Related papers: Universality of parametric Coupling Flows over par…
Invertible neural networks based on coupling flows (CF-INNs) have various machine learning applications such as image synthesis and representation learning. However, their desirable characteristics such as analytic invertibility come at the…
We introduce Neural Conjugate Flows (NCF), a class of neural network architectures equipped with exact flow structure. By leveraging topological conjugation, we prove that these networks are not only naturally isomorphic to a continuous…
Invertible neural networks (INNs) are neural network architectures with invertibility by design. Thanks to their invertibility and the tractability of Jacobian, INNs have various machine learning applications such as probabilistic modeling,…
We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for…
Normalizing flows are a widely used class of latent-variable generative models with a tractable likelihood. Affine-coupling (Dinh et al, 2014-16) models are a particularly common type of normalizing flows, for which the Jacobian of the…
We introduce an abstract neural flow framework for neural networks and neural operators. The framework contains two continuous-depth models, namely neural flows with composition and separation structures, and covers both finite-dimensional…
We present a novel theoretical framework for understanding the expressive power of normalizing flows. Despite their prevalence in scientific applications, a comprehensive understanding of flows remains elusive due to their restricted…
Invertible convolutions have been an essential element for building expressive normalizing flow-based generative models since their introduction in Glow. Several attempts have been made to design invertible $k \times k$ convolutions that…
Continuous normalizing flows (CNFs) are a generative method for learning probability distributions, which is based on ordinary differential equations. This method has shown remarkable empirical success across various applications, including…
Flow-based models are powerful tools for designing probabilistic models with tractable density. This paper introduces Convex Potential Flows (CP-Flow), a natural and efficient parameterization of invertible models inspired by the optimal…
Morphing is a long-standing problem in vision and computer graphics, requiring a time-dependent warping for feature alignment and a blending for smooth interpolation. Recently, multilayer perceptrons (MLPs) have been explored as implicit…
Diffeomorphisms play a crucial role while searching for shapes with fixed topological properties, allowing for smooth deformation of template shapes. Several approaches use diffeomorphism for shape search. However, these approaches employ…
We show that universality in chaotic elements can be lifted to that in complex systems. We construct a globally coupled Flow lattice (GCFL), an analog of a globally coupled Map lattice (GCML). We find that Duffing GCFL shows the same…
We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems. Such invariant functions includes the much studied translation-invariant ones…
Normalizing flows leverage the Change of Variables Formula (CVF) to define flexible density models. Yet, the requirement of smooth transformations (diffeomorphisms) in the CVF poses a significant challenge in the construction of these…
In this paper we propose a Deep Learning architecture to approximate diffeomorphisms diffeotopic to the identity. We consider a control system of the form $\dot x = \sum_{i=1}^lF_i(x)u_i$, with linear dependence in the controls, and we use…
We describe generalizations of the universal approximation theorem for neural networks to maps invariant or equivariant with respect to linear representations of groups. Our goal is to establish network-like computational models that are…
Normalizing Flows (NFs) are able to model complicated distributions p(y) with strong inter-dimensional correlations and high multimodality by transforming a simple base density p(z) through an invertible neural network under the change of…
The universal approximation theorem is generalised to uniform convergence on the (noncompact) input space $\mathbb{R}^n$. All continuous functions that vanish at infinity can be uniformly approximated by neural networks with one hidden…
Convolutional neural networks are the most widely used type of neural networks in applications. In mathematical analysis, however, mostly fully-connected networks are studied. In this paper, we establish a connection between both network…