe fine-grained semantic understanding and makes them vulnerable to data leakage and overfitting. To address this limitation, we introduce CK-Arena, a dynamic benchmark for conceptual knowledge evaluation based on a multi agent social deduction game, namely the Undercover game. In this setting, LLM based agents are assigned subtly different concept words and must describe, distinguish, and infer conceptual properties from others' statements. Model performance is evaluated through both game level outcomes and the semantic quality of generated descriptions. Furthermore, CK-Arena leverages the interaction process to automatically construct high quality question answering data for fine grained diagnostic analysis. Experimental results show that conceptual understanding varies substantially across models and categories, and is not strictly aligned with overall model capability. The data and code are available at the project homepage: https://ck-arena.site.

Language models traditionally used for cross-domain generalization have recently demonstrated task-specific reasoning. However, their top-down training approach on general corpora is insufficient for acquiring abstractions needed for deep domain expertise. This may require a bottom-up approach that acquires expertise by learning to compose simple domain concepts into more complex ones. A knowledge graph (KG) provides this compositional structure, where domain primitives are represented as head-relation-tail edges and their paths encode higher-level concepts. We present a task generation pipeline that synthesizes tasks directly from KG primitives, enabling models to acquire and compose them for reasoning. We fine-tune language models on the resultant KG-grounded curriculum to demonstrate domain-specific superintelligence. While broadly applicable, we validate our approach in medicine, where reliable KGs exist. Using a medical KG, we curate 24,000 reasoning tasks paired with thinking traces derived from diverse medical primitives. We fine-tune the QwQ-32B model on this curriculum to obtain QwQ-Med-3 that takes a step towards medical superintelligence. We also introduce ICD-Bench, an evaluation suite to quantify reasoning abilities across 15 medical domains. Our experiments demonstrate that QwQ-Med-3 significantly outperforms state-of-the-art reasoning models on ICD-Bench categories. Further analysis reveals that QwQ-Med-3 utilizes acquired primitives to widen the performance gap on the hardest tasks of ICD-Bench. Finally, evaluation on medical question-answer benchmarks shows that QwQ-Med-3 transfers acquired expertise to enhance the base model's performance. While the industry's approach to artificial general intelligence (AGI) emphasizes broad expertise, we envision a future in which AGI emerges from the composable interaction of efficient domain-specific superintelligent agents.

Large Language Models (LLMs) have made remarkable strides in reasoning tasks, yet their performance often falters on novel and complex problems. Domain-specific continued pretraining (CPT) methods, such as those tailored for mathematical reasoning, have shown promise but lack transferability to broader reasoning tasks. In this work, we pioneer the use of Graph Problem Reasoning (GPR) to enhance the general reasoning capabilities of LLMs. GPR tasks, spanning pathfinding, network analysis, numerical computation, and topological reasoning, require sophisticated logical and relational reasoning, making them ideal for teaching diverse reasoning patterns. To achieve this, we introduce GraphPile, the first large-scale corpus specifically designed for CPT using GPR data. Spanning 10.9 billion tokens across 23 graph tasks, the dataset includes chain-of-thought, program-of-thought, trace of execution, and real-world graph data. Using GraphPile, we train GraphMind on popular base models Llama 3 and 3.1, as well as Gemma 2, achieving up to 4.9 percent higher accuracy in mathematical reasoning and up to 21.2 percent improvement in non-mathematical reasoning tasks such as logical and commonsense reasoning. By being the first to harness GPR for enhancing reasoning patterns and introducing the first dataset of its kind, our work bridges the gap between domain-specific pretraining and universal reasoning capabilities, advancing the adaptability and robustness of LLMs.

We present a case study in semi-autonomous mathematics discovery, using Gemini to systematically evaluate 700 conjectures labeled 'Open' in Bloom's Erdős Problems database. We employ a hybrid methodology: AI-driven natural language verification to narrow the search space, followed by human expert evaluation to gauge correctness and novelty. We address 13 problems that were marked 'Open' in the database: 5 through seemingly novel autonomous solutions, and 8 through identification of previous solutions in the existing literature. Our findings suggest that the 'Open' status of the problems was through obscurity rather than difficulty. We also identify and discuss issues arising in applying AI to math conjectures at scale, highlighting the difficulty of literature identification and the risk of ''subconscious plagiarism'' by AI. We reflect on the takeaways from AI-assisted efforts on the Erdős Problems.

In their recent Nature Human Behaviour paper, "Emergent analogical reasoning in large language models," (Webb, Holyoak, and Lu, 2023) the authors argue that "large language models such as GPT-3 have acquired an emergent ability to find zero-shot solutions to a broad range of analogy problems." In this response, we provide counterexamples of the letter string analogies. In our tests, GPT-3 fails to solve even the easiest variants of the problems presented in the original paper. Zero-shot reasoning is an extraordinary claim that requires extraordinary evidence. We do not see that evidence in our experiments. To strengthen claims of humanlike reasoning such as zero-shot reasoning, it is important that the field develop approaches that rule out data memorization.

We introduce a benchmark to evaluate the capability of AI to solve problems in theoretical physics, focusing on high-energy theory and cosmology. The first iteration of our benchmark consists of 57 problems of varying difficulty, from undergraduate to research level. These problems are novel in the sense that they do not come from public problem collections. We evaluate our data set on various open and closed language models, including o3-mini, o1, DeepSeek-R1, GPT-4o and versions of Llama and Qwen. While we find impressive progress in model performance with the most recent models, our research-level difficulty problems are mostly unsolved. We address challenges of auto-verifiability and grading, and discuss common failure modes. While currently state-of-the art models are still of limited use for researchers, our results show that AI assisted theoretical physics research may become possible in the near future. We discuss the main obstacles towards this goal and possible strategies to overcome them. The public problems and solutions, results for various models, and updates to the data set and score distribution, are available on the website of the dataset tpbench.org.

A multi-decade exploration into the theoretical foundations of artificial and natural general intelligence, which has been expressed in a series of books and papers and used to guide a series of practical and research-prototype software systems, is reviewed at a moderate level of detail. The review covers underlying philosophies (patternist philosophy of mind, foundational phenomenological and logical ontology), formalizations of the concept of intelligence, and a proposed high level architecture for AGI systems partly driven by these formalizations and philosophies. The implementation of specific cognitive processes such as logical reasoning, program learning, clustering and attention allocation in the context and language of this high level architecture is considered, as is the importance of a common (e.g. typed metagraph based) knowledge representation for enabling "cognitive synergy" between the various processes. The specifics of human-like cognitive architecture are presented as manifestations of these general principles, and key aspects of machine consciousness and machine ethics are also treated in this context. Lessons for practical implementation of advanced AGI in frameworks such as OpenCog Hyperon are briefly considered.

Large language models (LLMs) are known to struggle with complicated reasoning tasks such as math word problems (MWPs). In this paper, we present how analogy from similarly structured questions can improve LLMs' problem-solving capabilities for MWPs. Specifically, we rely on the retrieval of problems with similar computational graphs to the given question to serve as exemplars in the prompt, providing the correct reasoning path for the generation model to refer to. Empirical results across six math word problem datasets demonstrate the effectiveness of our proposed method, which achieves a significant improvement of up to 6.7 percent on average in absolute value, compared to baseline methods. These results highlight our method's potential in addressing the reasoning challenges in current LLMs.

We present Hermes 4, a family of hybrid reasoning models that combine structured, multi-turn reasoning with broad instruction-following ability. We describe the challenges encountered during data curation, synthesis, training, and evaluation, and outline the solutions employed to address these challenges at scale. We comprehensively evaluate across mathematical reasoning, coding, knowledge, comprehension, and alignment benchmarks, and we report both quantitative performance and qualitative behavioral analysis. To support open research, all model weights are published publicly at https://huggingface.co/collections/NousResearch/hermes-4-collection-68a731bfd452e20816725728

Combinatorial problems are present in a wide range of industries. Constraint Programming (CP) is a well-suited problem-solving paradigm, but its core process, namely constraint modelling, is a bottleneck for wider adoption. Aiming to alleviate this bottleneck, recent studies have explored using Large Language Models (LLMs) as modelling assistants, transforming combinatorial problem descriptions to executable constraint models, similar to coding assistants. However, the existing evaluation datasets for constraint modelling are often limited to small, homogeneous, or domain-specific instances, which do not capture the diversity of real-world scenarios. This work addresses this gap by introducing CP-Bench, a novel benchmark dataset that includes a diverse set of well-known combinatorial problem classes sourced from the CP community, structured explicitly for evaluating LLM-driven CP modelling. With this dataset, and given the variety of constraint modelling frameworks, we compare and evaluate the modelling capabilities of LLMs for three distinct constraint modelling systems, which vary in abstraction level and underlying syntax: the high-level MiniZinc language and Python-based CPMpy library, and the lower-level Python interface of the OR-Tools CP-SAT solver. In order to enhance the ability of LLMs to produce valid constraint models, we systematically evaluate the use of prompt-based and inference-time compute methods adapted from existing LLM-based code generation research. Our results underscore the modelling convenience provided by Python-based frameworks, as well as the effectiveness of documentation-rich system prompts, which, augmented with repeated sampling and self-verification, achieve further improvements, reaching up to 70\% accuracy on this new, highly challenging benchmark.

Large Reasoning Models (LRMs) have demonstrated remarkable problem-solving abilities in mathematics, as evaluated by existing benchmarks exclusively on well-defined problems. However, such evaluation setup constitutes a critical gap, since a genuine intelligent agent should not only solve problems (as a math quiz solver), but also be able~to ask for information when the problems lack sufficient information, enabling proactivity in responding users' requests. To bridge such gap, we proposes a new dataset consisting of two types of incomplete problems with diverse contexts. Based on the dataset, our systematical evaluation of LRMs reveals their inability in proactively asking for information. In addition, we uncover the behaviors related to overthinking and hallucination of LRMs, and highlight the potential and challenges of supervised fine-tuning in learning such ability. We hope to provide new insights in developing LRMs with genuine intelligence, rather than just solving problems.

