Related papers: A Note on the Modeling Power of Different Graph Ty…
Implicit models, an emerging model class, compute outputs by iterating a single parameter block to a fixed point. This architecture realizes an infinite-depth, weight-tied network that trains with constant memory, significantly reducing…
A visibility representation is a classical drawing style of planar graphs. It displays the vertices of a graph as horizontal vertex-segments, and each edge is represented by a vertical edge-segment touching the segments of its end vertices;…
Expressivity and generalization are two critical aspects of graph neural networks (GNNs). While significant progress has been made in studying the expressivity of GNNs, much less is known about their generalization capabilities,…
In recent years, the Graph Model has become increasingly popular, especially in the application domain of social networks. The model has been semantically augmented with properties and labels attached to the graph elements. It is difficult…
This paper explores the properties of directed graphs, termed generalized action graphs, which exhibit a strong connection to certain number sequences. Focusing on the structural and combinatorial aspects, we investigate the conditions…
Graphs on integer points of polytopes whose edges come from a set of allowed differences are studied. It is shown that any simple graph can be embedded in that way. The minimal dimension of such a representation is the fiber dimension of…
In this thesis we present a semantic representation formalism based on directed graphs and explore its linguistic adequacy and explanatory benefits in the semantics of plurality and quantification. Our graph language covers the essentials…
Motivated by interpretability and reliability, we investigate whether large language models (LLMs) deploy universal geometric structures to encode discrete, graph-structured knowledge. To this end, we present two complementary experimental…
We characterise the structure of those graphs of a given order which maximise the number of connected induced subgraphs for seven different graph classes, each with other prescribed parameters like minimum degree, independence number,…
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…
We study the first order theory of structures over graphs i.e. structures of the form ($\mathcal{G},\tau$) where $\mathcal{G}$ is the set of all (isomorphism types of) finite undirected graphs and $\tau$ some vocabulary. We define the…
For a representation of a Lie algebra, one can construct a diagram of the representation, i. e. a directed graph with edges labeled by matrix elements of the representation. This article explains how to use these diagrams to describe normal…
We derive representation theorems for exchangeable distributions on finite and infinite graphs using elementary arguments based on geometric and graph-theoretic concepts. Our results elucidate some of the key differences, and their…
In this paper, we extend the recently introduced concept of partially dual ribbon graphs to graphs. We then go on to characterize partial duality of graphs in terms of bijections between edge sets of corresponding graphs. This result…
Property graph manages data by vertices and edges. Each vertex and edge can have a property map, storing ad hoc attribute and its value. Label can be attached to vertices and edges to group them. While this schema-less methodology is very…
Multiplex graphs, characterised by their layered structure, exhibit informative interdependencies within layers that are crucial for understanding complex network dynamics. Quantifying the interaction and shared information among these…
In this note, we introduce the notion of support graph to define explanations for any model of a logic program. An explanation is an acyclic support graph that, for each true atom in the model, induces a proof in terms of program rules…
Today we have a good theoretical understanding of the representational power of Graph Neural Networks (GNNs). For example, their limitations have been characterized in relation to a hierarchy of Weisfeiler-Lehman (WL) isomorphism tests.…
Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results…
Causality has traditionally been a scientific way to generate knowledge by relating causes to effects. From an imaginery point of view, causal graphs are a helpful tool for representing and infering new causal information. In previous…