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Information theory of decisions and actions
, 2010
"... The perceptionaction cycle is often defined as “the circular flow of information between an organism and its environment in the course of a sensory guided sequence of actions towards a goal ” (Fuster 2001, 2006). The question we address in this paper is in what sense this “flow of information ” can ..."
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The perceptionaction cycle is often defined as “the circular flow of information between an organism and its environment in the course of a sensory guided sequence of actions towards a goal ” (Fuster 2001, 2006). The question we address in this paper is in what sense this “flow of information ” can be described by Shannon’s measures of information introduced in his mathematical theory of communication. We provide an affirmative answer to this question using an intriguing analogy between Shannon’s classical model of communication and the PerceptionActionCycle. In particular, decision and action sequences turn out to be directly analogous to codes in communication, and their complexity — the minimal number of (binary) decisions required for reaching a goal — directly bounded by information measures, as in communication. This analogy allows us to extend the standard Reinforcement Learning framework. The latter considers the future expected reward in the course of a behaviour sequence towards a goal (valuetogo). Here, we additionally incorporate a measure of information associated with this sequence: the cumulated information processing cost or bandwidth required to specify the future decision and action sequence (informationtogo). Using a graphical model, we derive a recursive Bellman optimality equation for information measures, in analogy to Reinforcement Learning; from this, we obtain new algorithms for calculating the optimal tradeoff between the valuetogo and the required informationtogo, unifying the ideas behind the Bellman and the BlahutArimoto iterations. This tradeoff between valuetogo and informationtogo provides a complete analogy with the compressiondistortion tradeoff in source coding. The present new formulation connects seemingly unrelated optimization problems. The algorithm is demonstrated on grid world examples.
Changing Structures in Midstream: Learning Along the Statistical Garden Path
, 2009
"... Previous studies of auditory statistical learning have typically presented learners with sequential structural information that is uniformly distributed across the entire exposure corpus. Here we present learners with nonuniform distributions of structural information by altering the organization of ..."
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Previous studies of auditory statistical learning have typically presented learners with sequential structural information that is uniformly distributed across the entire exposure corpus. Here we present learners with nonuniform distributions of structural information by altering the organization of trisyllabic nonsense words at midstream. When this structural change was unmarked by lowlevel acoustic cues, or even when cued by a pitch change, only the first of the two structures was learned. However, both structures were learned when there was an explicit cue to the midstream change or when exposure to the second structure was tripled in duration. These results demonstrate that successful extraction of the structure in an auditory statistical learning task reduces the ability to learn subsequent structures, unless the presence of two structures is marked explicitly or the exposure to the second is quite lengthy. The mechanisms by which learners detect and use changes in distributional information to maintain sensitivity to multiple structures are discussed from both behavioral and computational perspectives.
On the Vocabulary of GrammarBased Codes and the Logical Consistency of Texts
, 2008
"... The article presents a new interpretation for Zipf’s law in natural language which relies on two areas of information theory. We reformulate the problem of grammarbased compression and investigate properties of strongly nonergodic stationary processes. The motivation for the joint discussion is to ..."
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The article presents a new interpretation for Zipf’s law in natural language which relies on two areas of information theory. We reformulate the problem of grammarbased compression and investigate properties of strongly nonergodic stationary processes. The motivation for the joint discussion is to prove a proposition with a simple informal statement: If an nletter long text describes n β independent facts in a random but consistent way then the text contains at least n β /log n different words. In the formal statement, two specific postulates are adopted. Firstly, the words are understood as the nonterminal symbols of the shortest grammarbased encoding of the text. Secondly, the texts are assumed to be emitted by a nonergodic source, with the described facts being binary IID variables that are asymptotically predictable in a shiftinvariant way. The proof of the formal proposition applies several new tools. These
Predictive information and emergent cooperativity in a chain of mobile robots
"... Measures of complexity are of immediate interest for the field of autonomous robots both as a means to classify the behavior and as an objective function for the autonomous development of robot behavior. In the present paper we consider predictive information in sensor space as a measure for the beh ..."
