# Equivariant Manifold Flows

@article{Katsman2021EquivariantMF, title={Equivariant Manifold Flows}, author={Isay Katsman and Aaron Lou and D. Lim and Qingxuan Jiang and Ser-Nam Lim and Christopher De Sa}, journal={ArXiv}, year={2021}, volume={abs/2107.08596} }

Tractably modelling distributions over manifolds has long been an important goal in the natural sciences. Recent work has focused on developing general machine learning models to learn such distributions. However, for many applications these distributions must respect manifold symmetries—a trait which most previous models disregard. In this paper, we lay the theoretical foundations for learning symmetry-invariant distributions on arbitrary manifolds via equivariant manifold flows. We… Expand

#### 2 Citations

Implicit Riemannian Concave Potential Maps

- Mathematics, Computer Science
- 2021

This work combines ideas from implicit neural layers and optimal transport theory to propose a generalisation of existing work on exponential map flows, Implicit Riemannian Concave Potential Maps, IRCPMs, which have some nice properties such as simplicity of incorporating symmetries and are less expensive than ODE-flows. Expand

Equivariant Discrete Normalizing Flows

- Computer Science
- 2021

At its core, generative modeling seeks to uncover the underlying factors that give rise to observed data that can often be modelled as the natural symmetries that manifest themselves through… Expand

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