NEURAL CONSTRAINT INFERENCE: INFERRING EN-ERGY CONSTRAINTS IN INTERACTING SYSTEMS

Abstract

Systems consisting of interacting agents are prevalent in the world, ranging from dynamical systems in physics to complex biological networks. To build systems which can interact robustly in the real world, it is thus important to be able to infer the precise interactions governing such systems. Existing approaches typically discover such interactions by explicitly modeling the feedforward dynamics of the trajectories. In this work, we propose Neural Constraint Inference (NCI) model as an alternative approach to discover such interactions: it discovers a set of relational constraints, represented as energy functions, which when optimized reconstruct the original trajectory. We illustrate how NCI can faithfully predict future trajectory dynamics, achieving more consistent long-rollouts than existing approaches. We show that the constraints discovered by NCI are disentangled and may be intermixed with constraints from other trajectories. Finally, we illustrate how those constraints enable the incorporation of external test-time constraints.

1. INTRODUCTION

Dynamical systems are ubiquitous in both nature and everyday life. Such systems emerge naturally in scientific settings such as chemical pathways and particle dynamics as well as everyday settings such as in sports teams or social events. Such dynamical systems may be decomposed as a set of different interacting components, where the interactions with respect to each other lead to complex dynamics. Modeling the underlying dynamics of such systems is hard: often times we only have access to example trajectories, without knowledge of the underlying interactions or the dynamics that govern them. Consider the scenario given in Figure 1 , consisting of a set of NBA players playing a basketball game. While the motion of individual players may appear stochastic in nature, each player aims to score the basket on the opposite team's side of the court. Thus, we may utilize sets of interactions to explain their behaviors -a group of players on the defensive team serve as a zone defense, preventing players from the opposite team from getting close to the basket. Simultaneously, a group of offensive players moves towards the goal, while a group of defensive players moves to intercept them and prevent them from scoring. By applying our underlying knowledge of these interactions between players, we may forecast the future dynamics of the basketball game significantly more accurately. Most works modeling such complex dynamics do not explicitly disentangle individual interactions between objects. Instead, they rely on a learned network to implicitly disentangle them (Battaglia et al., 2016; Gilmer et al., 2017; van Steenkiste et al., 2018) . In contrast, Kipf et al. (2018) propose Neural Relation Inference (NRI), which learns a structured set of explicit interaction models between objects and show how such explicit interaction modeling enables more effective downstream predictions. In this work, we argue that we should instead model and disentangle interactions between objects



Figure 1: Interactions between NBA players. Complex dynamics, such as the player trajectories in the NBA, may be explained using a simple set of interactions. In this setting, one team of players aims to block a separate team from scoring.

