Related papers: Generative Learning for Slow Manifolds and Bifurca…
Deep generative models with latent variables have been used lately to learn joint representations and generative processes from multi-modal data. These two learning mechanisms can, however, conflict with each other and representations can…
Numerical models of electromyographic (EMG) signals have provided a huge contribution to our fundamental understanding of human neurophysiology and remain a central pillar of motor neuroscience and the development of human-machine…
Constrained generative modeling is fundamental to applications such as robotic control and autonomous driving, where models must respect physical laws and safety-critical constraints. In real-world settings, these constraints rarely take…
Generative adversarial networks (GANs) have been remarkably successful in learning complex high dimensional real word distributions and generating realistic samples. However, they provide limited control over the generation process.…
Biological systems commonly exhibit complex spatiotemporal patterns whose underlying generative mechanisms pose a significant analytical challenge. Traditional approaches to spatiodynamic inference rely on dimensionality reduction through…
Manifold learning approaches seek the intrinsic, low-dimensional data structure within a high-dimensional space. Mainstream manifold learning algorithms, such as Isomap, UMAP, $t$-SNE, Diffusion Map, and Laplacian Eigenmaps do not use data…
Multivariate time series forecasting is a challenging task because the data involves a mixture of long- and short-term patterns, with dynamic spatio-temporal dependencies among variables. Existing graph neural networks (GNN) typically model…
Extensive empirical evidence demonstrates that conditional generative models are easier to train and perform better than unconditional ones by exploiting the labels of data. So do score-based diffusion models. In this paper, we analyze the…
This study employs scientific machine learning to identify transient time series of dynamical systems near a fold bifurcation of periodic solutions. The unique aspect of this work is that a convolutional neural network (CNN) is trained with…
Nonlinear and non-stationary processes are prevalent in various natural and physical phenomena, where system dynamics can change qualitatively due to bifurcation phenomena. Traditional machine learning methods have advanced our ability to…
Deep latent generative models have attracted increasing attention due to the capacity of combining the strengths of deep learning and probabilistic models in an elegant way. The data representations learned with the models are often…
Score-based generative models can effectively learn the distribution of data by estimating the gradient of the distribution. Due to the multi-step denoising characteristic, researchers have recently considered combining score-based…
We propose a conditional stochastic interpolation (CSI) method for learning conditional distributions. CSI is based on estimating probability flow equations or stochastic differential equations that transport a reference distribution to the…
Deep generative models are tremendously successful in learning low-dimensional latent representations that well-describe the data. These representations, however, tend to much distort relationships between points, i.e. pairwise distances…
We introduce Equilibrium Matching (EqM), a generative modeling framework built from an equilibrium dynamics perspective. EqM discards the non-equilibrium, time-conditional dynamics in traditional diffusion and flow-based generative models…
Manifold-valued data naturally arises in medical imaging. In cognitive neuroscience, for instance, brain connectomes base the analysis of coactivation patterns between different brain regions on the analysis of the correlations of their…
Deep generative models are increasingly becoming integral parts of the in silico molecule design pipeline and have dual goals of learning the chemical and structural features that render candidate molecules viable while also being flexible…
We introduce Statistical Flow Matching (SFM), a novel and mathematically rigorous flow-matching framework on the manifold of parameterized probability measures inspired by the results from information geometry. We demonstrate the…
Controllable molecular graph generation is essential for material and drug discovery, where generated molecules must satisfy diverse property constraints. While recent advances in graph diffusion models have improved generation quality,…
In standard generative deep learning models, such as autoencoders or GANs, the size of the parameter set is proportional to the complexity of the generated data distribution. A significant challenge is to deploy resource-hungry deep…