Dongchen Li

Xiaotie Deng, Dongchen Li, Hanyu Li

AI in Math deals with mathematics in a constructive manner so that reasoning becomes automated, less laborious, and less error-prone. For algorithms, the question becomes how to automate analyses for specific problems. For the first time, this work provides an automatic method for approximation analysis on a well-studied problem in theoretical computer science: computing approximate Nash equilibria in two-player games. We observe that such algorithms can be reformulated into a search-and-mix paradigm, which involves a search phase followed by a mixing phase. By doing so, we are able to fully automate the procedure of designing and analyzing the mixing phase. For example, we illustrate how to perform our method with a program to analyze the approximation bounds of all the algorithms in the literature. Same approximation bounds are computed without any hand-written proof. Our automatic method heavily relies on the LP-relaxation structure in approximate Nash equilibria. Since many approximation algorithms and online algorithms adopt the LP relaxation, our approach may be extended to automate the analysis of other algorithms.

Yang Zhao, Li Du, Xiao Ding et al.

Large language models (LLMs) have shown great potential across various industries due to their remarkable ability to generalize through instruction tuning. However, the limited availability of domain-specific data significantly hampers their performance on specialized tasks. While existing methods primarily focus on selecting training data from general datasets that are similar to the target domain, they often fail to consider the joint distribution of instructions, resulting in inefficient learning and suboptimal knowledge transfer. To address these challenges, we introduce G2IS (Gradient-based Graph Instruction Selection), a novel method that constructs a mixed gradient-based instruction graph to capture the joint distribution and interdependencies between instructions. By accounting for the relationships between instructions, G2IS improves domain adaptation efficiency. Additionally, we propose a gradient walk algorithm to refine the data selection process, enhancing both training effectiveness and efficiency. Our experiments demonstrate that G2IS outperforms traditional methods across various domain adaptation tasks, yielding significant performance gains, particularly in complex, data-scarce scenarios. These results underscore the potential of G2IS in advancing the development of large, domain-specific models.

Dongchen Li, Jitao Liang, Wei Li et al.

Large Language Models (LLMs) hold significant promise for improving clinical decision support and reducing physician burnout by synthesizing complex, longitudinal cancer Electronic Health Records (EHRs). However, their implementation in this critical field faces three primary challenges: the inability to effectively process the extensive length and multilingual nature of patient records for accurate temporal analysis; a heightened risk of clinical hallucination, as conventional grounding techniques such as Retrieval-Augmented Generation (RAG) do not adequately incorporate process-oriented clinical guidelines; and unreliable evaluation metrics that hinder the validation of AI systems in oncology. To address these issues, we propose CliCARE, a framework for Grounding Large Language Models in Clinical Guidelines for Decision Support over Longitudinal Cancer Electronic Health Records. The framework operates by transforming unstructured, longitudinal EHRs into patient-specific Temporal Knowledge Graphs (TKGs) to capture long-range dependencies, and then grounding the decision support process by aligning these real-world patient trajectories with a normative guideline knowledge graph. This approach provides oncologists with evidence-grounded decision support by generating a high-fidelity clinical summary and an actionable recommendation. We validated our framework using large-scale, longitudinal data from a private Chinese cancer dataset and the public English MIMIC-IV dataset. In these diverse settings, CliCARE significantly outperforms strong baselines, including leading long-context LLMs and Knowledge Graph-enhanced RAG methods. The clinical validity of our results is supported by a robust evaluation protocol, which demonstrates a high correlation with assessments made by expert oncologists.

Hanyu Li, Dongchen Li, Xiaotie Deng

Algorithm design and analysis is a cornerstone of computer science, but it confronts a major challenge. Proving an algorithm's performance guarantee across all inputs has traditionally required extensive and often error-prone human effort. While AI has shown great success in finding solutions to specific problem instances, automating the discovery of general algorithms with such provable guarantees has remained a significant barrier. This challenge stems from the difficulty of integrating the creative process of algorithm design with the rigorous process of formal analysis. To address this gap, we propose LegoNE, a framework that tightly fuses these two processes for the fundamental and notoriously difficult problem of computing approximate Nash equilibria. LegoNE automatically translates any algorithm written by a simple Python-like language into a constrained optimization problem. Solving this problem derives and proves the algorithm's approximation bound. Using LegoNE, a state-of-the-art large language model rediscovered the state-of-the-art algorithm for two-player games within hours, a feat that had taken human researchers 15 years to achieve. For three-player games, the model discovered a novel algorithm surpassing all existing human-designed ones. This work demonstrates a new human-machine collaborative paradigm for theoretical science: humans reason at a higher-abstract level, using symbols to compress the search space, and AI explores within it, achieving what neither could alone.