Related papers: Learning to Prove from Synthetic Theorems

When we test a theory using data, it is common to focus on correctness: do the predictions of the theory match what we see in the data? But we also care about completeness: how much of the predictable variation in the data is captured by…

Interactive Theorem Provers (ITPs) are an indispensable tool in the arsenal of formal method experts as a platform for construction and (formal) verification of proofs. The complexity of the proofs in conjunction with the level of expertise…

Automated Theorem Proving (ATP) deals with the development of computer programs being able to show that some conjectures (queries) are a logical consequence of a set of axioms (facts and rules). There exists several successful ATPs where…

This paper attempts to address the issues of machine learning in its current implementation. It is known that machine learning algorithms require a significant amount of data for training purposes, whereas recent developments in deep…

One of the biggest challenges in machine learning is data collection. Training data is an important part since it determines how the model will behave. In object classification, capturing a large number of images per object and in different…

Synthetic-to-real data translation using generative adversarial learning has achieved significant success in improving synthetic data. Yet, limited studies focus on deep evaluation and comparison of adversarial training on general-purpose…

Synthetic data is a standard component in training large language models, yet systematic comparisons across design dimensions, including rephrasing strategy, generator model, and source data, remain absent. We conduct extensive controlled…

Modern language model-based AI systems are remarkably powerful, yet their capabilities remain fundamentally capped by their human creators in three key ways. First, although a model's weights can be updated via fine-tuning, acquiring new…

Traditional automated theorem provers have relied on manually tuned heuristics to guide how they perform proof search. Recently, however, there has been a surge of interest in the design of learning mechanisms that can be integrated into…

In this article we consider a version of the challenging problem of learning from datasets whose size is too limited to allow generalisation beyond the training set. To address the challenge we propose to use a transfer learning approach…

When working on intelligent tutor systems designed for mathematics education and its specificities, an interesting objective is to provide relevant help to the students by anticipating their next steps. This can only be done by knowing,…

This article describes an evaluation of Automated Theorem Proving (ATP) systems on problems taken from the QMLTP library of first-order modal logic problems. Principally, the problems are translated to both typed first-order and…

Semantically meaningful sentence embeddings are important for numerous tasks in natural language processing. To obtain such embeddings, recent studies explored the idea of utilizing synthetically generated data from pretrained language…

The combination of verifiable languages and LLMs has significantly influenced both the mathematical and computer science communities because it provides a rigorous foundation for theorem proving. Recent advancements in the field provide…

Training on model-generated synthetic data is a promising approach for finetuning LLMs, but it remains unclear when it helps or hurts. In this paper, we investigate this question for math reasoning via an empirical study, followed by…

The goal of inductive program synthesis is for a machine to automatically generate a program from user-supplied examples. A key underlying assumption is that humans can provide sufficient examples to teach a concept to a machine. To…

Formal methods apply algorithms based on mathematical principles to enhance the reliability of systems. It would only be natural to try to progress from verification, model checking or testing a system against its formal specification into…

Recent advances in large language model (LLM) training have highlighted the need for diverse, high-quality instruction data. Recently, many works are exploring synthetic data generation using LLMs. However, they primarily focus on prompt…

We present the Theorem Prover Museum, and initiative to conserve -- and make publicly available -- the sources and source-related artefacts of automated reasoning systems. Theorem provers have been at the forefront of Artificial…

Conjecturing and theorem proving are activities at the center of mathematical practice and are difficult to separate. In this paper, we propose a framework for completing incomplete conjectures and incomplete proofs. The framework can turn…