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We present a framework for training trustworthy large language model (LLM) agents for optimization modeling via a verifiable synthetic data generation pipeline. Focusing on linear and mixed-integer linear programming, our approach begins…
Formal verification via theorem proving enables the expressive specification and rigorous proof of software correctness, but it is difficult to scale due to the significant manual effort and expertise required. While Large Language Models…
Large language models have made significant progress in mathematical reasoning, which serves as an important testbed for AI and could impact scientific research if further advanced. By scaling reasoning with reinforcement learning that…
Recently, using Large Language Models (LLMs) to generate optimization models from natural language descriptions has became increasingly popular. However, a major open question is how to validate that the generated models are correct and…
Recent advancements in Chain-of-Thoughts (CoT) and Program-of-Thoughts (PoT) methods have greatly enhanced language models' mathematical reasoning capabilities, facilitating their integration into instruction tuning datasets with LLMs.…
Writing accurate numerical software is hard because of many sources of unavoidable uncertainties, including finite numerical precision of implementations. We present a programming model where the user writes a program in a real-valued…
The rapid advancement of Large Language Models (LLMs) poses a significant challenge to existing mathematical reasoning benchmarks. However, these benchmarks tend to become easier over time as LLMs can learn from the published benchmarks.…
Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information…
Building mathematical optimization models is critical in operations research (OR), while it requires substantial human expertise. Recent advancements have utilized large language models (LLMs) to automate this modeling process. However,…
Automatic software system optimization can improve software speed, reduce operating costs, and save energy. Traditional approaches to optimization rely on manual tuning and compiler heuristics, limiting their ability to generalize across…
Large language models (LLMs) can generate executable code from natural language descriptions, but the resulting programs frequently contain bugs due to hallucinations. In the absence of formal specifications, existing approaches attempt to…
Large Language Models (LLMs) are now integral across various domains and have demonstrated impressive performance. Progress, however, rests on the premise that benchmark scores are both accurate and reproducible. We demonstrate that the…
Compositional visual reasoning methods, which translate a complex query into a structured composition of feasible visual tasks, have exhibited a strong potential in complicated multi-modal tasks. Empowered by recent advances in large…
Recent advances in Large Language Models (LLMs) have demonstrated remarkable general reasoning capabilities. However, systematically evaluating and enhancing these reasoning capabilities is challenging due to the lack of controllable and…
In the contexts of automated reasoning (AR) and formal verification (FV), important decision problems are effectively encoded into Satisfiability Modulo Theories (SMT). In the last decade efficient SMT solvers have been developed for…
IIn computational geometry, the construction of essential primitives like convex hulls, Voronoi diagrams and Delaunay triangulations require the evaluation of the signs of determinants, which are sums of products. The same signs are needed…
Floating-point computations are quickly finding their way in the design of safety- and mission-critical systems, despite the fact that designing floating-point algorithms is significantly more difficult than designing integer algorithms.…
We consider the problems of liveness verification and liveness synthesis for recursive programs. The liveness verification problem (LVP) is to decide whether a given omega-context-free language is contained in a given omega-regular…
Satisfiability-based verification techniques, leveraging modern Boolean satisfiability (SAT) and Satisfiability Modulo Theories (SMT) solvers, have demonstrated efficacy in addressing practical problem instances within program analysis.…
Large language models (LLMs) have exhibited their problem-solving abilities in mathematical reasoning. Solving realistic optimization (OPT) problems in application scenarios requires advanced and applied mathematics ability. However,…