Related papers: Quiver Signal Processing (QSP)
Graphs are a fundamental representation of complex, nonlinear structured data across various domains, including social networks and quantum systems. Quantum Graph Recurrent Neural Networks (QGRNNs) have been proposed to model quantum…
Encoding images as a series of high-level constructs, such as brush strokes or discrete shapes, can often be key to both human and machine understanding. In many cases, however, data is only available in pixel form. We present a method for…
Graphs are a central tool in machine learning and information processing as they allow to conveniently capture the structure of complex datasets. In this context, it is of high importance to develop flexible models of signals defined over…
Current methods of graph signal processing rely heavily on the specific structure of the underlying network: the shift operator and the graph Fourier transform are both derived directly from a specific graph. In many cases, the network is…
In this paper, we propose a new homological method to study weighted directed networks. Our model of such networks is a directed graph $Q$ equipped with a weight function $w$ on the set $Q_{1}$ of arrows in $Q$. We require that the range…
This paper proposes a brain-inspired approach to quantum machine learning with the goal of circumventing many of the complications of other approaches. The fact that quantum processes are unitary presents both opportunities and challenges.…
How can we effectively encode evolving information over dynamic graphs into low-dimensional representations? In this paper, we propose DyRep, an inductive deep representation learning framework that learns a set of functions to efficiently…
Graph signal processing deals with signals which are observed on an irregular graph domain. While many approaches have been developed in classical graph theory to cluster vertices and segment large graphs in a signal independent way, signal…
In this paper, we explore a process called neural teleportation, a mathematical consequence of applying quiver representation theory to neural networks. Neural teleportation "teleports" a network to a new position in the weight space and…
Neural networks are often represented as graphs of connections between neurons. However, despite their wide use, there is currently little understanding of the relationship between the graph structure of the neural network and its…
Knowledge representation learning has been commonly adopted to incorporate knowledge graph (KG) into various online services. Although existing knowledge representation learning methods have achieved considerable performance improvement,…
Graph Neural Networks (GNNs) have emerged as powerful tools for learning representations of graph-structured data. In addition to real-valued GNNs, quaternion GNNs also perform well on tasks on graph-structured data. With the aim of…
Network topology inference is a prominent problem in Network Science. Most graph signal processing (GSP) efforts to date assume that the underlying network is known, and then analyze how the graph's algebraic and spectral characteristics…
The emergence of explainability methods has enabled a better comprehension of how deep neural networks operate through concepts that are easily understood and implemented by the end user. While most explainability methods have been designed…
The purpose of this paper is to outline a generalised model for representing hybrids of relational-categorical, symbolic, perceptual-sensory and perceptual-latent data, so as to embody, in the same architectural data layer, representations…
Explainable artificial intelligence (XAI) is an important area in the AI community, and interpretability is crucial for building robust and trustworthy AI models. While previous work has explored model-level and instance-level explainable…
Graph representation learning aims to effectively encode high-dimensional sparse graph-structured data into low-dimensional dense vectors, which is a fundamental task that has been widely studied in a range of fields, including machine…
Graph signal processing, like the graph Fourier transform, requires the full graph signal at every vertex of the graph. However, in practice, only signals at a subset of vertices may be available. We propose a subgraph signal processing…
Analyzing large-scale graphs provides valuable insights in different application scenarios. While many graph processing systems working on top of distributed infrastructures have been proposed to deal with big graphs, the tasks of profiling…
Recent studies have highlighted the limitations of message-passing based graph neural networks (GNNs), e.g., limited model expressiveness, over-smoothing, over-squashing, etc. To alleviate these issues, Graph Transformers (GTs) have been…