The increasing adoption and commercialization of generalized Large Language Models (LLMs) have profoundly impacted various aspects of our daily lives. Initially embraced by the computer science community, the versatility of LLMs has found its way into diverse domains. In particular, the software engineering realm has witnessed the most transformative changes. With LLMs increasingly serving as AI Pair Programming Assistants spurred the development of specialized models aimed at aiding software engineers. Although this new paradigm offers numerous advantages, it also presents critical challenges and open problems. To identify the potential and prevailing obstacles, we systematically reviewed contemporary scholarly publications, emphasizing the perspectives of software developers and usability concerns. Preliminary findings underscore pressing concerns about data privacy, bias, and misinformation. Additionally, we identified several usability challenges, including prompt engineering, increased cognitive demands, and mistrust. Finally, we introduce 12 open problems that we have identified through our survey, covering these various domains.

This report overviews our ongoing work in enriching chain-of-thoughts datasets requiring arithmetical reasoning with the integration of non-parametric components, such as a calculator. We conduct an analysis of prominent relevant datasets such as GSM8K, Ape210K, AQuA-RAT, and MathQA and propose a machine-processable HTML-like format specifically tailored for working with semi-structured chains. By converting the datasets into this unified format, we enable the effective integration of large language models and symbolic systems, empowering them to tackle arithmetical reasoning tasks more efficiently.

Large Language Models (LLMs) have shown remarkable abilities in structured reasoning and symbolic tasks, with coding emerging as a particular area of strength. This success has sparked growing interest in applying LLMs to mathematics, both in informal problem-solving and formal theorem proving. However, progress in formal mathematics has proven to be significantly more difficult, despite surface-level similarities between programming and proof construction. This discrepancy raises important questions about how LLMs ``reason'', how they are supervised, and whether they internally track a notion of computational or deductive state. In this article, we address the state-of-the-art of the discipline, focusing on recent models and benchmarks, and explore three central issues at the intersection of machine learning and mathematical cognition: (i) the trade-offs between formal and informal mathematics as training domains; (ii) the deeper reasons why proof generation remains more brittle than code synthesis; (iii) and the question of whether LLMs represent, or merely mimic, a notion of evolving logical state. Our goal is not to draw hard boundaries, but to identify where the current limits lie, and how they might be extended.

Recent advances in large language models (LLMs) have opened new avenues for accelerating scientific research. While models are increasingly capable of assisting with routine tasks, their ability to contribute to novel, expert-level mathematical discovery is less understood. We present a collection of case studies demonstrating how researchers have successfully collaborated with advanced AI models, specifically Google's Gemini-based models (in particular Gemini Deep Think and its advanced variants), to solve open problems, refute conjectures, and generate new proofs across diverse areas in theoretical computer science, as well as other areas such as economics, optimization, and physics. Based on these experiences, we extract common techniques for effective human-AI collaboration in theoretical research, such as iterative refinement, problem decomposition, and cross-disciplinary knowledge transfer. While the majority of our results stem from this interactive, conversational methodology, we also highlight specific instances that push beyond standard chat interfaces. These include deploying the model as a rigorous adversarial reviewer to detect subtle flaws in existing proofs, and embedding it within a "neuro-symbolic" loop that autonomously writes and executes code to verify complex derivations. Together, these examples highlight the potential of AI not just as a tool for automation, but as a versatile, genuine partner in the creative process of scientific discovery.

Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis of inferring, learning, and exploiting laws, axioms, and symbol manipulation rules. In this paper, we present a new challenge for the evaluation (and eventually the design) of neural architectures and similar system, developing a task suite of mathematics problems involving sequential questions and answers in a free-form textual input/output format. The structured nature of the mathematics domain, covering arithmetic, algebra, probability and calculus, enables the construction of training and test splits designed to clearly illuminate the capabilities and failure-modes of different architectures, as well as evaluate their ability to compose and relate knowledge and learned processes. Having described the data generation process and its potential future expansions, we conduct a comprehensive analysis of models from two broad classes of the most powerful sequence-to-sequence architectures and find notable differences in their ability to resolve mathematical problems and generalize their knowledge.

Recent advances in language models have demonstrated their capability to solve mathematical reasoning problems, achieving near-perfect accuracy on grade-school level math benchmarks like GSM8K. In this paper, we formally study how language models solve these problems. We design a series of controlled experiments to address several fundamental questions: (1) Can language models truly develop reasoning skills, or do they simply memorize templates? (2) What is the model's hidden (mental) reasoning process? (3) Do models solve math questions using skills similar to or different from humans? (4) Do models trained on GSM8K-like datasets develop reasoning skills beyond those necessary for solving GSM8K problems? (5) What mental process causes models to make reasoning mistakes? (6) How large or deep must a model be to effectively solve GSM8K-level math questions? Our study uncovers many hidden mechanisms by which language models solve mathematical questions, providing insights that extend beyond current understandings of LLMs.

This paper introduces a new metamodel-based knowledge representation that significantly improves autonomous learning and adaptation. While interest in hybrid machine learning / symbolic AI systems leveraging, for example, reasoning and knowledge graphs, is gaining popularity, we find there remains a need for both a clear definition of knowledge and a metamodel to guide the creation and manipulation of knowledge. Some of the benefits of the metamodel we introduce in this paper include a solution to the symbol grounding problem, cumulative learning, and federated learning. We have applied the metamodel to problems ranging from time series analysis, computer vision, and natural language understanding and have found that the metamodel enables a wide variety of learning mechanisms ranging from machine learning, to graph network analysis and learning by reasoning engines to interoperate in a highly synergistic way. Our metamodel-based projects have consistently exhibited unprecedented accuracy, performance, and ability to generalize. This paper is inspired by the state-of-the-art approaches to AGI, recent AGI-aspiring work, the granular computing community, as well as Alfred Korzybski's general semantics. One surprising consequence of the metamodel is that it not only enables a new level of autonomous learning and optimal functioning for machine intelligences, but may also shed light on a path to better understanding how to improve human cognition.

We have recently witnessed a number of impressive results on hard mathematical reasoning problems with language models. At the same time, the robustness of these models has also been called into question; recent works have shown that models can rely on shallow patterns in the problem description when generating a solution. Building on the idea of behavioral testing, we propose a novel framework, which pins down the causal effect of various factors in the input, e.g., the surface form of the problem text, the operands, and math operators on the output solution. By grounding the behavioral analysis in a causal graph describing an intuitive reasoning process, we study the behavior of language models in terms of robustness and sensitivity to direct interventions in the input space. We apply our framework on a test bed of math word problems. Our analysis shows that robustness does not appear to continuously improve as a function of size, but the GPT-3 Davinci models (175B) achieve a dramatic improvement in both robustness and sensitivity compared to all other GPT variants.

Large Language Models (LLMs) perform well in general QA but often struggle in domain-specific scenarios. Retrieval-Augmented Generation (RAG) introduces external knowledge but suffers from hallucinations and latency due to noisy retrievals. Continued pretraining internalizes domain knowledge but is costly and lacks cross-domain flexibility. We attribute this challenge to the long-tail distribution of domain knowledge, which leaves partial yet useful internal knowledge underutilized. We further argue that knowledge acquisition should be progressive, mirroring human learning: first understanding concepts, then applying them to complex reasoning. To address this, we propose Selct2Know (S2K), a cost-effective framework that internalizes domain knowledge through an internal-external knowledge self-selection strategy and selective supervised fine-tuning. We also introduce a structured reasoning data generation pipeline and integrate GRPO to enhance reasoning ability. Experiments on medical, legal, and financial QA benchmarks show that S2K consistently outperforms existing methods and matches domain-pretrained LLMs with significantly lower cost.

We propose a framework for classifying the capabilities and behavior of Artificial General Intelligence (AGI) models and their precursors. This framework introduces levels of AGI performance, generality, and autonomy, providing a common language to compare models, assess risks, and measure progress along the path to AGI. To develop our framework, we analyze existing definitions of AGI, and distill six principles that a useful ontology for AGI should satisfy. With these principles in mind, we propose "Levels of AGI" based on depth (performance) and breadth (generality) of capabilities, and reflect on how current systems fit into this ontology. We discuss the challenging requirements for future benchmarks that quantify the behavior and capabilities of AGI models against these levels. Finally, we discuss how these levels of AGI interact with deployment considerations such as autonomy and risk, and emphasize the importance of carefully selecting Human-AI Interaction paradigms for responsible and safe deployment of highly capable AI systems.

Large Language Models (LLMs) have shown superior capability to solve reasoning problems with programs. While being a promising direction, most of such frameworks are trained and evaluated in settings with a prior knowledge of task requirements. However, as LLMs become more capable, it is necessary to assess their reasoning abilities in more realistic scenarios where many real-world problems are open-ended with ambiguous scope, and often require multiple formalisms to solve. To investigate this, we introduce the task of reasoning in the wild, where an LLM is tasked to solve a reasoning problem of unknown type by identifying the subproblems and their corresponding formalisms, and writing a program to solve each subproblem, guided by a tactic. We create a large tactic-guided trajectory dataset containing detailed solutions to a diverse set of reasoning problems, ranging from well-defined single-form reasoning (e.g., math, logic), to ambiguous and hybrid ones (e.g., commonsense, combined math and logic). This allows us to test various aspects of LLMs reasoning at the fine-grained level such as the selection and execution of tactics, and the tendency to take undesired shortcuts. In experiments, we highlight that existing LLMs fail significantly on problems with ambiguous and mixed scope, revealing critical limitations and overfitting issues (e.g. accuracy on GSM8K drops by at least 50\%). We further show the potential of finetuning a local LLM on the tactic-guided trajectories in achieving better performance. Project repo is available at github.com/gblackout/Reason-in-the-Wild

We present KNOW--the Knowledge Navigator Ontology for the World--the first ontology designed to capture everyday knowledge to augment large language models (LLMs) in real-world generative AI use cases such as personal AI assistants. Our domain is human life, both its everyday concerns and its major milestones. We have limited the initial scope of the modeled concepts to only established human universals: spacetime (places, events) plus social (people, groups, organizations). The inclusion criteria for modeled concepts are pragmatic, beginning with universality and utility. We compare and contrast previous work such as Schema.org and Cyc--as well as attempts at a synthesis of knowledge graphs and language models--noting how LLMs already encode internally much of the commonsense tacit knowledge that took decades to capture in the Cyc project. We also make available code-generated software libraries for the 12 most popular programming languages, enabling the direct use of ontology concepts in software engineering. We emphasize simplicity and developer experience in promoting AI interoperability.

