AETv2: AutoEncoding Transformations for Self-Supervised Representation Learning by Minimizing Geodesic Distances in Lie Groups

TL;DR

AETv2 introduces a novel self-supervised learning method that encodes transformations on Lie groups using geodesic distances, improving representation learning by better capturing the transformation manifold.

Contribution

It proposes a new approach to measure transformation deviations on Lie groups using geodesic distances, enhancing self-supervised learning effectiveness.

Findings

AETv2 outperforms previous models in multiple tasks.

Using geodesic distances improves transformation estimation accuracy.

The method effectively captures the manifold structure of transformations.

Abstract

Self-supervised learning by predicting transformations has demonstrated outstanding performances in both unsupervised and (semi-)supervised tasks. Among the state-of-the-art methods is the AutoEncoding Transformations (AET) by decoding transformations from the learned representations of original and transformed images. Both deterministic and probabilistic AETs rely on the Euclidean distance to measure the deviation of estimated transformations from their groundtruth counterparts. However, this assumption is questionable as a group of transformations often reside on a curved manifold rather staying in a flat Euclidean space. For this reason, we should use the geodesic to characterize how an image transform along the manifold of a transformation group, and adopt its length to measure the deviation between transformations. Particularly, we present to autoencode a Lie group of homography transformations PG(2) to learn image representations. For this, we make an estimate of the intractable Riemannian logarithm by projecting PG(2) to a subgroup of rotation transformations SO(3) that allows the closed-form expression of geodesic distances. Experiments demonstrate the proposed AETv2 model outperforms the previous version as well as the other state-of-the-art self-supervised models in multiple tasks.