Related papers: Copula & Marginal Flows: Disentangling the Margina…

Generative flows models enjoy the properties of tractable exact likelihood and efficient sampling, which are composed of a sequence of invertible functions. In this paper, we incorporate matrix exponential into generative flows. Matrix…

Deep generative modeling has seen impressive advances in recent years, to the point where it is now commonplace to see simulated samples (e.g., images) that closely resemble real-world data. However, generation quality is generally…

For multivariate distributions in the domain of attraction of a max-stable distribution, the tail copula and the stable tail dependence function are equivalent ways to capture the dependence in the upper tail. The empirical versions of…

Recent efforts have extended the flow-matching framework to discrete generative modeling. One strand of models directly works with the continuous probabilities instead of discrete tokens, which we colloquially refer to as Continuous-State…

Many feedforward neural networks (NNs) generate continuous and piecewise-linear (CPWL) mappings. Specifically, they partition the input domain into regions on which the mapping is affine. The number of these so-called linear regions offers…

Current long-tailed semi-supervised learning methods assume that labeled data exhibit a long-tailed distribution, and unlabeled data adhere to a typical predefined distribution (i.e., long-tailed, uniform, or inverse long-tailed). However,…

Learning, taking into account full distribution of the data, referred to as generative, is not feasible with deep neural networks (DNNs) because they model only the conditional distribution of the outputs given the inputs. Current solutions…

We connect a large class of Generative Deep Networks (GDNs) with spline operators in order to derive their properties, limitations, and new opportunities. By characterizing the latent space partition, dimension and angularity of the…

Deep Generative Models are frequently used to learn continuous representations of complex data distributions using a finite number of samples. For any generative model, including pre-trained foundation models with Diffusion or Transformer…

Diffusion and flow-based generative models have achieved remarkable success in domains such as image synthesis, video generation, and natural language modeling. In this work, we extend these advances to weight space learning by leveraging…

Deep generative frameworks including GANs and normalizing flow models have proven successful at filling in missing values in partially observed data samples by effectively learning -- either explicitly or implicitly -- complex,…

Recently developed generative methods, including invertible rescaling network (IRN) based and generative adversarial network (GAN) based methods, have demonstrated exceptional performance in image rescaling. However, IRN-based methods tend…

In this article, we review the literature on statistical theories of neural networks from three perspectives: approximation, training dynamics and generative models. In the first part, results on excess risks for neural networks are…

It has repeatedly been observed that loss minimization by stochastic gradient descent (SGD) leads to heavy-tailed distributions of neural network parameters. Here, we analyze a continuous diffusion approximation of SGD, called homogenized…

Generating molecular graphs is a challenging task due to their discrete nature and the competitive objectives involved. Diffusion models have emerged as SOTA approaches in data generation across various modalities. For molecular graphs,…

Graph convolutional networks (GCNs) are \emph{discriminative models} that directly model the class posterior $p(y|\mathbf{x})$ for semi-supervised classification of graph data. While being effective, as a representation learning approach,…

Deep generative neural networks (DGNNs) have achieved realistic and high-quality data generation. In particular, the adversarial training scheme has been applied to many DGNNs and has exhibited powerful performance. Despite of recent…

The anomaly detection method presented by this paper has a special feature: it does not only indicate whether an observation is anomalous or not but also tells what exactly makes an anomalous observation unusual. Hence, it provides support…

We propose a new way of thinking about deep neural networks, in which the linear and non-linear components of the network are naturally derived and justified in terms of principles in probability theory. In particular, the models…

Classical models for multivariate or spatial extremes are mainly based upon the asymptotically justified max-stable or generalized Pareto processes. These models are suitable when asymptotic dependence is present, i.e., the joint tail…