Related papers: Atlas Generative Models and Geodesic Interpolation
Generative adversarial networks (GANs) have been recently applied as a novel emulation technique for large scale structure simulations. Recent results show that GANs can be used as a fast, efficient and computationally cheap emulator for…
There has been a growing interest in statistical inference from data satisfying the so-called manifold hypothesis, assuming data points in the high-dimensional ambient space to lie in close vicinity of a submanifold of much lower dimension.…
Unsupervised domain mapping has attracted substantial attention in recent years due to the success of models based on the cycle-consistency assumption. These models map between two domains by fooling a probabilistic discriminator, thereby…
The geometry of generative models serves as the basis for interpolation, model inspection, and more. Unfortunately, most generative models lack a principal notion of geometry without restrictive assumptions on either the model or the data…
In traditional generative modeling, good data representation is very often a base for a good machine learning model. It can be linked to good representations encoding more explanatory factors that are hidden in the original data. With the…
The commonly used latent space embedding techniques, such as Principal Component Analysis, Factor Analysis, and manifold learning techniques, are typically used for learning effective representations of homogeneous data. However, they do…
Graph Neural Networks usually rely on the assumption that the graph topology is available to the network as well as optimal for the downstream task. Latent graph inference allows models to dynamically learn the intrinsic graph structure of…
Undirected graphical models are compact representations of joint probability distributions over random variables. To solve inference tasks of interest, graphical models of arbitrary topology can be trained using empirical risk minimization.…
Utilization of classification latent space information for downstream reconstruction and generation is an intriguing and a relatively unexplored area. In general, discriminative representations are rich in class-specific features but are…
The advent of generative adversarial networks (GAN) has enabled new capabilities in synthesis, interpolation, and data augmentation heretofore considered very challenging. However, one of the common assumptions in most GAN architectures is…
In the era of generative AI, deep generative models (DGMs) with latent representations have gained tremendous popularity. Despite their impressive empirical performance, the statistical properties of these models remain underexplored. DGMs…
In this paper, we propose a method to learn a minimizing geodesic within a data manifold. Along the learned geodesic, our method can generate high-quality interpolations between two given data samples. Specifically, we use an autoencoder…
Natural data observed in $\mathbb{R}^n$ is often constrained to an $m$-dimensional manifold $\mathcal{M}$, where $m < n$. This work focuses on the task of building theoretically principled generative models for such data. Current generative…
A wide range of applications require learning image generation models whose latent space effectively captures the high-level factors of variation present in the data distribution. The extent to which a model represents such variations…
Different encodings of datapoints in the latent space of latent-vector generative models may result in more or less effective and disentangled characterizations of the different explanatory factors of variation behind the data. Many works…
Generative adversarial networks (GANs) provide an algorithmic framework for constructing generative models with several appealing properties: they do not require a likelihood function to be specified, only a generating procedure; they…
Spatial networks are networks whose graph topology is constrained by their embedded spatial space. Understanding the coupled spatial-graph properties is crucial for extracting powerful representations from spatial networks. Therefore,…
We propose an algorithm grounded in dynamical systems theory that generalizes manifold learning from a global state representation, to a network of local interacting manifolds termed a Generative Manifold Network (GMN). Manifolds are…
Memory units have been widely used to enrich the capabilities of deep networks on capturing long-term dependencies in reasoning and prediction tasks, but little investigation exists on deep generative models (DGMs) which are good at…
Deep generative models like variational autoencoders approximate the intrinsic geometry of high dimensional data manifolds by learning low-dimensional latent-space variables and an embedding function. The geometric properties of these…