Related papers: Equivariant Finite Normalizing Flows
Normalizing flows are deep generative models that enable efficient likelihood estimation and sampling through invertible transformations. A key challenge is to design linear layers that enhance expressiveness while maintaining efficient…
Graph neural networks (GNNs) have shown promise in learning unstructured mesh-based simulations of physical systems, including fluid dynamics. In tandem, geometric deep learning principles have informed the development of equivariant…
Generative models are a promising tool to address the sampling problem in multi-body and condensed-matter systems in the framework of statistical mechanics. In this work, we show that normalizing flows can be used to learn a transformation…
Equivariance of linear neural network layers is well studied. In this work, we relax the equivariance condition to only be true in a projective sense. We propose a way to construct a projectively equivariant neural network through building…
Bifurcation phenomena in nonlinear dynamical systems often lead to multiple coexisting stable solutions, particularly in the presence of symmetry breaking. Deterministic machine learning models are unable to capture this multiplicity,…
Data-driven modeling of collective dynamics is a challenging problem because emergent phenomena in multi-agent systems are often shaped by long-range interactions among individuals. For example, in bird flocks and fish schools, long-range…
Flow-based generative models have highly desirable properties like exact log-likelihood evaluation and exact latent-variable inference, however they are still in their infancy and have not received as much attention as alternative…
Normalizing flows are a powerful tool for generative modelling, density estimation and posterior reconstruction in Bayesian inverse problems. In this paper, we introduce proximal residual flows, a new architecture of normalizing flows.…
Normalizing Flows (NF) are Generative models which transform a simple prior distribution into the desired target. They however require the design of an invertible mapping whose Jacobian determinant has to be computable. Recently introduced,…
This monograph introduces a framework for genuine proper equivariant stable homotopy theory for Lie groups. The adjective `proper' alludes to the feature that equivalences are tested on compact subgroups, and that the objects are built from…
A prominent goal of representation learning research is to achieve representations which are factorized in a useful manner with respect to the ground truth factors of variation. The fields of disentangled and equivariant representation…
Normalizing flows have emerged as an important family of deep neural networks for modelling complex probability distributions. In this note, we revisit their coupling and autoregressive transformation layers as probabilistic graphical…
Normalizing flows are a powerful technique for obtaining reparameterizable samples from complex multimodal distributions. Unfortunately, current approaches are only available for the most basic geometries and fall short when the underlying…
Continuous Normalizing Flows (CNFs) are a class of generative models that transform a prior distribution to a model distribution by solving an ordinary differential equation (ODE). We propose to train CNFs on manifolds by minimizing…
Incorporating group symmetries via equivariance into neural networks has emerged as a robust approach for overcoming the efficiency and data demands of modern deep learning. While most existing approaches, such as group convolutions and…
Normalising flows are generative models that transform a complex density into a simpler density through the use of bijective transformations enabling both density estimation and data generation from a single model. %However, the requirement…
Real-world data with underlying structure, such as pictures of faces, are hypothesized to lie on a low-dimensional manifold. This manifold hypothesis has motivated state-of-the-art generative algorithms that learn low-dimensional data…
Recent improvements in generative adversarial visual synthesis incorporate real and fake image transformation in a self-supervised setting, leading to increased stability and perceptual fidelity. However, these approaches typically involve…
In the past, normalizing generative flows have emerged as a promising class of generative models for natural images. This type of model has many modeling advantages: the ability to efficiently compute log-likelihood of the input data, fast…
Normalizing flows are bijective mappings between inputs and latent representations with a fully factorized distribution. They are very attractive due to exact likelihood valuation and efficient sampling. However, their effective capacity is…