# Equivariant Manifold Flows

@inproceedings{Katsman2021EquivariantMF, title={Equivariant Manifold Flows}, author={Isay Katsman and Aaron Lou and Derek Lim and Qingxuan Jiang and Ser-Nam Lim and Christopher De Sa}, booktitle={NeurIPS}, year={2021} }

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…

## 6 Citations

### Implicit Riemannian Concave Potential Maps

- MathematicsArXiv
- 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.

### Equivariant Discrete Normalizing Flows

- Mathematics, Computer ScienceArXiv
- 2021

This paper theoretically proves the existence of an equivariant map for compact groups whose actions are on compact spaces and construction of G-Residual Flows are proved to be universal, in the sense that an G-equivariant diffeomorphism can be exactly mapped by a G-residual flow.

### Equivariant Finite Normalizing Flows

- Mathematics
- 2021

Generative modelling seeks to uncover the underlying factors that give rise to observed data that can often be modeled as the natural symmetries that manifest themselves through in-variances and…

### R IEMANNIAN N EURAL SDE: L EARNING S TOCHASTIC R EPRESENTATIONS ON M ANIFOLDS

- Mathematics
- 2022

In recent years, the neural stochastic differential equation (NSDE) has gained attention in modeling stochastic representations, while NSDE brings a great success in various types of applications.…

### Symmetry-Based Representations for Artificial and Biological General Intelligence

- BiologyFrontiers in Computational Neuroscience
- 2022

It is argued that symmetry transformations are a fundamental principle that can guide the search for what makes a good representation, and may be an important general framework that determines the structure of the universe, constrains the nature of natural tasks and consequently shapes both biological and artificial intelligence.

### E NERGY -I NSPIRED M OLECULAR C ONFORMATION O PTIMIZATION

- Computer Science
- 2022

A neural energy minimization formulation that casts the prediction problem into an unrolled optimization process, where a neural network is parametrized to learn the gradient of an implicit conformational energy landscape, can not only reinterpret and unify many of the existing models but also derive new variants of SE(3)-equivariant neural networks in a principled manner.

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