Paul Williams

Indiana University, Cognitive Science, Faculty Member

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Supervisors: Randall Beer and Risto Miikkulainen
Address: Cognitive Science Program
Eigenmann 841
1900 E 10th St
Indiana University
Bloomington, IN 47406-7512
plw@indiana.edu
http://pages.iu.edu/~plw/

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Papers by Paul Williams

Information Processing and Dynamics in Minimally Cognitive Agents

There has been considerable debate in the literature about the relative merits of information pro... more There has been considerable debate in the literature about the relative merits of information processing vs. dynamical approaches to understanding cognitive processes. In this paper, we explore the relationship between these two styles of explanation using a model agent evolved to solve a relational categorization task. Specifically, we separately analyze the operation of this agent using the mathematical tools of information theory and dynamical systems theory. Information-theoretic analysis reveals how task-relevant information flows through the system to be combined into a categorization decision. Dynamical analysis reveals the key geometrical and temporal interrelationships underlying the categorization decision. Finally, we propose a framework for directly relating these two different styles of explanation and discuss the possible implications of our analysis for some of the ongoing debates in cognitive science.

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Environmental Feedback Drives Multiple Behaviors from the Same Neural Circuit

The ability of a single neural circuit to produce qualitatively distinct behaviors is typically a... more The ability of a single neural circuit to produce qualitatively distinct behaviors is typically attributed to some adaptive mechanism in the circuit itself. However, neural circuits are also embedded in particular bodies and environments, and feedback through the sensorimotor loop may also serve to drive behavioral differentiation. Here we explore the ability of a single neural circuit to produce qualitatively different behaviors based on changing patterns of environmental feedback. Agents equipped with two sets of effectors and controlled by fixed neural circuits are evolved to catch circles under three different motor conditions. In one condition, the agent must coordinate both sets of effectors, while in each of the other conditions one set of effectors is lesioned and the agent must rely on the other set alone to accomplish the task. A detailed behavioral analysis of the best evolved agent is reported, providing numerous insights into its evolved behavioral mechanism. The agent is found to produce significantly different motor outputs in each of the three conditions, to rely on continuous environmental feedback for successful behavior, and to switch flexibly between different behavioral conditions.

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Towards a Synergy-Based Approach to Measuring Information Modification

Distributed computation in artificial life and complex systems is often described in terms of com... more Distributed computation in artificial life and complex systems is often described in terms of component operations on information: information storage, transfer and modification. Information modification remains poorly described however, with the popularly-understood examples of glider and particle collisions in cellular automata being only quantitatively identified to date using a heuristic (separable information) rather than a proper information-theoretic measure. We outline how a recently- introduced axiomatic framework for measuring information redundancy and synergy, called partial information decomposition, can be applied to a perspective of distributed computation in order to quantify component operations on information. Using this framework, we propose a new measure of information modification that captures the intuitive understanding of information modification events as those involving interactions between two or more information sources. We also consider how the local dynamics of information modification in space and time could be measured, and suggest a new axiom that redundancy measures would need to meet in order to make such local measurements. Finally, we evaluate the potential for existing redundancy measures to meet this localizability axiom.

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Partial Information Decomposition as a Spatiotemporal Filter

Understanding the mechanisms of distributed computation in cellular automata requires techniques ... more Understanding the mechanisms of distributed computation in cellular automata requires techniques for characterizing the emergent structures that underlie information processing in such systems. Recently, techniques from information theory have been brought to bear on this problem. Building on this work, we utilize the new technique of partial information decomposition to show that previous information-theoretic measures can confound distinct sources of information. We then propose a new set of filters and demonstrate that they more cleanly separate out the background domains, particles, and collisions that are typically associated with information storage, transfer, and modification in cellular automata.

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Information Dynamics: Its Theory and Application to Embodied Cognitive Systems

In this thesis, I develop a novel framework for quantifying the information dynamics of brain-bod... more In this thesis, I develop a novel framework for quantifying the information dynamics of brain-body-environment systems, and demonstrate its application to several model agents. I begin by extending one of the core concepts of information theory—the mutual information—into a new method for decomposing informational relationships be- tween multiple variables, called partial information decomposition. Then, using partial information decomposition as the theoretical backbone, I derive techniques for quantifying the flow of information both within and between the components of a brain-body-environment system. Finally, I apply these techniques to analyze specific examples of embodied cognitive behavior, analyzing model agents that perform a simple relational comparison task between two visually presented objects. I explore questions such as how these agents extract and store information about individual objects, and how they integrate information about different objects. Among other key findings, this analysis shows how agents utilize their bodies to actively elicit and structure information from their environments, and use their bodies as extra degrees of freedom to store and process information, illustrating some of the unique ways that embodiment can influence intelligent behavior.

