Equivariant Deep Dynamical Model for Motion Prediction

TL;DR

This paper introduces an SO(3) equivariant deep dynamical model (EqDDM) that leverages symmetry-aware neural networks to improve motion prediction accuracy by learning structured, transformation-aware representations.

Contribution

The paper presents a novel SO(3) equivariant deep dynamical model that explicitly incorporates symmetry transformations into the learning process for enhanced motion prediction.

Findings

EqDDM outperforms existing models on motion prediction tasks.

Equivariant networks improve the interpretability of learned representations.

Structured symmetry-aware representations lead to better generalization.

Abstract

Learning representations through deep generative modeling is a powerful approach for dynamical modeling to discover the most simplified and compressed underlying description of the data, to then use it for other tasks such as prediction. Most learning tasks have intrinsic symmetries, i.e., the input transformations leave the output unchanged, or the output undergoes a similar transformation. The learning process is, however, usually uninformed of these symmetries. Therefore, the learned representations for individually transformed inputs may not be meaningfully related. In this paper, we propose an SO(3) equivariant deep dynamical model (EqDDM) for motion prediction that learns a structured representation of the input space in the sense that the embedding varies with symmetry transformations. EqDDM is equipped with equivariant networks to parameterize the state-space emission and transition models. We demonstrate the superior predictive performance of the proposed model on various motion data.