Large language models have achieved near-expert performance in structured reasoning domains like mathematics and programming, yet their ability to perform compositional multi-hop reasoning in specialized scientific fields remains limited. We propose a bottom-up learning paradigm in which models are grounded in axiomatic domain facts and compose them to solve complex, unseen tasks. To this end, we present a post-training pipeline, based on a combination of supervised fine-tuning and reinforcement learning (RL), in which knowledge graphs act as implicit reward models. By deriving novel reward signals from knowledge graph paths, we provide verifiable, scalable, and grounded supervision that encourages models to compose intermediate axioms rather than optimize only final answers during RL. We validate this approach in the medical domain, training a 14B model on short-hop reasoning paths (1-3 hops) and evaluating its zero-shot generalization to complex multi-hop queries (4-5 hops). Our experiments show that path-derived rewards act as a "compositional bridge", enabling our model to significantly outperform much larger models and frontier systems like GPT-5.2 and Gemini 3 Pro, on the most difficult reasoning tasks. Furthermore, we demonstrate the robustness of our approach to adversarial perturbations against option-shuffling stress tests. This work suggests that grounding the reasoning process in structured knowledge is a scalable and efficient path toward intelligent reasoning.

Large language models (LLMs) have demonstrated exceptional performance in reasoning tasks such as mathematics and coding, matching or surpassing human capabilities. However, these impressive reasoning abilities face significant challenges in specialized domains. Taking Go as an example, although AlphaGo has established the high performance ceiling of AI systems in Go, mainstream LLMs still struggle to reach even beginner-level proficiency, let alone perform natural language reasoning. This performance gap between general-purpose LLMs and domain experts is significantly limiting the application of LLMs on a wider range of domain-specific tasks. In this work, we aim to bridge the divide between LLMs' general reasoning capabilities and expert knowledge in domain-specific tasks. We perform mixed fine-tuning with structured Go expertise and general long Chain-of-Thought (CoT) reasoning data as a cold start, followed by reinforcement learning to integrate expert knowledge in Go with general reasoning capabilities. Through this methodology, we present LoGos, a powerful LLM that not only maintains outstanding general reasoning abilities, but also conducts Go gameplay in natural language, demonstrating effective strategic reasoning and accurate next-move prediction. LoGos achieves performance comparable to human professional players, substantially surpassing all existing LLMs. Through this work, we aim to contribute insights on applying general LLM reasoning capabilities to specialized domains. We will release the first large-scale Go dataset for LLM training, the first LLM Go evaluation benchmark, and the first general LLM that reaches human professional-level performance in Go at: https://github.com/Entarochuan/LoGos.

The synergy between symbolic knowledge, often represented by Knowledge Graphs (KGs), and the generative capabilities of neural networks is central to advancing neurosymbolic AI. A primary bottleneck in realizing this potential is the difficulty of automating KG construction, which faces challenges related to output reliability, consistency, and verifiability. These issues can manifest as structural inconsistencies within the generated graphs, such as the formation of disconnected isolated islands of data or the inaccurate conflation of abstract classes with specific instances. To address these challenges, we propose HyDRA, a Hybrid-Driven Reasoning Architecture designed for verifiable KG automation. Given a domain or an initial set of documents, HyDRA first constructs an ontology via a panel of collaborative neurosymbolic agents. These agents collaboratively agree on a set of competency questions (CQs) that define the scope and requirements the ontology must be able to answer. Given these CQs, we build an ontology graph that subsequently guides the automated extraction of triplets for KG generation from arbitrary documents. Inspired by design-by-contracts (DbC) principles, our method leverages verifiable contracts as the primary control mechanism to steer the generative process of Large Language Models (LLMs). To verify the output of our approach, we extend beyond standard benchmarks and propose an evaluation framework that assesses the functional correctness of the resulting KG by leveraging symbolic verifications as described by the neurosymbolic AI framework, SymbolicAI. This work contributes a hybrid-driven architecture for improving the reliability of automated KG construction and the exploration of evaluation methods for measuring the functional integrity of its output. The code is publicly available.

Mathematical reasoning, a core aspect of human cognition, is vital across many domains, from educational problem-solving to scientific advancements. As artificial general intelligence (AGI) progresses, integrating large language models (LLMs) with mathematical reasoning tasks is becoming increasingly significant. This survey provides the first comprehensive analysis of mathematical reasoning in the era of multimodal large language models (MLLMs). We review over 200 studies published since 2021, and examine the state-of-the-art developments in Math-LLMs, with a focus on multimodal settings. We categorize the field into three dimensions: benchmarks, methodologies, and challenges. In particular, we explore multimodal mathematical reasoning pipeline, as well as the role of (M)LLMs and the associated methodologies. Finally, we identify five major challenges hindering the realization of AGI in this domain, offering insights into the future direction for enhancing multimodal reasoning capabilities. This survey serves as a critical resource for the research community in advancing the capabilities of LLMs to tackle complex multimodal reasoning tasks.

This study focuses on improving the performance of lightweight Large Language Models (LLMs) in mathematical reasoning tasks. We introduce a novel method for measuring mathematical logic similarity and design an automatic screening mechanism to construct a set of reference problems that integrate both semantic and logical similarity. By employing carefully crafted positive and negative example prompts, we guide the model towards adopting sound reasoning logic. To the best of our knowledge, this is the first attempt to utilize retrieval-enhanced generation for mathematical problem-solving. Experimental results demonstrate that our method achieves a 15.8% improvement over the Chain of Thought approach on the SVAMP dataset and a 21.5 % improvement on the GSM8K dataset. Further application of this method to a large-scale model with 175 billion parameters yields performance comparable to the best results on both aforementioned datasets. Finally, we conduct an analysis of errors during the reasoning process, providing valuable insights and directions for future research on reasoning tasks using large language models.

Large language models now solve many benchmark math problems at near-expert levels, yet this progress has not fully translated into reliable performance in real-world applications. We study this gap through contextual mathematical reasoning, where the mathematical core must be formulated from descriptive scenarios. We introduce ContextMATH, a benchmark that repurposes AIME and MATH-500 problems into two contextual settings: Scenario Grounding (SG), which embeds abstract problems into realistic narratives without increasing reasoning complexity, and Complexity Scaling (CS), which transforms explicit conditions into sub-problems to capture how constraints often appear in practice. Evaluating 61 proprietary and open-source models, we observe sharp drops: on average, open-source models decline by 13 and 34 points on SG and CS, while proprietary models drop by 13 and 20. Error analysis shows that errors are dominated by incorrect problem formulation, with formulation accuracy declining as original problem difficulty increases. Correct formulation emerges as a prerequisite for success, and its sufficiency improves with model scale, indicating that larger models advance in both understanding and reasoning. Nevertheless, formulation and reasoning remain two complementary bottlenecks that limit contextual mathematical problem solving. Finally, we find that fine-tuning with scenario data improves performance, whereas formulation-only training is ineffective. However, performance gaps are only partially alleviated, highlighting contextual mathematical reasoning as a central unsolved challenge for LLMs.

Domain-specific intelligence demands specialized knowledge and sophisticated reasoning for problem-solving, posing significant challenges for large language models (LLMs) that struggle with knowledge hallucination and inadequate reasoning capabilities under constrained parameter budgets. Inspired by Bloom's Taxonomy in educational theory, we propose Retrieval-Augmented Reasoning Modeling (RARE), a novel paradigm that decouples knowledge storage from reasoning optimization. RARE externalizes domain knowledge to retrievable sources and internalizes domain-specific reasoning patterns during training. Specifically, by injecting retrieved knowledge into training prompts with masked losses, RARE transforms learning objectives from rote memorization to contextualized reasoning. It enables models to bypass parameter-intensive memorization and prioritize the development of higher-order cognitive processes. Extensive experiments demonstrate that lightweight RARE-trained models (e.g., Llama-3.1-8B) could achieve state-of-the-art performance, surpassing retrieval-augmented GPT-4 and DeepSeek-R1 up to approximately 20\% accuracy. RARE establishes a paradigm shift where maintainable external knowledge bases synergize with compact, reasoning-optimized models, collectively driving more scalable domain-specific intelligence.

Despite outstanding processes in many tasks, Large Language Models (LLMs) still lack accuracy when dealing with highly technical domains. Especially, telecommunications (telco) is a particularly challenging domain due the large amount of lexical, semantic and conceptual peculiarities. Yet, this domain holds many valuable use cases, directly linked to industrial needs. Hence, this paper studies how LLMs can be adapted to the telco domain. It reports our effort to (i) collect a massive corpus of domain-specific data (800M tokens, 80K instructions), (ii) perform adaptation using various methodologies, and (iii) benchmark them against larger generalist models in downstream tasks that require extensive knowledge of telecommunications. Our experiments on Llama-2-7b show that domain-adapted models can challenge the large generalist models. They also suggest that adaptation can be restricted to a unique instruction-tuning step, dicarding the need for any fine-tuning on raw texts beforehand.

Large language models (LLMs) have significantly advanced natural language understanding and demonstrated strong problem-solving abilities. Despite these successes, most LLMs still struggle with solving mathematical problems due to the intricate reasoning required. This paper investigates the mathematical problem-solving capabilities of LLMs using the newly developed "MathOdyssey" dataset. The dataset includes diverse mathematical problems at high school and university levels, created by experts from notable institutions to rigorously test LLMs in advanced problem-solving scenarios and cover a wider range of subject areas. By providing the MathOdyssey dataset as a resource to the AI community, we aim to contribute to the understanding and improvement of AI capabilities in complex mathematical problem-solving. We conduct benchmarking on open-source models, such as Llama-3 and DBRX-Instruct, and closed-source models from the GPT series and Gemini models. Our results indicate that while LLMs perform well on routine and moderately difficult tasks, they face significant challenges with Olympiad-level problems and complex university-level questions. Our analysis shows a narrowing performance gap between open-source and closed-source models, yet substantial challenges remain, particularly with the most demanding problems. This study highlights the ongoing need for research to enhance the mathematical reasoning of LLMs. The dataset, results, and code are publicly available.

