On Discovery of Local Independence over Continuous Variables via Neural Contextual Decomposition

Conditional independence provides a way to understand causal relationships among the variables of interest. An underlying system may exhibit more fine-grained causal relationships especially between a variable and its parents, which will be called the local independence relationships. One of the most widely studied local relationships is Context-Specific Independence (CSI), which holds in a specific assignment of conditioned variables. However, its applicability is often limited since it does not allow continuous variables: data conditioned to the specific value of a continuous variable contains few instances, if not none, making it infeasible to test independence. In this work, we define and characterize the local independence relationship that holds in a specific set of joint assignments of parental variables, which we call context-set specific independence (CSSI). We then provide a canonical representation of CSSI and prove its fundamental properties. Based on our theoretical findings, we cast the problem of discovering multiple CSSI relationships in a system as finding a partition of the joint outcome space. Finally, we propose a novel method, coined neural contextual decomposition (NCD), which learns such partition by imposing each set to induce CSSI via modeling a conditional distribution. We empirically demonstrate that the proposed method successfully discovers the ground truth local independence relationships in both synthetic dataset and complex system reflecting the real-world physical dynamics.

Unsupervised Dynamics Prediction with Object-Centric Kinematics

Human perception involves discerning complex multi-object scenes into time-static object appearance (\ie, size, shape, color) and time-varying object motion (\ie, location, velocity, acceleration). This innate ability to unconsciously understand the environment is the motivation behind the success of dynamics modeling. Object-centric representations have emerged as a promising tool for dynamics prediction, yet they primarily focus on the objects' appearance, often overlooking other crucial attributes. In this paper, we propose Object-Centric Kinematics (OCK), a framework for dynamics prediction leveraging object-centric representations. Our model utilizes a novel component named object kinematics, which comprises low-level structured states of objects' position, velocity, and acceleration. The object kinematics are obtained via either implicit or explicit approaches, enabling comprehensive spatiotemporal object reasoning, and integrated through various transformer mechanisms, facilitating effective object-centric dynamics modeling. Our model demonstrates superior performance when handling objects and backgrounds in complex scenes characterized by a wide range of object attributes and dynamic movements. Moreover, our model demonstrates generalization capabilities across diverse synthetic environments, highlighting its potential for broad applicability in vision-related tasks.