Related papers: Random Dot Product Graphs as Dynamical Systems: Li…
Diffusion-based generative models employ stochastic differential equations (SDEs) and their equivalent probability flow ordinary differential equations (ODEs) to establish a smooth transformation between complex high-dimensional data…
Many real-world networks evolve dynamically over time and present different types of connections between nodes, often called layers. In this work, we propose a latent position model for these objects, called the dynamic multiplex random dot…
Graph data often exhibits complex geometric heterogeneity, where structures with varying local curvature, such as tree-like hierarchies and dense communities, coexist within a single network. Existing geometric GNNs, which embed graphs into…
Flexible slender structures such as rods, ribbons, plates, and shells exhibit extreme nonlinear responses bending, twisting, buckling, wrinkling, and self contact, that defy conventional simulation frameworks. Discrete Differential Geometry…
Graph states are fundamental objects in the theory of quantum information due to their simple classical description and rich entanglement structure. They are also intimately related to IQP circuits, which have applications in quantum…
A complete representation of 3D objects requires characterizing the space of deformations in an interpretable manner, from articulations of a single instance to changes in shape across categories. In this work, we improve on a prior…
By their nature it is difficult to differentiate chaotic dynamical systems through measurement. In recent years, work has begun on using methods of Topological Data Analysis (TDA) to qualitatively type dynamical data by approximating the…
We propose a practical computational framework for detecting structural changes in parameter-dependent topological data. In many applications, such as time-series data analysis, anomaly detection, and monitoring of systems under changing…
Latent Diffusion Models (LDMs) achieve high-fidelity synthesis but suffer from latent space brittleness, causing discontinuous semantic jumps during editing. We introduce a Riemannian framework to diagnose this instability by analyzing the…
In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…
Generative adversarial networks (GANs) have emerged as a powerful unsupervised method to model the statistical patterns of real-world data sets, such as natural images. These networks are trained to map random inputs in their latent space…
In this paper, we deal with random attractors for dynamical systems forced by a deterministic noise. These kind of systems are modeled as skew products where the dynamics of the forcing process are described by the base transformation.…
Energy-based models for discrete domains, such as graphs, explicitly capture relative likelihoods, naturally enabling composable probabilistic inference tasks like conditional generation or enforcing constraints at test-time. However,…
We propose a novel Stochastic Differential Equation (SDE) framework to address the problem of learning uncertainty-aware representations for graph-structured data. While Graph Neural Ordinary Differential Equations (GNODEs) have shown…
Directed graphs naturally model systems with asymmetric, ordered relationships, essential to applications in biology, transportation, social networks, and visual understanding. Generating such graphs enables tasks such as simulation, data…
This paper investigates the problem of dynamical sampling for graph signals influenced by a constant source term. We consider signals evolving over time according to a linear dynamical system on a graph, where both the initial state and the…
Disentangled representation learning has recently attracted a significant amount of attention, particularly in the field of image representation learning. However, learning the disentangled representations behind a graph remains largely…
A curious phenomenon observed in some dynamical generative models is the following: despite learning errors in the score function or the drift vector field, the generated samples appear to shift \emph{along} the support of the data…
The graph-based variational autoencoder represents an architecture that can handle the uncertainty of different geological scenarios, such as depositional or structural, through the concept of a lowerdimensional latent space. The main…
Embryonic development leads to the reproducible and ordered appearance of complexity from egg to adult. The successive differentiation of different cell types, that elaborates this complexity, result from the activity of gene networks and…