Oracle-Preserving Latent Flows

TL;DR

This paper introduces a deep learning approach that discovers multiple continuous symmetries in datasets by modeling transformations with neural networks, utilizing a reduced-dimensional latent space and handling high-dimensional invariants.

Contribution

It presents a novel method combining latent space modeling and symmetry discovery, extending to high-dimensional oracles and demonstrating effectiveness on MNIST.

Findings

Successfully discovers multiple symmetries in datasets.

Handles high-dimensional invariance with neural network models.

Effective on MNIST digit dataset.

Abstract

We develop a deep learning methodology for the simultaneous discovery of multiple nontrivial continuous symmetries across an entire labelled dataset. The symmetry transformations and the corresponding generators are modeled with fully connected neural networks trained with a specially constructed loss function ensuring the desired symmetry properties. The two new elements in this work are the use of a reduced-dimensionality latent space and the generalization to transformations invariant with respect to high-dimensional oracles. The method is demonstrated with several examples on the MNIST digit dataset.