Related papers: Tinker, tailor, solver, proof
The likelihood of an automated reasoning program being of substantial assistance for a wide spectrum of applications rests with the nature of the options and parameters it offers on which to base needed strategies and methodologies. This…
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…
Many real-world and artificial systems and processes can be represented as graphs. Some examples of such systems include social networks, financial transactions, supply chains, and molecular structures. In many of these cases, one needs to…
In this paper, we analyze timed systems with data structures, using a rich interplay of logic and properties of graphs. We start by describing behaviors of timed systems using graphs with timing constraints. Such a graph is called…
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…
Despite the success of graph neural networks (GNNs) in various domains, they exhibit susceptibility to adversarial attacks. Understanding these vulnerabilities is crucial for developing robust and secure applications. In this paper, we…
In this paper, we proposed the \textit{link injection}, a novel method that helps any differentiable graph machine learning models to go beyond observed connections from the input data in an end-to-end learning fashion. It finds out (weak)…
This article introduces Globular, an online proof assistant for the formalization and verification of proofs in higher-dimensional category theory. The tool produces graphical visualizations of higher-dimensional proofs, assists in their…
Outliers are samples that are generated by different mechanisms from other normal data samples. Graphs, in particular social network graphs, may contain nodes and edges that are made by scammers, malicious programs or mistakenly by normal…
We present a simple iterative strategy for measuring the connection strength between a pair of vertices in a graph. The method is attractive in that it has a linear complexity and can be easily parallelized. Based on an analysis of the…
A biform theory is a combination of an axiomatic theory and an algorithmic theory that supports the integration of reasoning and computation. These are ideal for formalizing algorithms that manipulate mathematical expressions. A theory…
This tutorial review provides a guiding reference to researchers who want to have an overview of the large body of literature about graph spanners. It reviews the current literature covering various research streams about graph spanners,…
In this paper we state the basics for a signal processing framework on quiver representations. A quiver is a directed graph and a quiver representation is an assignment of vector spaces to the nodes of the graph and of linear maps between…
Pull-tabbing is an evaluation approach for functional logic computations, based on a graph transformation recently proposed, which avoids making irrevocable non-deterministic choices that would jeopardize the completeness of computations.…
Agentic theorem provers combine a reasoning model, retrieval, search, and a proof assistant verifier, yet it remains unclear which components actually improve finite-budget proof success and why they help on real mathematical workloads. We…
Differentiable inductive logic programming (ILP) techniques have proven effective at finding approximate rule-based solutions to link prediction and node classification problems on knowledge graphs; however, the common assumption of…
When a user connects to the Internet to fulfill his needs, he often encounters a huge amount of related information. Recommender systems are the techniques for massively filtering information and offering the items that users find them…
While subword tokenizers such as BPE and WordPiece are typically used to build vocabularies for NLP models, the method of decoding text into a sequence of tokens from these vocabularies is often left unspecified, or ill-suited to the method…
Explainability and effectiveness are two key aspects for building recommender systems. Prior efforts mostly focus on incorporating side information to achieve better recommendation performance. However, these methods have some weaknesses:…
We propose a synthesis of the two proof styles of interactive theorem proving: the procedural style (where proofs are scripts of commands, like in Coq) and the declarative style (where proofs are texts in a controlled natural language, like…