Related papers: Interaction Graphs: Exponentials
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,…
Recently there has been significant interest in using causal modelling techniques to understand the structure of physical theories. However, the notion of `causation' is limiting - insisting that a physical theory must involve causal…
Recent findings in neuroscience suggest that the human brain represents information in a geometric structure (for instance, through conceptual spaces). In order to communicate, we flatten the complex representation of entities and their…
Graph Neural Networks (GNNs) have advanced significantly in handling graph-structured data, but a comprehensive framework for evaluating explainability remains lacking. Existing evaluation frameworks primarily involve post-hoc explanations,…
Extremal Graph Theory is a very deep and wide area of modern combinatorics. It is very fast developing, and in this long but relatively short survey we select some of those results which either we feel very important in this field or which…
Learning efficient graph representation is the key to favorably addressing downstream tasks on graphs, such as node or graph property prediction. Given the non-Euclidean structural property of graphs, preserving the original graph data's…
Many complex systems involve interactions between more than two agents. Hypergraphs capture these higher-order interactions through hyperedges that may link more than two nodes. We consider the problem of embedding a hypergraph into…
Graph Neural Networks (GNNs) have emerged as a prominent framework for graph mining, leading to significant advances across various domains. Stemmed from the node-wise representations of GNNs, existing explanation studies have embraced the…
Graph Neural Networks (GNNs) have paved the way for being a cornerstone in graph-related learning tasks. Yet, the ability of GNNs to capture structural interactions within graphs remains under-explored. In this work, we address this gap by…
A new modelling approach for the analysis of weighted networks with ordinal/polytomous dyadic values is introduced. Specifically, it is proposed to model the weighted network connectivity structure using a hierarchical multilayer…
In this paper we present an extension of Peirce's existential graphs to provide a diagrammatic representation of expressions in Quantified Equilibrium Logic (QEL). Using this formalisation, logical connectives are replaced by encircled…
Let $G$ be a simple graph of order $n$ with degree sequence $(d)=(d_1,d_2,\ldots,d_n)$ and conjugate degree sequence $(d^*)=(d_1^*,d_2^*,\ldots,d_n^*)$. In \cite{AkbariGhorbaniKoolenObudi2010,DasMojallalGutman2017} it was proven that…
In this paper we establish a bridge between Topological Data Analysis and Geometric Deep Learning, adapting the topological theory of group equivariant non-expansive operators (GENEOs) to act on the space of all graphs weighted on vertices…
Understanding the decision-making process of Graph Neural Networks (GNNs) is crucial to their interpretability. Most existing methods for explaining GNNs typically rely on training auxiliary models, resulting in the explanations remain…
Linearity and ramification constraints have been widely used to weaken higher-order (primitive) recursion in such a way that the class of representable functions equals the class of polytime functions. We show that fine-tuning these two…
GNN-based approaches for learning general policies across planning domains are limited by the expressive power of $C_2$, namely; first-order logic with two variables and counting. This limitation can be overcame by transitioning to…
Graph neural networks (GNNs) are effective machine learning models for many graph-related applications. Despite their empirical success, many research efforts focus on the theoretical limitations of GNNs, i.e., the GNNs expressive power.…
Modelling how concepts are related is a central topic in Lexical Semantics. A common strategy is to rely on knowledge graphs (KGs) such as ConceptNet, and to model the relation between two concepts as a set of paths. However, KGs are…
Graph embedding (GE) methods embed nodes (and/or edges) in graph into a low-dimensional semantic space, and have shown its effectiveness in modeling multi-relational data. However, existing GE models are not practical in real-world…
We introduce a Geometry of Interaction model for higher-order quantum computation, and prove its adequacy for a full quantum programming language in which entanglement, duplication, and recursion are all available. Our model comes with a…