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Graph anomaly detection (GAD) aims to identify nodes or substructures whose behavior or attributes deviate significantly from the overall pattern in graph-structured data, with critical applications in financial risk control, social network…
Many real-world systems, such as moving planets, can be considered as multi-agent dynamic systems, where objects interact with each other and co-evolve along with the time. Such dynamics is usually difficult to capture, and understanding…
Understanding the dynamics of neural network parameters during training is one of the key challenges in building a theoretical foundation for deep learning. A central obstacle is that the motion of a network in high-dimensional parameter…
We study the dynamics of discrete-time regulatory networks on random digraphs. For this we define ensembles of deterministic orbits of random regulatory networks, and introduce some statistical indicators related to the long-term dynamics…
Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…
We study the discrete-to-continuum consistency of the training of shallow graph convolutional neural networks (GCNNs) on proximity graphs of sampled point clouds under a manifold assumption. Graph convolution is defined spectrally via the…
This paper addresses analytical aspects of deterministic, continuous-time dynamical systems defined on networks. The goal is to model and analyze certain phenomena which must be framed beyond the context of networked dynamical systems,…
Diffusion models have established themselves as state-of-the-art generative models across various data modalities, including images and videos, due to their ability to accurately approximate complex data distributions. Unlike traditional…
In the realm of applications where data dynamically evolves across spatial and temporal dimensions, Graph Neural Networks (GNNs) are often complemented by sequence modeling architectures, such as RNNs and transformers, to effectively model…
Reconstructing complex 3D interfaces from indirect measurements remains a grand challenge in scientific computing, particularly for ill-posed inverse problems like Electrical Impedance Tomography (EIT). Traditional shape optimization…
Spectral dimensionality reduction algorithms are widely used in numerous domains, including for recognition, segmentation, tracking and visualization. However, despite their popularity, these algorithms suffer from a major limitation known…
We study the problem of detecting latent geometric structure in random graphs. To this end, we consider the soft high-dimensional random geometric graph $\mathcal{G}(n,p,d,q)$, where each of the $n$ vertices corresponds to an independent…
Random graph models are frequently used as a controllable and versatile data source for experimental campaigns in various research fields. Generating such data-sets at scale is a non-trivial task as it requires design decisions typically…
This study aims to predict the spatio-temporal evolution of physical quantities observed in multi-layered display panels subjected to the drop impact of a ball. To model these complex interactions, graph neural networks have emerged as…
Dynamic graphs refer to graphs whose structure dynamically changes over time. Despite the benefits of learning vertex representations (i.e., embeddings) for dynamic graphs, existing works merely view a dynamic graph as a sequence of changes…
We focus on explicitly learning disentangled representation for natural image generation, where the underlying spatial structure and the rendering on the structure can be independently controlled respectively, yet using no tuple…
We propose Riemannian Denoising Diffusion Probabilistic Models (RDDPMs) for learning distributions on submanifolds of Euclidean space that are level sets of functions, including most of the manifolds relevant to applications. Existing…
Datasets such as images, text, or movies are embedded in high-dimensional spaces. However, in important cases such as images of objects, the statistical structure in the data constrains samples to a manifold of dramatically lower…
Inferring temporal interaction graphs and higher-order structure from neural signals is a key problem in building generative models for systems neuroscience. Foundation models for large-scale neural data represent shared latent structures…
Random geometric graphs are random graph models defined on metric measure spaces. A random geometric graph is generated by first sampling points from a metric space and then connecting each pair of sampled points independently with a…