Related papers: On classes of bounded tree rank, their interpretat…

The modular decomposition of a graph $G$ is a natural construction to capture key features of $G$ in terms of a labeled tree $(T,t)$ whose vertices are labeled as "series" ($1$), "parallel" ($0$) or "prime". However, full information of $G$…

Graphs serve as generic tools to encode the underlying relational structure of data. Often this graph is not given, and so the task of inferring it from nodal observations becomes important. Traditional approaches formulate a convex inverse…

In deep neural networks, better results can often be obtained by increasing the complexity of previously developed basic models. However, it is unclear whether there is a way to boost performance by decreasing the complexity of such models.…

Graph Neural Networks (GNN) exhibit superior performance in graph representation learning, but their inference cost can be high, due to an aggregation operation that can require a memory fetch for a very large number of nodes. This…

Graph Neural Networks (GNNs) have demonstrated remarkable performance in a wide range of tasks, such as node classification, link prediction, and graph classification, by exploiting the structural information in graph-structured data.…

Network (or graph) sparsification compresses a graph by removing inessential edges. By reducing the data volume, it accelerates or even facilitates many downstream analyses. Still, the accuracy of many sparsification methods, with…

Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the…

A \emph{sparsification} of a given graph $G$ is a sparser graph (typically a subgraph) which aims to approximate or preserve some property of $G$. Examples of sparsifications include but are not limited to spanning trees, Steiner trees,…

Graph neural networks (GNNs) are powerful tools on graph data. However, their predictions are mis-calibrated and lack interpretability, limiting their adoption in critical applications. To address this issue, we propose a new…

We introduces the umodules, a generalisation of the notion of graph module. The theory we develop captures among others undirected graphs, tournaments, digraphs, and $2-$structures. We show that, under some axioms, a unique decomposition…

Compact and I/O-efficient data representations play an important role in efficient algorithm design, as memory bandwidth and latency can present a significant performance bottleneck, slowing the computation by orders of magnitude. While…

Constrained counting is a fundamental problem in artificial intelligence. A promising new algebraic approach to constrained counting makes use of tensor networks, following a reduction from constrained counting to the problem of…

Learning on large graphs presents significant challenges, with traditional Message Passing Neural Networks suffering from computational and memory costs scaling linearly with the number of edges. We introduce the Intersecting Block Graph…

Treewidth is a parameter that emerged from the study of minor closed classes of graphs (i.e. classes closed under vertex and edge deletion, and edge contraction). It in some sense describes the global structure of a graph. Roughly, a graph…

The chain graph model admits both undirected and directed edges in one graph, where symmetric conditional dependencies are encoded via undirected edges and asymmetric causal relations are encoded via directed edges. Though frequently…

We introduce an architecture based on deep hierarchical decompositions to learn effective representations of large graphs. Our framework extends classic R-decompositions used in kernel methods, enabling nested part-of-part relations. Unlike…

Integrated Gradients (IG) is a common explainability technique to address the black-box problem of neural networks. Integrated gradients assumes continuous data. Graphs are discrete structures making IG ill-suited to graphs. In this work,…

Counterfactual examples have emerged as an effective approach to produce simple and understandable post-hoc explanations. In the context of graph classification, previous work has focused on generating counterfactual explanations by…

Despite the extreme popularity of deep learning in science and industry, its formal understanding is limited. This thesis puts forth notions of rank as key for developing a theory of deep learning, focusing on the fundamental aspects of…

Graphs are widely used as a popular representation of the network structure of connected data. Graph data can be found in a broad spectrum of application domains such as social systems, ecosystems, biological networks, knowledge graphs, and…