Structure or Noise?

We show how rate-distortion theory provides a mechanism for automated theory building by naturally distinguishing between regularity and randomness. We start from the simple principle that model variables should, as much as possible, render the future and past conditionally independent. From this, we construct an objective function for model making whose extrema embody the trade-off between a model's structural complexity and its predictive power. The solutions correspond to a hierarchy of models that, at each level of complexity, achieve optimal predictive power at minimal cost. In the limit of maximal prediction the resulting optimal model identifies a process's intrinsic organization by extracting the underlying causal states. In this limit, the model's complexity is given by the statistical complexity, which is known to be minimal for achieving maximum prediction. Examples show how theory building can profit from analyzing a process's causal compressibility, which is reflected in the optimal models' rate-distortion curve--the process's characteristic for optimally balancing structure and noise at different levels of representation.Comment: 6 pages, 2 figures; http://cse.ucdavis.edu/~cmg/compmech/pubs/son.htm

The physical observer in a Szilard engine with uncertainty

Information engines model ``Maxwell's demon" mechanistically. However, the demon's strategy is pre-described by an external experimenter, and information engines are conveniently designed such that observables contain complete information about variables pertinent to work extraction. In real world scenarios, it is more realistic to encounter partial observability, which forces the physical observer, a necessary part of the information engine, to make inferences from incomplete knowledge. Here, we use the fact that an algorithm for computing optimal strategies can be directly derived from maximizing overall engine work output. For a stylizedly simple decision problem, we discover interesting optimal strategies that differ notably from naive coarse graining. They inspire simple, yet compelling, parameterized soft coarse grainings, as a model class of near-perfect approximations

Thermodynamically rational decision making under uncertainty

Inference principles are postulated within statistics, they are not usually derived from any underlying physical constraints on real world observers. An exception to this rule is that in the context of partially observable information engines decision making can be based solely on physical arguments. An inference principle can be derived from minimization of the lower bound on average dissipation [Phys. Rev. Lett., 124(5), 050601], which is achievable with a quasi-static process. Thermodynamically rational decision strategies can be computed algorithmically with the resulting approach. Here, we use this to study an example of binary decision making under uncertainty that is very simple, yet just interesting enough to be non-trivial: observations are either entirely uninformative, or they carry complete certainty about the variable that needs to be known for successful energy harvesting. Solutions found algorithmically can be expressed in terms of parameterized soft partitions of the observable space. This allows for their interpretation, as well as for the analytical calculation of all quantities that characterize the decision problem and the thermodynamically rational strategies.Comment: 7 pages, 3 figure