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Measures of complexity are of immediate interest for the field of autonomous robots both as a means to classify the behavior and as an objective function for the autonomous development of robot behavior. In the present paper we consider predictive information in sensor space as a measure for the behavioral complexity of a chain of twowheel robots which are passively coupled and controlled by a closedloop reactive controller for each of the individual robots. The predictive information, the mutual information between the past and the future of a time series, is approximated by restricting the time horizons to a single time step. This is exact for Markovian systems but seems to work well also for our robotic system which is strongly nonMarkovian.When in a maze with many obstacles, the approximated predictive information of the sensor values of an individual robot is found to have a clear maximum for a controller which realizes the spontaneous cooperation of the robots in the chain so that large areas of the maze can be visited.
Statistical inference using weak chaos and infinite memory
 In Proceedings of the Int’l Workshop on StatisticalMechanical Informatics (IWSMI 2010
, 2010
"... Abstract. We describe a class of deterministic weakly chaotic dynamical systems with infinite memory. These “herding systems ” combine learning and inference into one algorithm, where moments or dataitems are converted directly into an arbitrarily long sequence of pseudosamples. This sequence has i ..."
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Abstract. We describe a class of deterministic weakly chaotic dynamical systems with infinite memory. These “herding systems ” combine learning and inference into one algorithm, where moments or dataitems are converted directly into an arbitrarily long sequence of pseudosamples. This sequence has infinite range correlations and as such is highly structured. We show that its information content, as measured by subextensive entropy, can grow as fast as K log T, which is faster than the usual 1 2 K log T for exchangeable sequences generated by random posterior sampling from a Bayesian model. In one dimension we prove that herding sequences are equivalent to Sturmian sequences which have complexity exactly log(T + 1). More generally, we advocate the application of the rich theoretical framework around nonlinear dynamical systems, chaos theory and fractal geometry to statistical learning. 1.
Information Driven Self Organization of Complex Robotic Behaviors
, 2013
"... SFI Working Papers contain accounts of scienti5ic work of the author(s) and do not necessarily represent the views of the Santa Fe Institute. We accept papers intended for publication in peer‐reviewed journals or proceedings volumes, but not papers that have already appeared in print. Except for pa ..."
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SFI Working Papers contain accounts of scienti5ic work of the author(s) and do not necessarily represent the views of the Santa Fe Institute. We accept papers intended for publication in peer‐reviewed journals or proceedings volumes, but not papers that have already appeared in print. Except for papers by our external faculty, papers must be based on work done at SFI, inspired by an invited visit to or collaboration at SFI, or funded by an SFI grant. ©NOTICE: This working paper is included by permission of the contributing author(s) as a means to ensure timely distribution of the scholarly and technical work on a non‐commercial basis. Copyright and all rights therein are maintained by the author(s). It is understood that all persons copying this information will adhere to the terms and constraints invoked by each author's copyright. These works may be reposted only with the explicit permission of the copyright holder. www.santafe.edu SANTA FE INSTITUTEInformation driven selforganization of complex robotic behaviors
Thinking about the brain
 Physics of Biomolecules and Cells
, 2002
"... We all are fascinated by the phenomena of intelligent behavior, as generated both by our own brains and by the brains of other animals. As physicists we would like to understand if there are some general principles that govern the structure and dynamics of the neural circuits that underlie these phe ..."
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We all are fascinated by the phenomena of intelligent behavior, as generated both by our own brains and by the brains of other animals. As physicists we would like to understand if there are some general principles that govern the structure and dynamics of the neural circuits that underlie these phenomena. At the molecular level there is an extraordinary universality, but these mechanisms are surprisingly complex. This raises the question of how the brain selects from these diverse mechanisms and adapts to compute “the right thing ” in each context. One approach is to ask what problems the brain really solves. There are several examples— from the ability of the visual system to count photons on a dark night to our gestalt recognition of statistical tendencies toward symmetry in random patterns—where the performance of the system in fact approaches some fundamental physical or statistical limits. This suggests that some sort of optimization principles may be at work, and there are examples
Embodied Inference: or “I think therefore I am, if I am what I think”
"... This chapter considers situated and embodied cognition in terms of the freeenergy principle. The freeenergy formulation starts with the premise that biological agents must actively resist a natural tendency to disorder. It appeals to the idea that agents are essentially inference machines that ..."
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This chapter considers situated and embodied cognition in terms of the freeenergy principle. The freeenergy formulation starts with the premise that biological agents must actively resist a natural tendency to disorder. It appeals to the idea that agents are essentially inference machines that