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Formal proofs are challenging to write even for experienced experts. Recent progress in Neural Theorem Proving (NTP) shows promise in expediting this process. However, the formal corpora available on the Internet are limited compared to the…

Computer Algebra systems are widely spread because of some of their remarkable features such as their ease of use and performance. Nonetheless, this focus on performance sometimes leads to unwanted consequences: algorithms and computations…

Neural networks are increasingly deployed in scientific, safety critical, and mission critical pipelines, yet verification and analysis are often performed outside the programming environment that defines and runs the model. This creates a…

While Graph Neural Networks (GNNs) recently became powerful tools in graph learning tasks, considerable efforts have been spent on improving GNNs' structural encoding ability. A particular line of work proposed subgraph GNNs that use…

A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful…

Computers and algorithms play an ever-increasing role in obtaining new results in graph theory. In this survey, we present a broad range of techniques used in computer-assisted graph theory, including the exhaustive generation of all…

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…

We study mathematical discovery through the lens of neurosymbolic reasoning, where an AI agent powered by a large language model (LLM), coupled with symbolic computation tools, and human strategic direction, jointly produced a new result in…

Large language models (LLMs) increasingly excel at mathematical reasoning, but their unreliability limits their utility in mathematics research. A mitigation is using LLMs to generate formal proofs in languages like Lean. We perform the…

We introduce a resource adaptive agent mechanism which supports the user in interactive theorem proving. The mechanism uses a two layered architecture of agent societies to suggest appropriate commands together with possible command…

Large Language Models (LLMs) have garnered significant attention for several years now. Recently, their use as independently reasoning agents has been proposed. In this work, we test the potential of such agents for knowledge discovery in…

The automated generation of exercises may substantially reduce the time educators devote to manual exercise design. A major obstacle to the integration of such automation into teaching practice, however, lies in the ability to control the…

The development of artificial intelligence systems with advanced reasoning capabilities represents a persistent and long-standing research question. Traditionally, the primary strategy to address this challenge involved the adoption of…

Theorem proving in natural mathematical language - the mixture of symbolic and natural language used by humans - plays a central role in mathematical advances and education, and tests aspects of reasoning that are core to intelligence. Yet…

Machine learning, and representation learning in particular, has the potential to facilitate drug discovery by screening a large chemical space in silico. A successful approach for representing molecules is to treat them as a graph and…

Graph neural networks (GNNs) have various practical applications, such as drug discovery, recommendation engines, and chip design. However, GNNs lack transparency as they cannot provide understandable explanations for their predictions. To…

In proof assistants, the physical proximity between two formal mathematical concepts is a strong predictor of their mutual relevance. Furthermore, lemmas with close proximity regularly exhibit similar proof structures. We show that this…

We expect an increase in the frequency and severity of cyber-attacks that comes along with the need for efficient security countermeasures. The process of attributing a cyber-attack helps to construct efficient and targeted mitigating and…

This work explores the application of deep learning, a machine learning technique that uses deep neural networks (DNN) in its core, to an automated theorem proving (ATP) problem. To this end, we construct a statistical model which…

Reasoning on knowledge graphs is a challenging task because it utilizes observed information to predict the missing one. Particularly, answering complex queries based on first-order logic is one of the crucial tasks to verify learning to…