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 large-scale 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 training-free framework that leverages formal language to detect ill-defined problems, where a variable-constraint 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.

The rapid advancement of large language models (LLMs) has transformed the landscape of agentic information seeking capabilities through the integration of tools such as search engines and web browsers. However, current mainstream approaches for enabling LLM web search proficiency face significant challenges: supervised fine-tuning struggles with data production in open-search domains, while RL converges quickly, limiting their data utilization efficiency. To address these issues, we propose EvolveSearch, a novel iterative self-evolution framework that combines SFT and RL to enhance agentic web search capabilities without any external human-annotated reasoning data. Extensive experiments on seven multi-hop question-answering (MHQA) benchmarks demonstrate that EvolveSearch consistently improves performance across iterations, ultimately achieving an average improvement of 4.7% over the current state-of-the-art across seven benchmarks, opening the door to self-evolution agentic capabilities in open web search domains.

Retrieval-augmented generation (RAG) enables large language models (LLMs) to address queries beyond their internal knowledge by integrating domain knowledge in specialized corpus, which necessitates the generation of benchmarks on specific corpus to evaluate RAG systems. However, existing automated generation methods exhibit Weak Applicability and Weak Scalability. Weak Applicability refers to the reliance on metadata from specific corpora for query generation, constraining applicability to other corpora. Weak Scalability is characterized by fixed query content after generation, unable to dynamically increase difficulty, limiting scalability of the query. To overcome these issues, we propose AutoEvolve, an applicable approach for dynamically evolving queries to construct scalable RAG benchmarks. Our approach is grounded in three key innovations: (i) a corpus-agnostic method for constructing the universal entity-document graph; (ii) a suite of evolution operations designed to dynamically update queries; and (iii) a difficulty-guided metric that directs query evolution process. Through experiments on three generated benchmarks, we demonstrate that AutoEvolve evolves queries that are significantly more challenging, paving the way for more applicable and scalable RAG evaluations.