arXiv subjects

Yufan Cai

Publications and source records attributed to Yufan Cai.

7 recordsLinked to original sources

arXiv2026

X-RAY: Mapping LLM Reasoning Capability via Formalized and Calibrated Probes

Large language models (LLMs) achieve promising performance, yet their ability to reason remains poorly understood. Existing evaluations largely emphasize task-level accuracy, often conflating pattern matching with reasoning capability. We present X-RAY, an explainable reasoning analysis system that maps the LLM reasoning capability using calibrated, formally verified probes. We model reasoning capability as a function of extractable \textit{structure}, operationalized through formal properties such as constraint interaction, reasoning depth, and solution-space geometry. X-Ray generates probes via formal tools with controlled structural variations, enabling precise isolation of incremental structural information through formal calibration and verification. We evaluate state-of-the-art LLMs on problems ranging from junior-level to advanced in mathematics, physics, and chemistry. Our analysis reveals a systematic asymmetry in LLM reasoning: models are relatively robust to constraint refinement, where additional conditions shrink an existing solution space, but degrade sharply under solution-space restructuring, where modifications alter the underlying structural form of the solution manifold. Moreover, calibrated formal probes differentiate models that appear indistinguishable on standard benchmarks and reveal failure modes that are structurally interpretable rather than opaque. Beyond evaluation, our framework is contamination-free and supports the training and testing of reasoning models.

cs.AI↗

arXiv2026

Uncertainty Reasoning with Large Language Models for Explainable Disease Diagnosis

Clinical decision-making requires reasoning over incomplete, imprecise, and linguistically expressed patient narratives. While large language models (LLMs) excel at extracting latent information from natural language, they lack the verifiability and interpretability essential for trustworthy medical AI. We propose a neuro-symbolic reasoning framework that aligns LLMs with formal logic to enable explainable and formally verifiable medical diagnosis. Patient descriptions and clinical guidelines are embedded into a neural knowledge base, where LLMs extract structured medical entities, temporal relations, and fuzzy symptom patterns, which are decoded into a symbolic knowledge base expressed in fuzzy logic and declarative rules. We perform two-stage reasoning: (1) inductive symbolic generalization to capture diagnostic patterns from encoded narratives, and (2) inference verification via a logic programming engine to derive and validate diagnoses consistent with clinical standards. Each symptom is treated as a fuzzy predicate with probabilistic weights, and inference paths are auditable, adjustable, and compatible with physician feedback. Unlike purely statistical methods, our system supports iterative refinement: misalignment between LLM-generated diagnoses and ground truth can be traced, explained, and corrected through formal rules. By combining logic-based transparency, LLM adaptability, and probabilistic robustness, the framework enables human-aligned healthcare inference with strong generalization and verifiable, step-by-step reasoning chains. We validate our framework on public benchmarks, demonstrating effective reconciliation of symbolic reasoning and LLMs with real-world clinical narratives. Results show performance comparable to state-of-the-art LLMs, while additionally providing interpretable reasoning paths and formally verifiable diagnostic conclusions.

cs.AI↗

arXiv2026

Towards Trustworthy Legal AI through LLM Agents and Formal Reasoning

Legal decisions should be logical and based on statutory laws. While large language models(LLMs) are good at understanding legal text, they cannot provide verifiable justifications. We present L4L, a solver-centric framework that enforces formal alignment between LLM-based legal reasoning and statutory laws. The framework integrates role-differentiated LLM agents with SMT-backed verification, combining the flexibility of natural language with the rigor of symbolic reasoning. Our approach operates in four stages: (1) Statute Knowledge Building, where LLMs autoformalize legal provisions into logical constraints and validate them through case-level testing; (2) Dual Fact-and-Statute Extraction, in which the prosecutor-and defense-aligned agents independently map case narratives to argument tuples; (3) Solver-Centric Adjudication, where SMT solvers check the legal admissibility and consistency of the arguments against the formalized statute knowledge; (4) Judicial Rendering, in which a judge agent integrates solver-validated reasoning with statutory interpretation and similar precedents to produce a legally grounded verdict. Experiments on public legal benchmarks show that L4L consistently outperforms baselines, while providing auditable justifications that enable trustworthy legal AI.

