Intrinsic computation of a Monod-Wyman-Changeux molecule

Abstract

Causal states are minimal sufficient statistics of prediction of a stochastic process, their coding cost is called statistical complexity, and the implied causal structure yields a sense of the process' "intrinsic computation". We discuss how statistical complexity changes with slight variations on a biologically-motivated dynamical model, that of a Monod-Wyman-Changeux molecule. Perturbations to nonexistent transitions cause statistical complexity to jump from finite to infinite, while perturbations to existent transitions cause relatively slight variations in the statistical complexity. The same is not true for excess entropy, the mutual information between past and future. We discuss the implications of this for the relationship between intrinsic and useful computation of biological sensory systems.

arXiv commentThe main claim of the paper is actually incorrect due to a huge technical error, and although there are still correct results in this paper, this paper as written should be withdrawn

References in corpus (10)

• Computational Mechanics: Pattern and Prediction, Structure and Simplicity
• Short-Term Memory in Orthogonal Neural Networks
• Time's Barbed Arrow: Irreversibility, Crypticity, and Stored Information
• Anatomy of a Bit: Information in a Time Series Observation
• Prediction, Retrodiction, and The Amount of Information Stored in the Present
• Complexity Through Nonextensivity
• Informational and Causal Architecture of Discrete-Time Renewal Processes
• Informational and Causal Architecture of Continuous-time Renewal and Hidden Semi-Markov Processes
• Nearly Maximally Predictive Features and Their Dimensions
• Structure and Randomness of Continuous-Time Discrete-Event Processes