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Generalized Measures of Information Transfer

Transfer entropy provides a general tool for analyzing the magnitudes and directions—but not the ... more Transfer entropy provides a general tool for analyzing the magnitudes and directions—but not the kinds—of information transfer in a system. We extend transfer entropy in two complementary ways. First, we distinguish state-dependent from state-independent transfer, based on whether a source’s influence depends on the state of the target. Second, for multiple sources, we distinguish between unique, redundant, and synergistic transfer. The new measures are demonstrated on several systems that extend examples from previous literature.

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Information Dynamics of Evolved Agents

Information-theoretic techniques have received much recent attention as tools for the analysis of... more Information-theoretic techniques have received much recent attention as tools for the analysis of embodied agents. However, while techniques for quantifying static information structure are well-established, the application of information theory to the analysis of temporal behavior is still in its infancy. Here we formulate a novel information-theoretic approach for analyzing the dynamics of information flow in embodied systems. To demonstrate our approach, we apply it to analyze a previously evolved model of relational categorization. The results of this analysis demonstrate 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.

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Nonnegative Decomposition of Multivariate Information

Of the various attempts to generalize information theory to multiple variables, the most widely u... more Of the various attempts to generalize information theory to multiple variables, the most widely utilized, interaction information, suffers from the problem that it is sometimes negative. Here we reconsider from first principles the general structure of the information that a set of sources provides about a given variable. We begin with a new definition of redundancy as the minimum information that any source provides about each possible outcome of the variable, averaged over all possible outcomes. We then show how this measure of redundancy induces a lattice over sets of sources that clarifies the general structure of multivariate information. Finally, we use this redundancy lattice to propose a definition of partial information atoms that exhaustively decompose the Shannon information in a multivariate system in terms of the redundancy between synergies of subsets of the sources. Unlike interaction information, the atoms of our partial information decomposition are never negative and always support a clear interpretation as informational quantities. Our analysis also demonstrates how the negativity of interaction information can be explained by its confounding of redundancy and synergy.

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Animals and Animats: Why not both iguanas?

Webb's argument assumes a recipe for modeling that goes something like this. Through years of pai... more Webb's argument assumes a recipe for modeling that goes something like this. Through years of painstaking experimental work, biologists collect extensive data about certain aspects of, say, a neuroethological system of interest. The first job of the modeler is to synthesize some subset of this existing data into a model of that system. This model may take different forms, including mathematical, computational, or robotic, depending on the nature of the system being modeled, the particular scientific questions of interest, and the skills of the modeler. Once constructed, experiments can be carried out on the model. For example, a model of cricket phonotaxis can be placed in different acoustic environments, or particular model neurons or connections can be lesioned. If these experiments

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Evolving Referential Communication in Embodied Dynamical Agents

This paper presents results from three experiments which investigate the evolution of referential... more This paper presents results from three experiments which investigate the evolution of referential communication in embodied dynamical agents. Agents, interacting with only simple sensors and motors, are evolved in a task which requires one agent to communicate the locations of spatially distant targets to another agent. The results from these experiments demonstrate a variety of successful communication strategies, providing a first step towards understanding the emergence of referential communication in terms of coordinated behavioral interactions.

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An Embodied Dynamical Approach to Relational Categorization

This paper presents a novel approach to the study of relational categorization based on the evolu... more This paper presents a novel approach to the study of relational categorization based on the evolution of simulated agents in a relational task. In contrast to most previous models of relational categorization, which begin by assuming abstract representations and role-filler binding mechanisms, we begin by studying relational behavior in embodied dynamical agents, which results in a wider range of possibilities for relational mechanisms. The mathematical tools of dynamical systems theory are used to analyze the relational mechanism of the best evolved agent, and we then identify some of the insights offered by this analysis.

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Grounding Language in Descriptions of Scenes

The problem of how abstract symbols, such as those in systems of natural language, may be grounde... more The problem of how abstract symbols, such as those in systems of natural language, may be grounded in perceptual information presents a significant challenge to several areas of research. This paper presents the GLIDES model, a neural network architecture that shows how this symbol-grounding problem can be solved through learned relationships between simple visual scenes and linguistic descriptions. Unlike previous models of symbol grounding, the model’s learning is completely unsupervised, utilizing the principles of self organization and Hebbian learning and allowing direct visualization of how concepts are formed and grounding occurs. Two sets of experiments were conducted to evaluate the model. In the first set, linguistic test stimuli were presented and the scenes that were generated by the model were evaluated as the grounding of the language. In the second set, the model was presented with visual test samples and its language generation capabilities based on the grounded representations were assessed. The results demonstrate that symbols can be grounded based on associations of perceptual and linguistic representations, and the grounding can be made transparent. This transparency leads to unique insights into symbol grounding, including how many-to-many mappings between symbols and referents can be maintained and how concepts can be formed from cooccurrence relationships.

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