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Despite the success of large language models (LLMs), the task of theorem proving still remains one of the hardest reasoning tasks that is far from being fully solved. Prior methods using language models have demonstrated promising results,…

Neural theorem proving has advanced rapidly in the past year, reaching IMO gold-medalist capabilities and producing formal proofs that span thousands of lines. Although such proofs are mechanically verified by formal systems like Lean,…

We show that interactive protocols between a prover and a verifier, a well-known tool of complexity theory, can be used in practice to certify the correctness of automated reasoning tools. Theoretically, interactive protocols exist for all…

We describe an inductive logic programming (ILP) approach called learning from failures. In this approach, an ILP system (the learner) decomposes the learning problem into three separate stages: generate, test, and constrain. In the…

Prompt learning methods have significantly extended the transferability of pre-trained Vision-Language Models (VLMs) like CLIP for various downstream tasks. These methods adopt handcraft templates or learnable vectors to provide text or…

Probing classifiers have emerged as one of the prominent methodologies for interpreting and analyzing deep neural network models of natural language processing. The basic idea is simple -- a classifier is trained to predict some linguistic…

Theorem proving is a fundamental aspect of mathematics, spanning from informal reasoning in natural language to rigorous derivations in formal systems. In recent years, the advancement of deep learning, especially the emergence of large…

The availability of pre-trained models (PTMs) has enabled faster deployment of machine learning across applications by reducing the need for extensive training. Techniques like quantization and distillation have further expanded PTM…

Neural theorem proving combines large language models (LLMs) with proof assistants such as Lean, where the correctness of formal proofs can be rigorously verified, leaving no room for hallucination. With existing neural theorem provers…

We develop combinatorial test generation algorithms for progressively more powerful theorem provers, covering formula languages ranging from the implicational fragment of intuitionistic logic to full intuitionistic propositional logic. Our…

As recommender systems become increasingly sophisticated and complex, they often suffer from lack of fairness and transparency. Providing robust and unbiased explanations for recommendations has been drawing more and more attention as it…

Large Language Models (LLMs) have demonstrated significant potential in generating mathematical proofs. However, a persistent challenge is that LLMs occasionally make mistakes, while even a minor mistake can invalidate an entire proof.…

Motivated by the transfer of proofs between proof systems, and in particular from first order automated theorem provers (ATPs) to interactive theorem provers (ITPs), we specify an extension of the TPTP derivation text format to describe…

Although interactive learning puts the user into the loop, the learner remains mostly a black box for the user. Understanding the reasons behind queries and predictions is important when assessing how the learner works and, in turn, trust.…

We propose an online training procedure for a transformer-based automated theorem prover. Our approach leverages a new search algorithm, HyperTree Proof Search (HTPS), inspired by the recent success of AlphaZero. Our model learns from…

Neural networks have shown substantial promise at automatic theorem-proving in interactive proof assistants (ITPs) like Lean and Coq. However, most neural theorem-proving models are restricted to specific ITPs, leaving out opportunities for…

Autonomous systems use extensively learning-enabled components such as deep neural networks (DNNs) for prediction and decision making. In this paper, we utilize a feedback loop between learning-enabled components used for classification and…

Many techniques for the automated verification of distributed protocols have been developed over the past several years, but their performance is still unpredictable and their failure modes can be opaque for industrial scale verification…

As language models have become increasingly successful at a wide array of tasks, different prompt engineering methods have been developed alongside them in order to adapt these models to new tasks. One of them is Tree-of-Thoughts (ToT), a…

Development of Interactive Theorem Provers has led to the creation of big libraries and varied infrastructures for formal proofs. However, despite (or perhaps due to) their sophistication, the re-use of libraries by non-experts or across…