Related papers: Local Reasoning for Global Graph Properties
Most automated verifiers for separation logic target the symbolic-heap fragment, disallowing both the magic-wand operator and the application of classical Boolean operators to spatial formulas. This is not surprising, as support for the…
Spatiotemporal graph neural networks have shown to be effective in time series forecasting applications, achieving better performance than standard univariate predictors in several settings. These architectures take advantage of a graph…
The guessing number of a directed graph (digraph), equivalent to the entropy of that digraph, was introduced as a direct criterion on the solvability of a network coding instance. This paper makes two contributions on the guessing number.…
Graph Neural Networks (GNNs) achieve strong performance on node classification tasks but remain difficult to interpret, particularly with respect to which input features drive their predictions. Existing global GNN explainers operate at the…
Local complement is a graph operation formalized by Bouchet which replaces the neighborhood of a chosen vertex with its edge-complement. This operation induces an equivalence relation on graphs; determining the size of the resulting…
Graphs are fundamental objects that find widespread applications across computer science and beyond. Graph Theory has yielded deep insights about structural properties of various families of graphs, which are leveraged in the design and…
Graph retrieval-augmented generation (GraphRAG) has emerged as a powerful paradigm for enhancing large language models (LLMs) with external knowledge. It leverages graphs to model the hierarchical structure between specific concepts,…
The literature on word-representable graphs is quite rich, and a number of variations of the original definition have been proposed over the years. We are initiating a systematic study of such variations based on formal languages. In our…
A theory of graded manifolds can be viewed as a generalization of differential geometry of smooth manifolds. It allows one to work with functions which locally depend not only on ordinary real variables, but also on $\mathbb{Z}$-graded…
Graph filtering is the cornerstone operation in graph signal processing (GSP). Thus, understanding it is key in developing potent GSP methods. Graph filters are local and distributed linear operations, whose output depends only on the local…
This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives…
Despite incredible progress, many neural architectures fail to properly generalize beyond their training distribution. As such, learning to reason in a correct and generalizable way is one of the current fundamental challenges in machine…
Suppose we want to construct some structure on a bounded-degree graph, e.g., an almost maximum matching, and we want to decide about each edge depending only on its constant-radius neighborhood. We examine and compare the strengths of…
Graph neural networks are increasingly becoming the go-to approach in various fields such as computer vision, computational biology and chemistry, where data are naturally explained by graphs. However, unlike traditional convolutional…
We consider Hoare-style verification for the graph programming language GP 2. In previous work, graph properties were specified by so-called E-conditions which extend nested graph conditions. However, this type of assertions is not easy to…
Program logics typically reason about an over-approximation of program behaviour to prove the absence of bugs. Recently, program logics have been proposed that instead prove the presence of bugs by means of under-approximate reasoning,…
A graph is a fundamental data model to represent various entities and their complex relationships in society and nature, such as social networks, transportation networks, and financial networks. Recently, large language models (LLMs) have…
Mining large graphs for information is becoming an increasingly important workload due to the plethora of graph structured data becoming available. An aspect of graph algorithms that has hitherto not received much interest is the effect of…
Graphical models use graphs to represent conditional independence structure in the distribution of a random vector. In stochastic processes, graphs may represent so-called local independence or conditional Granger causality. Under some…
In this work, we introduce a novel approach based on algebraic topology to enhance graph convolution and attention modules by incorporating local topological properties of the data. To do so, we consider the framework of sheaf neural…