The sequential process of conceptualization and instantiation is essential to generalizable commonsense reasoning as it allows the application of existing knowledge to unfamiliar scenarios. However, existing works tend to undervalue the step of instantiation and heavily rely on pre-built concept taxonomies and human annotations to collect both types of knowledge, resulting in a lack of instantiated knowledge to complete reasoning, high cost, and limited scalability. To tackle these challenges, we introduce CANDLE, a distillation framework that iteratively performs contextualized conceptualization and instantiation over commonsense knowledge bases by instructing large language models to generate both types of knowledge with critic filtering. By applying CANDLE to ATOMIC, we construct a comprehensive knowledge base comprising six million conceptualizations and instantiated commonsense knowledge triples. Both types of knowledge are firmly rooted in the original ATOMIC dataset, and intrinsic evaluations demonstrate their exceptional quality and diversity. Empirical results indicate that distilling CANDLE on student models provides benefits across four downstream tasks. Our code, data, and models are publicly available at https://github.com/HKUST-KnowComp/CANDLE.

Chain-of-Thought (CoT) prompting enhances the reasoning of large language models (LLMs) by decomposing problems into sequential steps, mimicking human logic and reducing errors. However, complex tasks with vast solution spaces and vague constraints often exceed the capacity of a single reasoning chain. Inspired by Minimal Free Resolution (MFR) in commutative algebra and algebraic geometry, we propose Syzygy of Thoughts (SoT)-a novel framework that extends CoT by introducing auxiliary, interrelated reasoning paths. SoT captures deeper logical dependencies, enabling more robust and structured problem-solving. MFR decomposes a module into a sequence of free modules with minimal rank, providing a structured analytical approach to complex systems. This method introduces the concepts of "Module", "Betti numbers","Freeness", "Mapping", "Exactness" and "Minimality", enabling the systematic decomposition of the original complex problem into logically complete minimal subproblems while preserving key problem features and reducing reasoning length. We tested SoT across diverse datasets (e.g., GSM8K, MATH) and models (e.g., GPT-4o-mini, Qwen2.5), achieving inference accuracy that matches or surpasses mainstream CoTs standards. Additionally, by aligning the sampling process with algebraic constraints, our approach enhances the scalability of inference time in LLMs, ensuring both transparent reasoning and high performance. Our code will be publicly available at https://github.com/dlMARiA/Syzygy-of-thoughts.

Human intelligence excels at combining basic skills to solve complex tasks. This capability is vital for Artificial Intelligence (AI) and should be embedded in comprehensive intelligent models, enabling them to harness expert models for complex task-solving towards Artificial General Intelligence (AGI). Large Language Models (LLMs) show promising learning and reasoning abilities, and can effectively use external models, tools or APIs to tackle complex problems. In this work, we introduce OpenAGI, an open-source AGI research platform designed for multi-step, real-world tasks. Specifically, OpenAGI uses a dual strategy, integrating standard benchmark tasks for benchmarking and evaluation, and open-ended tasks including more expandable models, tools or APIs for creative problem-solving. Tasks are presented as natural language queries to the LLM, which then selects and executes appropriate models. We also propose a Reinforcement Learning from Task Feedback (RLTF) mechanism that uses task results to improve the LLM's ability, which creates a self-improving AI feedback loop. While we acknowledge that AGI is a broad and multifaceted research challenge with no singularly defined solution path, the integration of LLMs with domain-specific expert models, inspired by mirroring the blend of general and specialized intelligence in humans, offers a promising approach towards AGI. We are open-sourcing the OpenAGI project's code, dataset, benchmarks, evaluation methods, and demo to foster community involvement in AGI advancement: https://github.com/agiresearch/OpenAGI.

Large Language Models (LLMs) have demonstrated promising capabilities in solving mathematical reasoning tasks, leveraging Chain-of-Thought (CoT) data as a vital component in guiding answer generation. Current paradigms typically generate CoT and answers directly for a given problem, diverging from human problem-solving strategies to some extent. Humans often solve problems by recalling analogous cases and leveraging their solutions to reason about the current task. Inspired by this cognitive process, we propose MetaLadder, a novel framework that explicitly prompts LLMs to recall and reflect on meta-problems, those structurally or semantically analogous problems, alongside their CoT solutions before addressing the target problem. Additionally, we introduce a problem-restating mechanism to enhance the model's comprehension of the target problem by regenerating the original question, which further improves reasoning accuracy. Therefore, the model can achieve reasoning transfer from analogical problems, mimicking human-like "learning from examples" and generalization abilities. Extensive experiments on mathematical benchmarks demonstrate that our MetaLadder significantly boosts LLMs' problem-solving accuracy, largely outperforming standard CoT-based methods (10.3\% accuracy gain) and other methods. Our code and data has been released at https://github.com/LHL3341/MetaLadder.

Recent advancements in building domain-specific large language models (LLMs) have shown remarkable success, especially in tasks requiring reasoning abilities like logical inference over complex relationships and multi-step problem solving. However, creating a powerful all-in-one LLM remains challenging due to the need for proprietary data and vast computational resources. As a resource-friendly alternative, we explore the potential of merging multiple expert models into a single LLM. Existing studies on model merging mainly focus on generalist LLMs instead of domain experts, or the LLMs under the same architecture and size. In this work, we propose an unconstrained model merging framework that accommodates both homogeneous and heterogeneous model architectures with a focus on reasoning tasks. A fine-grained layer-wise weight merging strategy is designed for homogeneous models merging, while heterogeneous model merging is built upon the probabilistic distribution knowledge derived from instruction-response fine-tuning data. Across 7 benchmarks and 9 reasoning-optimized LLMs, we reveal key findings that combinatorial reasoning emerges from merging which surpasses simple additive effects. We propose that unconstrained model merging could serve as a foundation for decentralized LLMs, marking a notable progression from the existing centralized LLM framework. This evolution could enhance wider participation and stimulate additional advancement in the field of artificial intelligence, effectively addressing the constraints posed by centralized models.

In this paper we introduce the olog, or ontology log, a category-theoretic model for knowledge representation (KR). Grounded in formal mathematics, ologs can be rigorously formulated and cross-compared in ways that other KR models (such as semantic networks) cannot. An olog is similar to a relational database schema; in fact an olog can serve as a data repository if desired. Unlike database schemas, which are generally difficult to create or modify, ologs are designed to be user-friendly enough that authoring or reconfiguring an olog is a matter of course rather than a difficult chore. It is hoped that learning to author ologs is much simpler than learning a database definition language, despite their similarity. We describe ologs carefully and illustrate with many examples. As an application we show that any primitive recursive function can be described by an olog. We also show that ologs can be aligned or connected together into a larger network using functors. The various methods of information flow and institutions can then be used to integrate local and global world-views. We finish by providing several different avenues for future research.

In most current research, large language models (LLMs) are able to perform reasoning tasks by generating chains of thought through the guidance of specific prompts. However, there still exists a significant discrepancy between their capability in solving complex reasoning problems and that of humans. At present, most approaches focus on chains of thought (COT) and tool use, without considering the adoption and application of human cognitive frameworks. It is well-known that when confronting complex reasoning challenges, humans typically employ various cognitive abilities, and necessitate interaction with all aspects of tools, knowledge, and the external environment information to accomplish intricate tasks. This paper introduces a novel intelligent framework, referred to as OlaGPT. OlaGPT carefully studied a cognitive architecture framework, and propose to simulate certain aspects of human cognition. The framework involves approximating different cognitive modules, including attention, memory, reasoning, learning, and corresponding scheduling and decision-making mechanisms. Inspired by the active learning mechanism of human beings, it proposes a learning unit to record previous mistakes and expert opinions, and dynamically refer to them to strengthen their ability to solve similar problems. The paper also outlines common effective reasoning frameworks for human problem-solving and designs Chain-of-Thought (COT) templates accordingly. A comprehensive decision-making mechanism is also proposed to maximize model accuracy. The efficacy of OlaGPT has been stringently evaluated on multiple reasoning datasets, and the experimental outcomes reveal that OlaGPT surpasses state-of-the-art benchmarks, demonstrating its superior performance. Our implementation of OlaGPT is available on GitHub: https://github.com/oladata-team/OlaGPT.

Large Language Models (LLMs) have achieved remarkable success in reasoning tasks with the development of prompting methods. However, existing prompting approaches cannot reuse insights of solving similar problems and suffer from accumulated errors in multi-step reasoning, since they prompt LLMs to reason from scratch. To address these issues, we propose \textit{Thought Propagation (TP)}, which explores the analogous problems and leverages their solutions to enhance the complex reasoning ability of LLMs. These analogous problems are related to the input one, with reusable solutions and problem-solving strategies. Thus, it is promising to propagate insights of solving previous analogous problems to inspire new problem-solving. To achieve this, TP first prompts LLMs to propose and solve a set of analogous problems that are related to the input one. Then, TP reuses the results of analogous problems to directly yield a new solution or derive a knowledge-intensive plan for execution to amend the initial solution obtained from scratch. TP is compatible with existing prompting approaches, allowing plug-and-play generalization and enhancement in a wide range of tasks without much labor in task-specific prompt engineering. Experiments across three challenging tasks demonstrate TP enjoys a substantial improvement over the baselines by an average of 12\% absolute increase in finding the optimal solutions in Shortest-path Reasoning, 13\% improvement of human preference in Creative Writing, and 15\% enhancement in the task completion rate of LLM-Agent Planning.

