GSO-2010: Paul Williams and Randy Beer
Information Dynamics of Embodied Agents
Information theory provides a powerful set of tools for the analysis of embodied agents. However, while methods for quantifying static information structure are well established, only recently have information-theoretic techniques been extended to consider structure over time. Here we present a novel information-theoretic toolset for analyzing the information dynamics of embodied agents, and demonstrate its application to a previously reported model of relational categorization (Williams & Beer, CogSci 2008).
The central idea of our approach is to explore how information about particular stimulus features flows through a brain-body-environment system. We begin by quantifying the information that sensory, neural, and motor components provide about a stimulus. Then we unroll these measures across time to explore how informational structure evolves during behavior. By further unrolling across values of the stimulus feature, we are able to trace how information about particular stimuli flows through the system. The aim of our analysis is then to understand the dynamic properties of this information flow.
Our analysis techniques are based on a newly developed method for decomposing multivariate information, called partial information (PI) decomposition (Williams & Beer, arXiv:1004.2515). PI-decomposition exhaustively decomposes the information from a set of variables into unique information, redundancies, and synergies between subsets of those variables. Using PI-decomposition, we derive measures that capture the dynamic properties of information gain, loss, and transfer. Information gain is defined as the unique information that a component contains at the current time step when information from previous time steps is excluded. Information loss is defined oppositely as the information that a component contained previously which it currently lacks. Information transfer is defined as the redundancy between a source and the information gained by a target. Information transfer also extends naturally to multiple components, allowing us to track information along arbitrarily complex paths.
We demonstrate these techniques by analyzing the relational categorization behavior of evolved model agents. We explore questions such as how the agents extract and store information about stimulus features, and how they integrate information about multiple features. In addition, we show how our techniques apply naturally to interactions spanning the brain-body and body-environment boundaries. For instance, we explore how one agent uses its body position to store information about a stimulus, representing a simple form of information offloading. We also examine how an agentÕs position and motion influence the information available at its sensors, corresponding to information self-structuring. The results of this analysis illustrate the unique strengths of our approach for exploring the detailed structure of information dynamics, and point towards a natural synergy between temporally-extended information theory and dynamical systems theory.