Related papers: Reasoning with !-Graphs
Recent work has shown that not only decision trees (DTs) may not be interpretable but also proposed a polynomial-time algorithm for computing one PI-explanation of a DT. This paper shows that for a wide range of classifiers, globally…
Bidirected graphs are a common generalisation of directed graphs where arcs can also be incoming to both their incident nodes, or outgoing from both their incident nodes. Such arcs allow a walk to change direction. Some algorithms can…
This is an expended and revised version of the preprint "Schematization of homotopy types". The purpose of this work is to introduce a notion of \emph{affine stacks}, which is a homotopy version of the notion of affine schemes, and to give…
Signed graphs are complex systems that represent trust relationships or preferences in various domains. Learning node representations in such graphs is crucial for many mining tasks. Although real-world signed relationships can be…
Recent large-scale reasoning models have achieved state-of-the-art performance on challenging mathematical benchmarks, yet the internal mechanisms underlying their success remain poorly understood. In this work, we introduce the notion of a…
Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks…
Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic called…
We present a light formalism for proofs that encodes their inferential structure, along with a system that transforms these representations into flow-chart diagrams. Such diagrams should improve the comprehensibility of proofs. We discuss…
E-graphs are a prominent data structure that has been increasing in popularity in recent years due to their expanding range of applications in various formal reasoning tasks. Often, they are used for equality saturation, a process of…
Graph neural networks (GNNs) are powerful graph-based deep-learning models that have gained significant attention and demonstrated remarkable performance in various domains, including natural language processing, drug discovery, and…
Graphs are mathematical tools that can be used to represent complex real-world systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently. However, it has…
Artificial intelligence (AI) has undergone a renaissance recently, making major progress in key domains such as vision, language, control, and decision-making. This has been due, in part, to cheap data and cheap compute resources, which…
This paper presents the first use of graph neural networks (GNNs) for higher-order proof search and demonstrates that GNNs can improve upon state-of-the-art results in this domain. Interactive, higher-order theorem provers allow for the…
Verifying the veracity of claims requires reasoning over a large knowledge base, often in the form of corpora of trustworthy sources. A common approach consists in retrieving short portions of relevant text from the reference documents and…
A paradigm that was successfully applied in the study of both pure and algorithmic problems in graph theory can be colloquially summarized as stating that "any graph is close to being the disjoint union of expanders". Our goal in this paper…
Knowledge graph reasoning is pivotal in various domains such as data mining, artificial intelligence, the Web, and social sciences. These knowledge graphs function as comprehensive repositories of human knowledge, facilitating the inference…
Long before the invention of Feynman diagrams, engineers were using similar diagrams to reason about electrical circuits and more general networks containing mechanical, hydraulic, thermodynamic and chemical components. We can formalize…
We study the problem of matching a string in a labeled graph. Previous research has shown that unless the Orthogonal Vectors Hypothesis (OVH) is false, one cannot solve this problem in strongly sub-quadratic time, nor index the graph in…
We propose a new approach to text semantic analysis and general corpus analysis using, as termed in this article, a "bi-gram graph" representation of a corpus. The different attributes derived from graph theory are measured and analyzed as…
Graphical models capture relations between entities in a wide range of applications including social networks, biology, and natural language processing, among others. Graph neural networks (GNN) are neural models that operate over graphs,…