Math Word Problems (MWPs) play a vital role in assessing the capabilities of Large Language Models (LLMs), yet current research primarily focuses on questions with concise contexts. The impact of longer contexts on mathematical reasoning remains under-explored. This study pioneers the investigation of Context Length Generalizability (CoLeG), which refers to the ability of LLMs to solve MWPs with extended narratives. We introduce Extended Grade-School Math (E-GSM), a collection of MWPs featuring lengthy narratives, and propose two novel metrics to evaluate the efficacy and resilience of LLMs in tackling these problems. Our analysis of existing zero-shot prompting techniques with proprietary LLMs along with open-source LLMs reveals a general deficiency in CoLeG. To alleviate these issues, we propose tailored approaches for different categories of LLMs. For proprietary LLMs, we introduce a new instructional prompt designed to mitigate the impact of long contexts. For open-source LLMs, we develop a novel auxiliary task for fine-tuning to enhance CoLeG. Our comprehensive results demonstrate the effectiveness of our proposed methods, showing improved performance on E-GSM. Additionally, we conduct an in-depth analysis to differentiate the effects of semantic understanding and reasoning efficacy, showing that our methods improves the latter. We also establish the generalizability of our methods across several other MWP benchmarks. Our findings highlight the limitations of current LLMs and offer practical solutions correspondingly, paving the way for further exploration of model generalizability and training methodologies.

In this paper, we aim to establish a simple, effective, and theoretically grounded benchmark for rigorously probing abstract reasoning in Large Language Models (LLMs). To achieve this, we first develop a mathematic framework that defines abstract reasoning as the ability to: (i) extract essential patterns independent of surface representations, and (ii) apply consistent rules to these abstract patterns. Based on this framework, we introduce two novel complementary metrics: \(\scoreGamma\) measures basic reasoning accuracy, while \(\scoreDelta\) quantifies a model's reliance on specific symbols rather than underlying patterns - a key indicator of true abstraction versus mere memorization. To implement this measurement, we design a benchmark: systematic symbol remapping in rule-based tasks, which forces models to demonstrate genuine pattern recognition beyond superficial token matching. Extensive LLM evaluations using this benchmark (commercial API models, 7B-70B, multi-agent) reveal:1) critical limitations in non-decimal arithmetic and symbolic reasoning; 2) persistent abstraction gaps despite chain-of-thought prompting; and 3) \(\scoreDelta\)'s effectiveness in robustly measuring memory dependence by quantifying performance degradation under symbol remapping, particularly highlighting operand-specific memorization. These findings underscore that current LLMs, despite domain-specific strengths, still lack robust abstract reasoning, highlighting key areas for future improvement.

The discipline of physics stands as a cornerstone of human intellect, driving the evolution of technology and deepening our understanding of the fundamental principles of the cosmos. Contemporary literature includes some works centered on the task of solving physics problems - a crucial domain of natural language reasoning. In this paper, we evaluate the performance of frontier LLMs in solving physics problems, both mathematical and descriptive. We also employ a plethora of inference-time techniques and agentic frameworks to improve the performance of the models. This includes the verification of proposed solutions in a cumulative fashion by other, smaller LLM agents, and we perform a comparative analysis of the performance that the techniques entail. There are significant improvements when the multi-agent framework is applied to problems that the models initially perform poorly on. Furthermore, we introduce a new evaluation benchmark for physics problems, {rm P{small HYSICS}E{small VAL}}, consisting of 19,609 problems sourced from various physics textbooks and their corresponding correct solutions scraped from physics forums and educational websites. Our code and data are publicly available at https://github.com/areebuzair/PhysicsEval.

Can machines truly think, reason and act in domains like humans? This enduring question continues to shape the pursuit of Artificial General Intelligence (AGI). Despite the growing capabilities of models such as GPT-4.5, DeepSeek, Claude 3.5 Sonnet, Phi-4, and Grok 3, which exhibit multimodal fluency and partial reasoning, these systems remain fundamentally limited by their reliance on token-level prediction and lack of grounded agency. This paper offers a cross-disciplinary synthesis of AGI development, spanning artificial intelligence, cognitive neuroscience, psychology, generative models, and agent-based systems. We analyze the architectural and cognitive foundations of general intelligence, highlighting the role of modular reasoning, persistent memory, and multi-agent coordination. In particular, we emphasize the rise of Agentic RAG frameworks that combine retrieval, planning, and dynamic tool use to enable more adaptive behavior. We discuss generalization strategies, including information compression, test-time adaptation, and training-free methods, as critical pathways toward flexible, domain-agnostic intelligence. Vision-Language Models (VLMs) are reexamined not just as perception modules but as evolving interfaces for embodied understanding and collaborative task completion. We also argue that true intelligence arises not from scale alone but from the integration of memory and reasoning: an orchestration of modular, interactive, and self-improving components where compression enables adaptive behavior. Drawing on advances in neurosymbolic systems, reinforcement learning, and cognitive scaffolding, we explore how recent architectures begin to bridge the gap between statistical learning and goal-directed cognition. Finally, we identify key scientific, technical, and ethical challenges on the path to AGI.

Conceptual combination is a cognitive process that merges basic concepts, enabling the creation of complex expressions. During this process, the properties of combination (e.g., the whiteness of a peeled apple) can be inherited from basic concepts, newly emerge, or be canceled. However, previous studies have evaluated a limited set of properties and have not examined the generative process. To address this gap, we introduce the Conceptual Combination with Property Type dataset (CCPT), which consists of 12.3K annotated triplets of noun phrases, properties, and property types. Using CCPT, we establish three types of tasks to evaluate LLMs for conceptual combination thoroughly. Our key findings are threefold: (1) Our automatic metric grading property emergence and cancellation closely corresponds with human judgments. (2) LLMs, including OpenAI's o1, struggle to generate noun phrases which possess given emergent properties. (3) Our proposed method, inspired by cognitive psychology model that explains how relationships between concepts are formed, improves performances in all generative tasks. The dataset and experimental code are available at https://github.com/seokwon99/CCPT.git.

To augment language models with the ability to reason, researchers usually prompt or finetune them to produce chain of thought reasoning steps before producing the final answer. However, although people use natural language to reason effectively, it may be that LMs could reason more effectively with some intermediate computation that is not in natural language. In this work, we explore an alternative reasoning approach: instead of explicitly producing the chain of thought reasoning steps, we use the language model's internal hidden states to perform implicit reasoning. The implicit reasoning steps are distilled from a teacher model trained on explicit chain-of-thought reasoning, and instead of doing reasoning "horizontally" by producing intermediate words one-by-one, we distill it such that the reasoning happens "vertically" among the hidden states in different layers. We conduct experiments on a multi-digit multiplication task and a grade school math problem dataset and find that this approach enables solving tasks previously not solvable without explicit chain-of-thought, at a speed comparable to no chain-of-thought.

Happiness computing based on large-scale online web data and machine learning methods is an emerging research topic that underpins a range of issues, from personal growth to social stability. Many advanced Machine Learning (ML) models with explanations are used to compute the happiness online assessment while maintaining high accuracy of results. However, domain knowledge constraints, such as the primary and secondary relations of happiness factors, are absent from these models, which limits the association between computing results and the right reasons for why they occurred. This article attempts to provide new insights into the explanation consistency from an empirical study perspective. Then we study how to represent and introduce domain knowledge constraints to make ML models more trustworthy. We achieve this through: (1) proving that multiple prediction models with additive factor attributions will have the desirable property of primary and secondary relations consistency, and (2) showing that factor relations with quantity can be represented as an importance distribution for encoding domain knowledge. Factor explanation difference is penalized by the Kullback-Leibler divergence-based loss among computing models. Experimental results using two online web datasets show that domain knowledge of stable factor relations exists. Using this knowledge not only improves happiness computing accuracy but also reveals more significative happiness factors for assisting decisions well.

Large language models (LLMs) have significantly advanced the field of natural language processing, with GPT models at the forefront. While their remarkable performance spans a range of tasks, adapting LLMs for real-world business scenarios still poses challenges warranting further investigation. This paper presents an empirical analysis aimed at bridging the gap in adapting LLMs to practical use cases. To do that, we select the question answering (QA) task of insurance as a case study due to its challenge of reasoning. Based on the task we design a new model relied on LLMs which are empowered by additional knowledge extracted from insurance policy rulebooks and DBpedia. The additional knowledge helps LLMs to understand new concepts of insurance for domain adaptation. Preliminary results on two QA datasets show that knowledge enhancement significantly improves the reasoning ability of GPT-3.5 (55.80% and 57.83% in terms of accuracy). The analysis also indicates that existing public knowledge bases, e.g., DBPedia is beneficial for knowledge enhancement. Our findings reveal that the inherent complexity of business scenarios often necessitates the incorporation of domain-specific knowledge and external resources for effective problem-solving.

Large language models increasingly expose reasoning traces, yet their underlying cognitive structure and steps remain difficult to identify and analyze beyond surface-level statistics. We adopt Schoenfeld's Episode Theory as an inductive, intermediate-scale lens and introduce ThinkARM (Anatomy of Reasoning in Models), a scalable framework that explicitly abstracts reasoning traces into functional reasoning steps such as Analysis, Explore, Implement, Verify, etc. When applied to mathematical problem solving by diverse models, this abstraction reveals reproducible thinking dynamics and structural differences between reasoning and non-reasoning models, which are not apparent from token-level views. We further present two diagnostic case studies showing that exploration functions as a critical branching step associated with correctness, and that efficiency-oriented methods selectively suppress evaluative feedback steps rather than uniformly shortening responses. Together, our results demonstrate that episode-level representations make reasoning steps explicit, enabling systematic analysis of how reasoning is structured, stabilized, and altered in modern language models.

Deduction, induction, and abduction are fundamental reasoning paradigms, core for human logical thinking. Although improving Large Language Model (LLM) reasoning has attracted significant research efforts, the extent to which the fundamental paradigms induce generalization has yet to be systematically explored. In this study, we shed light on how the interplay between these core paradigms influences LLMs' reasoning behavior. To this end, we first collect a new dataset of reasoning trajectories from symbolic tasks, each targeting one of the three fundamental paradigms, to abstract from concrete world knowledge. Then, we investigate effective ways for inducing these skills into LLMs. We experiment with a battery of methods including simple fine-tuning, and more complex approaches to increase model depth, or transform a dense model to a mixture-of-experts. We comprehensively evaluate induced models on realistic out-of-domain tasks, that are entirely formulated in natural language and contain real-world knowledge. Our results reveal that our approach yields strong generalizability with substantial performance gains (up to 14.60) across realistic tasks.

