Related papers: Graph classes through the lens of logic
The reasoning process of Graph Neural Networks is complex and considered opaque, limiting trust in their predictions. To alleviate this issue, prior work has proposed concept-based explanations, extracted from clusters in the model's node…
We propose a graph-based extension of Boolean logic called Boolean Graph Logic (BGL). Construing formula trees as the cotrees of cographs, we may state semantic notions such as evaluation and entailment in purely graph-theoretic terms,…
Classical path search assumes complete graphs and scalar optimization metrics, yet real infrastructure networks are incomplete and require multi-dimensional evaluation. We introduce the concept of traversal: a generalization of paths that…
Graph embedding techniques are pivotal in real-world machine learning tasks that operate on graph-structured data, such as social recommendation and protein structure modeling. Embeddings are mostly performed on the node level for learning…
Knowledge graphs are used to represent relational information in terms of triples. To enable learning about domains, embedding models, such as tensor factorization models, can be used to make predictions of new triples. Often there is…
We prove that every class of graphs $\mathscr C$ that is monadically stable and has bounded twin-width can be transduced from some class with bounded sparse twin-width. This generalizes analogous results for classes of bounded linear…
Graphs are commonly used to characterise interactions between objects of interest. Because they are based on a straightforward formalism, they are used in many scientific fields from computer science to historical sciences. In this paper,…
We study the first-order (FO) model checking problem of dense graphs, namely those which have FO interpretations in (or are FO transductions of) some sparse graph classes. We give a structural characterization of the graph classes which are…
Graph Transformers (GTs) have demonstrated a strong capability in modeling graph structures by addressing the intrinsic limitations of graph neural networks (GNNs), such as over-smoothing and over-squashing. Recent studies have proposed…
Recently a variety of methods have been developed to encode graphs into low-dimensional vectors that can be easily exploited by machine learning algorithms. The majority of these methods start by embedding the graph nodes into a…
Recently, the deep learning community has given growing attention to neural architectures engineered to learn problems in relational domains. Convolutional Neural Networks employ parameter sharing over the image domain, tying the weights of…
A contraction sequence of a graph consists of iteratively merging two of its vertices until only one vertex remains. The recently introduced twin-width graph invariant is based on contraction sequences. More precisely, if one puts red edges…
Modern communication networks are inherently complex in nature. First of all, they have a large number of heterogeneous components. Secondly, their connectivity is extremely dynamic. Nodes can come and go, links can be removed and added…
We present the basic ideas of forms (a generalization of Ehresmann's sketches) and their theories and models, more explicitly than in previous expositions. Forms provide the ability to specify mathematical structures and data types in any…
The recent proliferation of publicly available graph-structured data has sparked an interest in machine learning algorithms for graph data. Since most traditional machine learning algorithms assume data to be tabular, embedding algorithms…
Many real-world datasets can be naturally represented as graphs, spanning a wide range of domains. However, the increasing complexity and size of graph datasets present significant challenges for analysis and computation. In response, graph…
Graph compression is a data analysis technique that consists in the replacement of parts of a graph by more general structural patterns in order to reduce its description length. It notably provides interesting exploration tools for the…
Graph decompositions are the natural generalisation of tree decompositions where the decomposition tree is replaced by a genuine graph. Recently they found theoretical applications in the theory of sparsity, topological graph theory,…
Graph aggregation is the process of computing a single output graph that constitutes a good compromise between several input graphs, each provided by a different source. One needs to perform graph aggregation in a wide variety of…
Graphs provide a natural representation of relational structure that arises across diverse domains. Despite this ubiquity, graph structure is typically learned in a modality- and task-isolated manner, where graph representations are…