Learning to Decouple Complex Systems

TL;DR

This paper introduces a novel sequential learning method that decouples complex, cluttered systems into simpler sub-systems and a meta-system to better model interactions over time, especially with irregular data.

Contribution

It proposes a new approach using projected differential equations within a simplex to decouple complex systems and capture interactions, advancing modeling of irregular, cluttered sequential data.

Findings

Outperforms state-of-the-art on synthetic datasets

Effective in modeling complex interactions over time

Handles irregularly sampled data robustly

Abstract

A complex system with cluttered observations may be a coupled mixture of multiple simple sub-systems corresponding to latent entities. Such sub-systems may hold distinct dynamics in the continuous-time domain; therein, complicated interactions between sub-systems also evolve over time. This setting is fairly common in the real world but has been less considered. In this paper, we propose a sequential learning approach under this setting by decoupling a complex system for handling irregularly sampled and cluttered sequential observations. Such decoupling brings about not only subsystems describing the dynamics of each latent entity but also a meta-system capturing the interaction between entities over time. Specifically, we argue that the meta-system evolving within a simplex is governed by projected differential equations (ProjDEs). We further analyze and provide neural-friendly projection operators in the context of Bregman divergence. Experimental results on synthetic and real-world datasets show the advantages of our approach when facing complex and cluttered sequential data compared to the state-of-the-art.