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Coherent information structure in complex computation

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Abstract

We have recently presented a framework for the information dynamics of distributed computation that locally identifies the component operations of information storage, transfer, and modification. We have observed that while these component operations exist to some extent in all types of computation, complex computation is distinguished in having coherent structure in its local information dynamics profiles. In this article, we conjecture that coherent information structure is a defining feature of complex computation, particularly in biological systems or artificially evolved computation that solves human-understandable tasks. We present a methodology for studying coherent information structure, consisting of state-space diagrams of the local information dynamics and a measure of structure in these diagrams. The methodology identifies both clear and “hidden” coherent structure in complex computation, most notably reconciling conflicting interpretations of the complexity of the Elementary Cellular Automata rule 22.

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Notes

  1. See also (Shalizi et al. 2006) for a discussion of the term “coherent structure” referring to particles (including blinkers) in this context.

  2. Measured using the CimulA package (Rouquier 2005) over 600 time steps of 100,000 cells, with light cone depths of three time steps.

  3. Similar arguments are derived from average values of the separable information in (Lizier 2010), where collisions or non-trivial information modification events are observed to be frequent in chaotic dynamics (disturbing coherent computation) and comparatively rare in complex dynamics where they can have high impact in coherent computation.

  4. Indeed, the candidate measures considered in “Average information dynamics in CAs” did not capture its alignment with the known complex rules in this respect.

  5. On close inspection of the local information transfer profile for rule 22 in Fig. 1h, there do appear to be some weak coherent information transfer structures corresponding to the diagonal edges of the large white triangles in the raw states in Fig. 1b. They are weak or subtle in comparison to the gliders in rule 110 since they do not stand out against other information transfer in the background. That said, it is possibly these structures which are being captured as the coherent information structure by our analysis of rule 22 here. This would be interesting, since these triangular structures in rule 22 are related to the fractality of the “Sierpinski Gasket” that it can produce (Wolfram 2002).

  6. For example, t c(i, j =  −1, n, k) is almost completely specified by a(i, n, k) and t(i, j = 1, n, k) in ECAs, except for any difference in h(i, n) between the “0” and “1” states.

  7. This is similar to the manner in which the local information dynamics measures themselves reveal more about the underlying computation than their averages do.

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Authors and Affiliations

  1. CSIRO Information and Communications Technology Centre, P.O. Box 76, Epping, NSW, 1710, Australia

    Joseph T. Lizier & Mikhail Prokopenko

  2. School of Information Technologies, The University of Sydney, Sydney, NSW, 2006, Australia

    Joseph T. Lizier & Albert Y. Zomaya

  3. Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103, Leipzig, Germany

    Joseph T. Lizier

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  1. Joseph T. Lizier
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  2. Mikhail Prokopenko
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Correspondence to Joseph T. Lizier.

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Lizier, J.T., Prokopenko, M. & Zomaya, A.Y. Coherent information structure in complex computation. Theory Biosci. 131, 193–203 (2012). https://doi.org/10.1007/s12064-011-0145-9

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