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The representation of graphs is commonly based on the adjacency matrix concept. This formulation is the foundation of most algebraic and computational approaches to graph processing. The advent of deep learning language models offers a wide…

Gradual argumentation frameworks represent arguments and their relationships in a weighted graph. Their graphical structure and intuitive semantics makes them a potentially interesting tool for interpretable machine learning. It has been…

The analysis of the internal structure of trees is highly important for both forest experts, biological scientists, and the wood industry. Traditionally, CT-scanners are considered as the most efficient way to get an accurate inner…

Suppose $G$ is a tree. Graham's "Tree Reconstruction Conjecture" states that $G$ is uniquely determined by the integer sequence $|G|$, $|L(G)|$, $|L(L(G))|$, $|L(L(L(G)))|$, $\ldots$, where $L(H)$ denotes the line graph of the graph $H$.…

Graph Neural Networks (GNNs) have emerged as a flexible and powerful approach for learning over graphs. Despite this success, existing GNNs are constrained by their local message-passing architecture and are provably limited in their…

Retrieval-Augmented Generation (RAG) enhances Large Language Models (LLMs) by grounding responses in external knowledge during inference. However, conventiona RAG systems under-perform on structured tabular data, largely due to coarse…

Standard Retrieval-Augmented Generation (RAG) relies on chunk-based retrieval, whereas GraphRAG advances this approach by graph-based knowledge representation. However, existing graph-based RAG approaches are constrained by binary…

The connection between dependency trees and spanning trees is exploited by the NLP community to train and to decode graph-based dependency parsers. However, the NLP literature has missed an important difference between the two structures:…

Retrieval-augmented generation (RAG) has emerged as a paradigm for grounding large language models in external knowledge, yet most existing RAG systems assume centralized knowledge access and ample computation. These assumptions break down…

Hypergraph Convolutional Neural Networks (HGCNNs) have demonstrated their potential in modeling high-order relations preserved in graph-structured data. However, most existing convolution filters are localized and determined by the…

The rising computational and energy demands of deep learning, particularly in large-scale architectures such as foundation models and large language models (LLMs), pose significant challenges to sustainability. Traditional gradient-based…

We introduce a decomposition method for the distributed calculation of exact Euclidean Minimum Spanning Trees in high dimensions (where sub-quadratic algorithms are not effective), or more generalized geometric-minimum spanning trees of…

In many industries, as well as in academic research, information is primarily transmitted in the form of unstructured documents (this article, for example). Hierarchically-related data is rendered as tables, and extracting information from…

Reconstruction of evolutionary relationships between species is an important topic in the field of computational biology. Pairwise compatibility graphs (PCGs) are used to model such relationships. A graph is a PCG if its edges can be…

We propose Graph Tree Networks (GTNets), a deep graph learning architecture with a new general message passing scheme that originates from the tree representation of graphs. In the tree representation, messages propagate upward from the…

A variety of real-world systems can be modeled as bipartite networks. One of the most powerful and simple link prediction methods is Linear-Graph Autoencoder(LGAE) which has promising performance on challenging tasks such as link prediction…

Inferring predictive maps between multiple input and multiple output variables or tasks has innumerable applications in data science. Multi-task learning attempts to learn the maps to several output tasks simultaneously with information…

Graph Retrieval-Augmented Generation (GRAG or Graph RAG) architectures aim to enhance language understanding and generation by leveraging external knowledge. However, effectively capturing and integrating the rich semantic information…

A common assumption in multiple scientific applications is that the distribution of observed data can be modeled by a latent tree graphical model. An important example is phylogenetics, where the tree models the evolutionary lineages of a…

Large Language Models (LLMs) excel at code generation but struggle with complex problems. Retrieval-Augmented Generation (RAG) mitigates this issue by integrating external knowledge, yet retrieval models often miss relevant context, and…