cs.AI↗

arXiv2025

PAT-Agent: Autoformalization for Model Checking

Recent advances in large language models (LLMs) offer promising potential for automating formal methods. However, applying them to formal verification remains challenging due to the complexity of specification languages, the risk of hallucinated output, and the semantic gap between natural language and formal logic. We introduce PAT-Agent, an end-to-end framework for natural language autoformalization and formal model repair that combines the generative capabilities of LLMs with the rigor of formal verification to automate the construction of verifiable formal models. In PAT-Agent, a Planning LLM first extracts key modeling elements and generates a detailed plan using semantic prompts, which then guides a Code Generation LLM to synthesize syntactically correct and semantically faithful formal models. The resulting code is verified using the Process Analysis Toolkit (PAT) model checker against user-specified properties, and when discrepancies occur, a Repair Loop is triggered to iteratively correct the model using counterexamples. To improve flexibility, we built a web-based interface that enables users, particularly non-FM-experts, to describe, customize, and verify system behaviors through user-LLM interactions. Experimental results on 40 systems show that PAT-Agent consistently outperforms baselines, achieving high verification success with superior efficiency. The ablation studies confirm the importance of both planning and repair components, and the user study demonstrates that our interface is accessible and supports effective formal modeling, even for users with limited formal methods experience.

cs.SE↗

arXiv2024

The Fusion of Large Language Models and Formal Methods for Trustworthy AI Agents: A Roadmap

Large Language Models (LLMs) have emerged as a transformative AI paradigm, profoundly influencing daily life through their exceptional language understanding and contextual generation capabilities. Despite their remarkable performance, LLMs face a critical challenge: the propensity to produce unreliable outputs due to the inherent limitations of their learning-based nature. Formal methods (FMs), on the other hand, are a well-established computation paradigm that provides mathematically rigorous techniques for modeling, specifying, and verifying the correctness of systems. FMs have been extensively applied in mission-critical software engineering, embedded systems, and cybersecurity. However, the primary challenge impeding the deployment of FMs in real-world settings lies in their steep learning curves, the absence of user-friendly interfaces, and issues with efficiency and adaptability. This position paper outlines a roadmap for advancing the next generation of trustworthy AI systems by leveraging the mutual enhancement of LLMs and FMs. First, we illustrate how FMs, including reasoning and certification techniques, can help LLMs generate more reliable and formally certified outputs. Subsequently, we highlight how the advanced learning capabilities and adaptability of LLMs can significantly enhance the usability, efficiency, and scalability of existing FM tools. Finally, we show that unifying these two computation paradigms -- integrating the flexibility and intelligence of LLMs with the rigorous reasoning abilities of FMs -- has transformative potential for the development of trustworthy AI software systems. We acknowledge that this integration has the potential to enhance both the trustworthiness and efficiency of software engineering practices while fostering the development of intelligent FM tools capable of addressing complex yet real-world challenges.

cs.AI↗

arXiv2024

CoEdPilot: Recommending Code Edits with Learned Prior Edit Relevance, Project-wise Awareness, and Interactive Nature

Recent years have seen the development of LLM-based code generation. Compared to generating code in a software project, incremental code edits are empirically observed to be more frequent. The emerging code editing approaches usually formulate the problem as generating an edit based on known relevant prior edits and context. However, practical code edits can be more complicated. First, an editing session can include multiple (ir)relevant edits to the code under edit. Second, the inference of the subsequent edits is non-trivial as the scope of its ripple effect can be the whole project. In this work, we propose CoEdPilot, an LLM-driven solution to recommend code edits by discriminating the relevant edits, exploring their interactive natures, and estimating its ripple effect in the project. Specifically, CoEdPilot orchestrates multiple neural transformers to identify what and how to edit in the project regarding both edit location and edit content. When a user accomplishes an edit with an optional editing description, a Subsequent Edit Analysis first reports the most relevant files in the project with what types of edits (e.g., keep, insert, and replace) can happen for each line of their code. Next, an Edit-content Generator generates concrete edit options for the lines of code, regarding its relevant prior changes reported by an Edit-dependency Analyzer. Lastly, both the Subsequent Edit Analysis and the Edit-content Generator capture relevant prior edits as feedback to readjust their recommendations. We train our models by collecting over 180K commits from 471 open-source projects in 5 programming languages. Our extensive experiments show that CoEdPilot can well predict the edits (i.e., predicting edit location with an accuracy of 70.8%-85.3%, and the edit content with an exact match rate of 41.8% and BLEU4 score of 60.7)...

cs.SE↗

arXiv2024

Towards Large Language Model Aided Program Refinement

Program refinement involves correctness-preserving transformations from formal high-level specification statements into executable programs. Traditional verification tool support for program refinement is highly interactive and lacks automation. On the other hand, the emergence of large language models (LLMs) enables automatic code generations from informal natural language specifications. However, code generated by LLMs is often unreliable. Moreover, the opaque procedure from specification to code provided by LLM is an uncontrolled black box. We propose LLM4PR, a tool that combines formal program refinement techniques with informal LLM-based methods to (1) transform the specification to preconditions and postconditions, (2) automatically build prompts based on refinement calculus, (3) interact with LLM to generate code, and finally, (4) verify that the generated code satisfies the conditions of refinement calculus, thus guaranteeing the correctness of the code. We have implemented our tool using GPT4, Coq, and Coqhammer, and evaluated it on the HumanEval and EvalPlus datasets.

cs.SE↗