Math word problems are critical K-8 educational tools, but writing them is time-consuming and requires domain expertise. We suggest that language models can support K-8 math education by automatically generating problems at scale. To be educational, generated problems must be 1) solvable, 2) accurate, and 3) appropriate. Existing datasets are unlabeled for these criteria, making them ill-suited for training problem generators. We introduce MATHWELL, a Llama-2 (70B) model iteratively finetuned to generate K-8 math word problems using data from expert annotation. Using MATHWELL, we generate the largest English word problem dataset to date, containing 20,490 problems. 3,484 are scored by domain experts who find MATHWELL has a 40% higher share of problems that have executable solutions and meet all criteria than alternatives, with 74% of its problems with executable solutions being solvable, accurate, and appropriate.

Foundation models have emerged as critical components in a variety of artificial intelligence applications, and showcase significant success in natural language processing and several other domains. Meanwhile, the field of graph machine learning is witnessing a paradigm transition from shallow methods to more sophisticated deep learning approaches. The capabilities of foundation models to generalize and adapt motivate graph machine learning researchers to discuss the potential of developing a new graph learning paradigm. This paradigm envisions models that are pre-trained on extensive graph data and can be adapted for various graph tasks. Despite this burgeoning interest, there is a noticeable lack of clear definitions and systematic analyses pertaining to this new domain. To this end, this article introduces the concept of Graph Foundation Models (GFMs), and offers an exhaustive explanation of their key characteristics and underlying technologies. We proceed to classify the existing work related to GFMs into three distinct categories, based on their dependence on graph neural networks and large language models. In addition to providing a thorough review of the current state of GFMs, this article also outlooks potential avenues for future research in this rapidly evolving domain.

Probing and enhancing large language models' reasoning capacity remains a crucial open question. Here we re-purpose the reverse dictionary task as a case study to probe LLMs' capacity for conceptual inference. We use in-context learning to guide the models to generate the term for an object concept implied in a linguistic description. Models robustly achieve high accuracy in this task, and their representation space encodes information about object categories and fine-grained features. Further experiments suggest that the conceptual inference ability as probed by the reverse-dictionary task predicts model's general reasoning performance across multiple benchmarks, despite similar syntactic generalization behaviors across models. Explorative analyses suggest that prompting LLMs with descriptionRightarrowword examples may induce generalization beyond surface-level differences in task construals and facilitate models on broader commonsense reasoning problems.

With recent dramatic increases in AI system capabilities, there has been growing interest in utilizing machine learning for reasoning-heavy, quantitative tasks, particularly mathematics. While there are many resources capturing mathematics at the high-school, undergraduate, and graduate level, there are far fewer resources available that align with the level of difficulty and open endedness encountered by professional mathematicians working on open problems. To address this, we introduce a new collection of datasets, the Algebraic Combinatorics Dataset Repository (ACD Repo), representing either foundational results or open problems in algebraic combinatorics, a subfield of mathematics that studies discrete structures arising from abstract algebra. Further differentiating our dataset collection is the fact that it aims at the conjecturing process. Each dataset includes an open-ended research-level question and a large collection of examples (up to 10M in some cases) from which conjectures should be generated. We describe all nine datasets, the different ways machine learning models can be applied to them (e.g., training with narrow models followed by interpretability analysis or program synthesis with LLMs), and discuss some of the challenges involved in designing datasets like these.

The pursuit of automated scientific discovery has fueled progress from symbolic logic to modern AI, forging new frontiers in reasoning and pattern recognition. Transformers function as potential systems, where every possible relationship remains latent potentiality until tasks impose constraints, akin to measurement. Yet, refining their sampling requires more than probabilistic selection: solutions must conform to specific structures or rules, ensuring consistency and the invocation of general principles. We present Graph-PReFLexOR (Graph-based Preference-based Recursive Language Modeling for Exploratory Optimization of Reasoning), a framework that combines graph reasoning with symbolic abstraction to dynamically expand domain knowledge. Inspired by reinforcement learning, Graph-PReFLexOR defines reasoning as a structured mapping, where tasks yield knowledge graphs, abstract patterns, and ultimately, final answers. Inspired by category theory, it encodes concepts as nodes and their relationships as edges, supporting hierarchical inference and adaptive learning through isomorphic representations. Demonstrations include hypothesis generation, materials design, and creative reasoning, such as discovering relationships between mythological concepts like 'thin places' with materials science. We propose a 'knowledge garden growth' strategy that integrates insights across domains, promoting interdisciplinary connections. Results with a 3-billion-parameter Graph-PReFLexOR model show superior reasoning depth and adaptability, underscoring the potential for transparent, multidisciplinary AI-driven discovery. It lays the groundwork for general autonomous reasoning solutions.

A prevailing narrative in LLM post-training holds that supervised finetuning (SFT) memorizes while reinforcement learning (RL) generalizes. We revisit this claim for reasoning SFT with long chain-of-thought (CoT) supervision and find that cross-domain generalization is not absent but conditional, jointly shaped by optimization dynamics, training data, and base-model capability. Some reported failures are under-optimization artifacts: cross-domain performance first degrades before recovering and improving with extended training (a dip-and-recovery pattern), so shorttraining checkpoints can underestimate generalization. Data quality and structure both matter: low-quality solutions broadly hurt generalization,while verified long-CoT traces yield consistent cross-domain gains. Model capability is essential: stronger models internalize transferable procedural patterns (e.g., backtracking) even from a toy arithmetic game, while weaker ones imitate surface verbosity. This generalization is asymmetric, however: reasoning improves while safety degrades, reframing the question from whether reasoning SFT generalizes to under what conditions and at what cost.

Math reasoning has become the poster child of progress in large language models (LLMs), with new models rapidly surpassing human-level performance on benchmarks like MATH and AIME. But as math leaderboards improve week by week, it is worth asking: do these gains reflect broader problem-solving ability or just narrow overfitting? To answer this question, we evaluate over 20 open-weight reasoning-tuned models across a broad suite of tasks, including math, scientific QA, agent planning, coding, and standard instruction-following. We surprisingly find that most models that succeed in math fail to transfer their gains to other domains. To rigorously study this phenomenon, we conduct controlled experiments on Qwen3-14B models using math-only data but different tuning methods. We find that reinforcement learning (RL)-tuned models generalize well across domains, while supervised fine-tuning (SFT)-tuned models often forget general capabilities. Latent-space representation and token-space distribution shift analyses reveal that SFT induces substantial representation and output drift, while RL preserves general-domain structure. Our results suggest a need to rethink standard post-training recipes, particularly the reliance on SFT-distilled data for advancing reasoning models.

Recent proprietary models (e.g., o3) have begun to demonstrate strong multimodal reasoning capabilities. Yet, most existing open-source research concentrates on training text-only reasoning models, with evaluations limited to mainly mathematical and general-domain tasks. Therefore, it remains unclear how to effectively extend reasoning capabilities beyond text input and general domains. This paper explores a fundamental research question: Is reasoning generalizable across modalities and domains? Our findings support an affirmative answer: General-domain text-based post-training can enable such strong generalizable reasoning. Leveraging this finding, we introduce X-Reasoner, a vision-language model post-trained solely on general-domain text for generalizable reasoning, using a two-stage approach: an initial supervised fine-tuning phase with distilled long chain-of-thoughts, followed by reinforcement learning with verifiable rewards. Experiments show that X-Reasoner successfully transfers reasoning capabilities to both multimodal and out-of-domain settings, outperforming existing state-of-the-art models trained with in-domain and multimodal data across various general and medical benchmarks (Figure 1). Additionally, we find that X-Reasoner's performance in specialized domains can be further enhanced through continued training on domain-specific text-only data. Building upon this, we introduce X-Reasoner-Med, a medical-specialized variant that achieves new state of the art on numerous text-only and multimodal medical benchmarks.

Natural language descriptions of optimization or satisfaction problems are challenging to translate into correct MiniZinc models, as this process demands both logical reasoning and constraint programming expertise. We introduce Gala, a framework that addresses this challenge with a global agentic approach: multiple specialized large language model (LLM) agents decompose the modeling task by global constraint type. Each agent is dedicated to detecting and generating code for a specific class of global constraint, while a final assembler agent integrates these constraint snippets into a complete MiniZinc model. By dividing the problem into smaller, well-defined sub-tasks, each LLM handles a simpler reasoning challenge, potentially reducing overall complexity. We conduct initial experiments with several LLMs and show better performance against baselines such as one-shot prompting and chain-of-thought prompting. Finally, we outline a comprehensive roadmap for future work, highlighting potential enhancements and directions for improvement.

Step-by-step reasoning approaches like chain of thought (CoT) have proved to be very effective in inducing reasoning capabilities in large language models. However, the success of the CoT approach is fundamentally tied to the model size, and billion parameter-scale models are often needed to get CoT to work. In this paper, we propose a knowledge distillation approach that leverages the step-by-step CoT reasoning capabilities of larger models and distills these abilities into smaller models. In this work, we propose an alternative reasoning scheme, Socratic CoT, that learns a decomposition of the original problem into a sequence of subproblems and uses it to guide the intermediate reasoning steps. We use Socratic CoT to train a combination of two small distilled models: a problem decomposer and a subproblem solver. In practice, given a new problem, the two distilled models work in sync to decompose and solve complex problems. On multiple reasoning datasets (GSM8K, StrategyQA, and SVAMP), our proposed distillation strategies boosts the performance of smaller models over 70% compared to the baselines. Finally, we investigate when Socratic CoT is an effective alternative to CoT, demonstrating cases where a much smaller model (GPT-2 large) can outperform a 10X larger model (GPT-3 6B). Our code is available here: https://github.com/kumar-shridhar/Distiiling-LM

The goal of creating Artificial General Intelligence (AGI) -- or in other words of creating Turing machines (modern computers) that can behave in a way that mimics human intelligence -- has occupied AI researchers ever since the idea of AI was first proposed. One common theme in these discussions is the thesis that the ability of a machine to conduct convincing dialogues with human beings can serve as at least a sufficient criterion of AGI. We argue that this very ability should be accepted also as a necessary condition of AGI, and we provide a description of the nature of human dialogue in particular and of human language in general against this background. We then argue that it is for mathematical reasons impossible to program a machine in such a way that it could master human dialogue behaviour in its full generality. This is (1) because there are no traditional explicitly designed mathematical models that could be used as a starting point for creating such programs; and (2) because even the sorts of automated models generated by using machine learning, which have been used successfully in areas such as machine translation, cannot be extended to cope with human dialogue. If this is so, then we can conclude that a Turing machine also cannot possess AGI, because it fails to fulfil a necessary condition thereof. At the same time, however, we acknowledge the potential of Turing machines to master dialogue behaviour in highly restricted contexts, where what is called ``narrow'' AI can still be of considerable utility.

