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In the recent years, considerable attention has been paid to preserving structures and invariants in reduced basis methods, in order to enhance the stability and robustness of the reduced system. In the context of Hamiltonian systems,…

Semantic segmentation networks (SSNs) are central to safety-critical applications such as medical imaging and autonomous driving, where robustness under uncertainty is essential. However, existing probabilistic verification methods often…

Generative networks have shown remarkable success in learning complex data distributions, particularly in generating high-dimensional data from lower-dimensional inputs. While this capability is well-documented empirically, its theoretical…

Deep generative models (DGMs) are effective on learning multilayered representations of complex data and performing inference of input data by exploring the generative ability. However, little work has been done on examining or empowering…

Graph neural networks (GNNs) model nonlinear representations in graph data with applications in distributed agent coordination, control, and planning among others. Current GNN architectures assume ideal scenarios and ignore link…

Today's deep learning systems deliver high performance based on end-to-end training. While they deliver strong performance, these systems are hard to interpret. To address this issue, we propose Semantic Bottleneck Networks (SBN): deep…

Generative Adversarial Networks (GANs) have shown immense potential in fields such as text and image generation. Only very recently attempts to exploit GANs to statistical-mechanics models have been reported. Here we quantitatively test…

Deep generative models are universal tools for learning data distributions on high dimensional data spaces via a mapping to lower dimensional latent spaces. We provide a study of latent space geometries and extend and build upon previous…

State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the…

Representation learning over graph structure data has been widely studied due to its wide application prospects. However, previous methods mainly focus on static graphs while many real-world graphs evolve over time. Modeling such evolution…

Recent deep generative models are able to provide photo-realistic images as well as visual or textual content embeddings useful to address various tasks of computer vision and natural language processing. Their usefulness is nevertheless…

Neural forecasting of spatiotemporal time series drives both research and industrial innovation in several relevant application domains. Graph neural networks (GNNs) are often the core component of the forecasting architecture. However, in…

With the usage of appropriate inductive biases, Counterfactual Generative Networks (CGNs) can generate novel images from random combinations of shape, texture, and background manifolds. These images can be utilized to train an invariant…

In recent years, considerable progress has been made in the visual quality of Generative Adversarial Networks (GANs). Even so, these networks still suffer from degradation in quality for high-frequency content, stemming from a spectrally…

Deep generative models have significantly advanced medical imaging analysis by enhancing dataset size and quality. Beyond mere data augmentation, our research in this paper highlights an additional, significant capacity of deep generative…

Growing interest in modelling complex systems from brains to societies to cities using networks has led to increased efforts to describe generative processes that explain those networks. Recent successes in machine learning have prompted…

Standard neural networks are often overconfident when presented with data outside the training distribution. We introduce HyperGAN, a new generative model for learning a distribution of neural network parameters. HyperGAN does not require…

Neural networks are complex functions of both their inputs and parameters. Much prior work in deep learning theory analyzes the distribution of network outputs at a fixed a set of inputs (e.g. a training dataset) over random initializations…

The generation of high-quality synthetic data presents significant challenges in machine learning research, particularly regarding statistical fidelity and uncertainty quantification. Existing generative models produce compelling synthetic…

Scattering transforms are a new type of summary statistics recently developed for the study of highly non-Gaussian processes, which have been shown to be very promising for astrophysical studies. In particular, they allow one to build…