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Numerical reasoning over natural language has been a long-standing goal for the research community. However, cutting-edge language models have proven difficult to reliably generalize to a broad range of numbers, although they have shown…

When mathematicians present proofs they usually adapt their explanations to their didactic goals and to the (assumed) knowledge of their addressees. Modern automated theorem provers, in contrast, present proofs usually at a fixed level of…

Current large language models can perform reasonably well on complex tasks that require step-by-step reasoning with few-shot learning. Are these models applying reasoning skills they have learnt during pre-training and reason outside of…

Many real world learning tasks involve complex or hard-to-specify objectives, and using an easier-to-specify proxy can lead to poor performance or misaligned behavior. One solution is to have humans provide a training signal by…

Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…

Enhancing the mathematical reasoning of large language models (LLMs) demands high-quality training data, yet conventional methods face critical challenges in scalability, cost, and data reliability. To address these limitations, we propose…

With the development of artificial intelligence (AI), large language models (LLM) are widely used in many fields. However, the reasoning ability of LLM is still very limited when it comes to mathematical reasoning. Mathematics plays an…

In this paper, we study the ability of large language models to learn specific mathematical rules such as distributivity or simplifying equations. We present an empirical analysis of their ability to generalize these rules, as well as to…

While large models pre-trained on high-quality data exhibit excellent performance on mathematical reasoning (e.g., GSM8k, MultiArith), it remains challenging to specialize smaller models for these tasks. Common approaches to address this…

A reliable technique for deductive program verification should be proven sound with respect to the semantics of the programming language. For each different language, the construction of a separate soundness proof is often a laborious…

Large Language Models (LLMs) exhibit impressive performance across various domains but still struggle with arithmetic reasoning tasks. Recent work shows the effectiveness of prompt design methods in enhancing reasoning capabilities.…

Being prompted to engage in reasoning has emerged as a core technique for using large language models (LLMs), deploying additional inference-time compute to improve task performance. However, as LLMs increase in both size and adoption,…

Mathematics is a highly specialized domain with its own unique set of challenges. Despite this, there has been relatively little research on natural language processing for mathematical texts, and there are few mathematical language…

Real number calculations on elementary functions are remarkably difficult to handle in mechanical proofs. In this paper, we show how these calculations can be performed within a theorem prover or proof assistant in a convenient and highly…

Large language models (LLMs) achieve impressive performance on complex mathematical benchmarks yet sometimes fail on basic math reasoning while generating unnecessarily verbose responses. In this paper, we present LLMThinkBench, a…

Mathematical reasoning remains a challenging area for large language models (LLMs), prompting the development of math-specific LLMs such as LLEMMA, DeepSeekMath, and Qwen2-Math, among others. These models typically follow a two-stage…

Chain-of-Thought reasoning has emerged as a powerful approach for solving complex mathematical and logical problems. However, it can often veer off track through incorrect or unsubstantiated inferences. Formal mathematical reasoning, which…

Recent studies have highlighted the limitations of large language models in mathematical reasoning, particularly their inability to capture the underlying logic. Inspired by meta-learning, we propose that models should acquire not only…

Mastery learning improves learning proficiency and efficiency. However, the overpractice of skills--students spending time on skills they have already mastered--remains a fundamental challenge for tutoring systems. Previous research has…

Accurate estimates of item difficulty are essential for valid assessment and effective adaptive learning. However, for newly created tasks, response data are typically unavailable. Pretesting and expert judgement can be costly and slow,…