Although demonstrating remarkable performance on reasoning tasks, Large Language Models (LLMs) still tend to fabricate unreliable responses when confronted with problems that are unsolvable or beyond their capability, severely undermining the reliability. Prior studies of LLM reliability have primarily focused on knowledge tasks to identify unanswerable questions, while mathematical reasoning tasks have remained unexplored due to the dearth of unsolvable math problems. To systematically investigate LLM reliability in mathematical reasoning tasks, we formulate the reliability evaluation for both solvable and unsolvable problems. We then develop a ReliableMath dataset which incorporates open-source solvable problems and high-quality unsolvable problems synthesized by our proposed construction workflow with human evaluations. Experiments are conducted on various LLMs with several key findings uncovered. LLMs fail to directly identify unsolvable problems and always generate fabricated responses. When instructing LLMs to indicate unsolvability using a reliable prompt, the reliability of larger-sized LLMs remains on solvable problems, but notably improves on unsolvable problems yet still falls short of solvable problems. However, small LLMs rarely show any progress despite employing reliable prompts. Therefore, we further propose an alignment strategy to enhance small LLMs' reliability, which can significantly improve LLM reliability performances on both in-domain and out-of-domain tasks.

In adapting LLMs to specific domains, achieving both domain expertise and reasoning ability remains an urgent challenge. This study proposes a general method for constructing high-quality synthetic instruction data for any domain, starting from domain-specific vocabulary. As a demonstration, we applied this method to the financial domain and constructed a large-scale instruction dataset totaling approximately 9.5 billion tokens with Chain-of-Thought reasoning traces. Evaluation results confirmed performance improvements over baseline models on financial benchmarks, demonstrating the effectiveness of our approach. We also report findings on the impact of reasoning trace length on performance and its limitations. Lastly, we open-source our models and datasets on https://huggingface.co/nri-ai .

Geometry problem solving (GPS) represents a critical frontier in artificial intelligence, with profound applications in education, computer-aided design, and computational graphics. Despite its significance, automating GPS remains challenging due to the dual demands of spatial understanding and rigorous logical reasoning. Recent advances in large models have enabled notable breakthroughs, particularly for SAT-level problems, yet the field remains fragmented across methodologies, benchmarks, and evaluation frameworks. This survey systematically synthesizes GPS advancements through three core dimensions: (1) benchmark construction, (2) textual and diagrammatic parsing, and (3) reasoning paradigms. We further propose a unified analytical paradigm, assess current limitations, and identify emerging opportunities to guide future research toward human-level geometric reasoning, including automated benchmark generation and interpretable neuro-symbolic integration.

Large Language Models (LLMs) have demonstrated exceptional capabilities in various natural language tasks, often achieving performances that surpass those of humans. Despite these advancements, the domain of mathematics presents a distinctive challenge, primarily due to its specialized structure and the precision it demands. In this study, we adopted a two-step approach for investigating the proficiency of LLMs in answering mathematical questions. First, we employ the most effective LLMs, as identified by their performance on math question-answer benchmarks, to generate answers to 78 questions from the Math Stack Exchange (MSE). Second, a case analysis is conducted on the LLM that showed the highest performance, focusing on the quality and accuracy of its answers through manual evaluation. We found that GPT-4 performs best (nDCG of 0.48 and P@10 of 0.37) amongst existing LLMs fine-tuned for answering mathematics questions and outperforms the current best approach on ArqMATH3 Task1, considering P@10. Our Case analysis indicates that while the GPT-4 can generate relevant responses in certain instances, it does not consistently answer all questions accurately. This paper explores the current limitations of LLMs in navigating complex mathematical problem-solving. Through case analysis, we shed light on the gaps in LLM capabilities within mathematics, thereby setting the stage for future research and advancements in AI-driven mathematical reasoning. We make our code and findings publicly available for research: https://github.com/gipplab/LLM-Investig-MathStackExchange

Large language models (LLMs) have shown strong performance on mathematical reasoning under well-posed conditions. However, real-world engineering problems require more than mathematical symbolic computation -- they need to deal with uncertainty, context, and open-ended scenarios. Existing benchmarks fail to capture these complexities. We introduce EngiBench, a hierarchical benchmark designed to evaluate LLMs on solving engineering problems. It spans three levels of increasing difficulty (foundational knowledge retrieval, multi-step contextual reasoning, and open-ended modeling) and covers diverse engineering subfields. To facilitate a deeper understanding of model performance, we systematically rewrite each problem into three controlled variants (perturbed, knowledge-enhanced, and math abstraction), enabling us to separately evaluate the model's robustness, domain-specific knowledge, and mathematical reasoning abilities. Experiment results reveal a clear performance gap across levels: models struggle more as tasks get harder, perform worse when problems are slightly changed, and fall far behind human experts on the high-level engineering tasks. These findings reveal that current LLMs still lack the high-level reasoning needed for real-world engineering, highlighting the need for future models with deeper and more reliable problem-solving capabilities. Our source code and data are available at https://github.com/EngiBench/EngiBench.

Ontologies and taxonomies of research fields are critical for managing and organising scientific knowledge, as they facilitate efficient classification, dissemination and retrieval of information. However, the creation and maintenance of such ontologies are expensive and time-consuming tasks, usually requiring the coordinated effort of multiple domain experts. Consequently, ontologies in this space often exhibit uneven coverage across different disciplines, limited inter-domain connectivity, and infrequent updating cycles. In this study, we investigate the capability of several large language models to identify semantic relationships among research topics within three academic domains: biomedicine, physics, and engineering. The models were evaluated under three distinct conditions: zero-shot prompting, chain-of-thought prompting, and fine-tuning on existing ontologies. Additionally, we assessed the cross-domain transferability of fine-tuned models by measuring their performance when trained in one domain and subsequently applied to a different one. To support this analysis, we introduce PEM-Rel-8K, a novel dataset consisting of over 8,000 relationships extracted from the most widely adopted taxonomies in the three disciplines considered in this study: MeSH, PhySH, and IEEE. Our experiments demonstrate that fine-tuning LLMs on PEM-Rel-8K yields excellent performance across all disciplines.

In this work, we use large language models (LLMs) to augment and accelerate research on the P versus NP problem, one of the most important open problems in theoretical computer science and mathematics. Specifically, we propose Socratic reasoning, a general framework that promotes in-depth thinking with LLMs for complex problem-solving. Socratic reasoning encourages LLMs to recursively discover, solve, and integrate problems while facilitating self-evaluation and refinement. Our pilot study on the P vs. NP problem shows that GPT-4 successfully produces a proof schema and engages in rigorous reasoning throughout 97 dialogue turns, concluding "P neq NP", which is in alignment with (Xu and Zhou, 2023). The investigation uncovers novel insights within the extensive solution space of LLMs, shedding light on LLM for Science.

Training Large Language Models (LLMs) for chain-of-thought reasoning presents a significant challenge: supervised fine-tuning on a single "golden" rationale hurts generalization as it penalizes equally valid alternatives, whereas reinforcement learning with verifiable rewards struggles with credit assignment and prohibitive computational cost. To tackle these limitations, we introduce InTRO (In-Token Rationality Optimization), a new framework that enables both token-level exploration and self-feedback for accurate and concise reasoning. Instead of directly optimizing an intractable objective over all valid reasoning paths, InTRO leverages correction factors-token-wise importance weights estimated by the information discrepancy between the generative policy and its answer-conditioned counterpart, for informative next token selection. This approach allows the model to perform token-level exploration and receive self-generated feedback within a single forward pass, ultimately encouraging accurate and concise rationales. Across six math-reasoning benchmarks, InTRO consistently outperforms other baselines, raising solution accuracy by up to 20% relative to the base model. Its chains of thought are also notably more concise, exhibiting reduced verbosity. Beyond this, InTRO enables cross-domain transfer, successfully adapting to out-of-domain reasoning tasks that extend beyond the realm of mathematics, demonstrating robust generalization.

We introduce Explanatory Learning (EL), a framework to let machines use existing knowledge buried in symbolic sequences -- e.g. explanations written in hieroglyphic -- by autonomously learning to interpret them. In EL, the burden of interpreting symbols is not left to humans or rigid human-coded compilers, as done in Program Synthesis. Rather, EL calls for a learned interpreter, built upon a limited collection of symbolic sequences paired with observations of several phenomena. This interpreter can be used to make predictions on a novel phenomenon given its explanation, and even to find that explanation using only a handful of observations, like human scientists do. We formulate the EL problem as a simple binary classification task, so that common end-to-end approaches aligned with the dominant empiricist view of machine learning could, in principle, solve it. To these models, we oppose Critical Rationalist Networks (CRNs), which instead embrace a rationalist view on the acquisition of knowledge. CRNs express several desired properties by construction, they are truly explainable, can adjust their processing at test-time for harder inferences, and can offer strong confidence guarantees on their predictions. As a final contribution, we introduce Odeen, a basic EL environment that simulates a small flatland-style universe full of phenomena to explain. Using Odeen as a testbed, we show how CRNs outperform empiricist end-to-end approaches of similar size and architecture (Transformers) in discovering explanations for novel phenomena.

