Related papers: Lemmas: Generation, Selection, Application
We explore the application of transformer-based language models to automated theorem proving. This work is motivated by the possibility that a major limitation of automated theorem provers compared to humans -- the generation of original…
Large Language Models (LLMs) are often used as automated judges to evaluate text, but their effectiveness can be hindered by various unintentional biases. We propose using linear classifying probes, trained by leveraging differences between…
In logical reasoning, it is often the case that only some of a collection of assumptions are needed to reach a conclusion. A strengthening lemma is an assertion that a given conclusion is independent in this sense of a particular…
Proving equivalence between functional programs is a fundamental problem in program verification, which often amounts to reasoning about algebraic data types (ADTs) and compositions of structural recursions. Modern theorem provers address…
We take two key steps in automating the open-ended discovery of new mathematical theories, a grand challenge in artificial intelligence. First, we introduce $\emph{FERMAT}$, a reinforcement learning (RL) environment that models concept…
Knowledge tagging for questions plays a crucial role in contemporary intelligent educational applications, including learning progress diagnosis, practice question recommendations, and course content organization. Traditionally, these…
Sentence Embedding stands as a fundamental task within the realm of Natural Language Processing, finding extensive application in search engines, expert systems, and question-and-answer platforms. With the continuous evolution of large…
We introduce and elaborate a novel formalism for the manipulation and analysis of proofs as objects in a global manner. In this first approach the formalism is restricted to first-order problems characterized by condensed detachment. It is…
Knowledge representation is a popular research field in IT. As mathematical knowledge is most formalized, its representation is important and interesting. Mathematical knowledge consists of various mathematical theories. In this paper we…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
The pursue of what are properties that can be identified to permit an automated reasoning program to generate and find new and interesting theorems is an interesting research goal (pun intended). The automatic discovery of new theorems is a…
We consider the problem of automated reasoning about dynamically manipulated data structures. The state-of-the-art methods are limited to the unfold-and-match (U+M) paradigm, where predicates are transformed via (un)folding operations…
The goal of the paper is to automatize the selection of mechanisms which are able to describe a set of measurements. In order to do so first we construct a set of possible mechanism fulfilling chemically reasonable requirements with a given…
Large language models (LLMs) increasingly help people solve problems, from debugging code to repairing machinery. This process requires generating plausible hypotheses from partial descriptions, then updating them as more information…
Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…
Batch prompting is a common technique in large language models (LLMs) used to process multiple inputs simultaneously, aiming to improve computational efficiency. However, as batch sizes increase, performance degradation often occurs due to…
The rapid advancement of large language models (LLMs) has enabled the generation of coherent essays, making AI-assisted writing increasingly common in educational and professional settings. Using large-scale empirical data, we examine and…
Hypothesis generation is a fundamental step in scientific discovery, yet it is increasingly challenged by information overload and disciplinary fragmentation. Recent advances in Large Language Models (LLMs) have sparked growing interest in…
Using multisets, we develop novel techniques for mechanizing the proofs of the synthesis conjectures for list-sorting algorithms, and we demonstrate them in the Theorema system. We use the classical principle of extracting the algorithm as…
Mathematicians and computer scientists are increasingly using proof assistants to formalize and check correctness of complex proofs. This is a non-trivial task in itself, however, with high demands on human expertise. Can we lower the bar…