Human cognition exhibits systematic compositionality, the algebraic ability to generate infinite novel combinations from finite learned components, which is the key to understanding and reasoning about complex logic. In this work, we investigate the compositionality of large language models (LLMs) in mathematical reasoning. Specifically, we construct a new dataset MathTrap by introducing carefully designed logical traps into the problem descriptions of MATH and GSM8K. Since problems with logical flaws are quite rare in the real world, these represent "unseen" cases to LLMs. Solving these requires the models to systematically compose (1) the mathematical knowledge involved in the original problems with (2) knowledge related to the introduced traps. Our experiments show that while LLMs possess both components of requisite knowledge, they do not spontaneously combine them to handle these novel cases. We explore several methods to mitigate this deficiency, such as natural language prompts, few-shot demonstrations, and fine-tuning. Additionally, we test the recently released OpenAI o1 model and find that human-like `slow thinking' helps improve the compositionality of LLMs. Overall, systematic compositionality remains an open challenge for large language models.

We present a novel approach to formalise and solve search-based problems using large language models, which significantly improves upon previous state-of-the-art results. We demonstrate the efficacy of this approach on the logic puzzles benchmark ZebraLogicBench. Instead of letting the LLM attempt to directly solve the puzzles, our method prompts the model to formalise the problem in a logic-focused domain-specific language (DSL) called Logic.py. This formalised representation is then solved using a constraint solver, leveraging the strengths of both the language model and the solver. Our approach achieves a remarkable 65% absolute improvement over the baseline performance of Llama 3.1 70B on ZebraLogicBench, setting a new state-of-the-art with an accuracy of over 90%. This significant advancement demonstrates the potential of combining language models with domain-specific languages and auxiliary tools on traditionally challenging tasks for LLMs.

Recent advances such as Chain-of-Thought prompting have significantly improved large language models (LLMs) in zero-shot medical reasoning. However, prompting-based methods often remain shallow and unstable, while fine-tuned medical LLMs suffer from poor generalization under distribution shifts and limited adaptability to unseen clinical scenarios. To address these limitations, we present TAGS, a test-time framework that combines a broadly capable generalist with a domain-specific specialist to offer complementary perspectives without any model fine-tuning or parameter updates. To support this generalist-specialist reasoning process, we introduce two auxiliary modules: a hierarchical retrieval mechanism that provides multi-scale exemplars by selecting examples based on both semantic and rationale-level similarity, and a reliability scorer that evaluates reasoning consistency to guide final answer aggregation. TAGS achieves strong performance across nine MedQA benchmarks, boosting GPT-4o accuracy by 13.8%, DeepSeek-R1 by 16.8%, and improving a vanilla 7B model from 14.1% to 23.9%. These results surpass several fine-tuned medical LLMs, without any parameter updates. The code will be available at https://github.com/JianghaoWu/TAGS.

In recent years, large language models have achieved breakthroughs on a wide range of benchmarks in natural language processing and continue to increase in performance. Recently, the advances of large language models have raised interest outside the natural language processing community and could have a large impact on daily life. In this paper, we pose the question: How will large language models and other foundation models shape the future product development process? We provide the reader with an overview of the subject by summarizing both recent advances in natural language processing and the use of information technology in the engineering design process. We argue that discourse should be regarded as the core of engineering design processes, and therefore should be represented in a digital artifact. On this basis, we describe how foundation models such as large language models could contribute to the design discourse by automating parts thereof that involve creativity and reasoning, and were previously reserved for humans. We describe how simulations, experiments, topology optimizations, and other process steps can be integrated into a machine-actionable, discourse-centric design process. Finally, we outline the future research that will be necessary for the implementation of the conceptualized framework.

Instance-specific algorithm configuration and algorithm portfolios have been shown to offer significant improvements over single algorithm approaches in a variety of application domains. In the SAT and CSP domains algorithm portfolios have consistently dominated the main competitions in these fields for the past five years. For a portfolio approach to be effective there are two crucial conditions that must be met. First, there needs to be a collection of complementary solvers with which to make a portfolio. Second, there must be a collection of problem features that can accurately identify structural differences between instances. This paper focuses on the latter issue: feature representation, because, unlike SAT, not every problem has well-studied features. We employ the well-known SATzilla feature set, but compute alternative sets on different SAT encodings of CSPs. We show that regardless of what encoding is used to convert the instances, adequate structural information is maintained to differentiate between problem instances, and that this can be exploited to make an effective portfolio-based CSP solver.

Recent advances in large language models (LLMs) have demonstrated remarkable capabilities in reasoning and tool utilization. However, the generalization of tool-augmented reinforcement learning (RL) across diverse domains remains underexplored. In this work, we investigate the cross-domain generalization of an LLM agent equipped with a code interpreter tool, which is exclusively trained on mathematical problem-solving tasks. Despite the restricted training domain, we evaluate the agent's performance across several distinct reasoning domains. The results reveal that RL-based tool usage learned from mathematical tasks can be effectively transferred to complex tasks in other domains, enabling great task performance and high token efficiency. To facilitate this cross-domain transfer, we propose a Tool Generalization Reinforcement Learning (TGRL) framework designed to promote domain-agnostic learning and skill migration, encompassing: (i) a standardized tool interface that abstracts domain-specific nuances through consistent formatting and explicit termination, fostering transferable invocation patterns; (ii) a dual-component reward system that decomposes rewards to incentivize generalizable behaviors like tool efficiency and reasoning abstraction, ensuring alignment and robustness across domain shifts; and (iii) an XML-based prompt template that separates thinking, tool calls, and responses to encourage modular, domain-invariant planning and coherent multi-turn interactions. Extensive experiments across diverse benchmarks validate our approach, achieving state-of-the-art performance and highlighting the cross-domain potential of Tool RL for LLM reasoning.

Recent studies of the applications of conversational AI tools, such as chatbots powered by large language models, to complex real-world knowledge work have shown limitations related to reasoning and multi-step problem solving. Specifically, while existing chatbots simulate shallow reasoning and understanding they are prone to errors as problem complexity increases. The failure of these systems to address complex knowledge work is due to the fact that they do not perform any actual cognition. In this position paper, we present Cognitive AI, a higher-level framework for implementing programmatically defined neuro-symbolic cognition above and outside of large language models. Specifically, we propose a dual-layer functional architecture for Cognitive AI that serves as a roadmap for AI systems that can perform complex multi-step knowledge work. We propose that Cognitive AI is a necessary precursor for the evolution of higher forms of AI, such as AGI, and specifically claim that AGI cannot be achieved by probabilistic approaches on their own. We conclude with a discussion of the implications for large language models, adoption cycles in AI, and commercial Cognitive AI development.

Large language models (LLMs) such as ChatGPT have shown remarkable capabilities in code generation. Despite their great success, their effectiveness within particular domains (e.g., web development) necessitates further evaluation. In this study, we conduct an empirical study of domain-specific code generation with LLMs. We demonstrate that LLMs exhibit sub-optimal performance in generating domain-specific code, due to their limited proficiency in utilizing domain-specific libraries. We further observe that incorporating API knowledge as prompts can empower LLMs to generate more professional code. Based on these findings, we further investigate how to efficiently incorporate API knowledge into the code generation process. We experiment with three strategies for incorporating domain knowledge, namely, external knowledge inquirer, chain-of-thought prompting, and chain-of-thought fine-tuning. We refer to these strategies as a new code generation approach called DomCoder. Experimental results show that all strategies of DomCoder lead to improvement in the effectiveness of domain-specific code generation under certain settings. The results also show that there is still ample room for further improvement, based on which we suggest possible future works.

Large Language Models (LLMs) demonstrate promising capabilities in solving simple scientific problems but often produce hallucinations for complex ones. While integrating LLMs with tools can increase reliability, this approach typically results in over-reliance on tools, diminishing the model's ability to solve simple problems through basic reasoning. In contrast, human experts first assess problem complexity using domain knowledge before choosing an appropriate solution approach. Inspired by this human problem-solving process, we propose a novel two-component fine-tuning method. In the first component World Knowledge Distillation (WKD), LLMs learn directly from solutions generated using tool's information to internalize domain knowledge. In the second component Tool Usage Adaptation (TUA), we partition problems into easy and hard categories based on the model's direct answering accuracy. While maintaining the same alignment target for easy problems as in WKD, we train the model to intelligently switch to tool usage for more challenging problems. We validate our method on six scientific benchmark datasets, spanning mathematics, climate science and epidemiology. On average, our models demonstrate a 28.18% improvement in answer accuracy and a 13.89% increase in tool usage precision across all datasets, surpassing state-of-the-art models including GPT-4o and Claude-3.5.

In this work, we introduce a novel evaluation paradigm for Large Language Models, one that challenges them to engage in meta-reasoning. This approach addresses critical shortcomings in existing math problem-solving benchmarks, traditionally used to evaluate the cognitive capabilities of agents. Our paradigm shifts the focus from result-oriented assessments, which often overlook the reasoning process, to a more holistic evaluation that effectively differentiates the cognitive capabilities among models. For example, in our benchmark, GPT-4 demonstrates a performance ten times more accurate than GPT3-5. The significance of this new paradigm lies in its ability to reveal potential cognitive deficiencies in LLMs that current benchmarks, such as GSM8K, fail to uncover due to their saturation and lack of effective differentiation among varying reasoning abilities. Our comprehensive analysis includes several state-of-the-art math models from both open-source and closed-source communities, uncovering fundamental deficiencies in their training and evaluation approaches. This paper not only advocates for a paradigm shift in the assessment of LLMs but also contributes to the ongoing discourse on the trajectory towards Artificial General Intelligence (AGI). By promoting the adoption of meta-reasoning evaluation methods similar to ours, we aim to facilitate a more accurate assessment of the true cognitive abilities of LLMs.

Large Language Models (LLMs) have demonstrated impressive reasoning abilities through test-time computation (TTC) techniques such as chain-of-thought prompting and tree-based reasoning. However, we argue that current reasoning LLMs (RLLMs) lack the ability to systematically explore the solution space. This paper formalizes what constitutes systematic problem solving and identifies common failure modes that reveal reasoning LLMs to be wanderers rather than systematic explorers. Through qualitative and quantitative analysis across multiple state-of-the-art LLMs, we uncover persistent issues: invalid reasoning steps, redundant explorations, hallucinated or unfaithful conclusions, and so on. Our findings suggest that current models' performance can appear to be competent on simple tasks yet degrade sharply as complexity increases. Based on the findings, we advocate for new metrics and tools that evaluate not just final outputs but the structure of the reasoning process itself.