Schema Selection and Stochastic Inference in Modular Environments

Abstract

Given a set of stimuli presenting views of some environment, how can one characterize the natural modules or “objects ” that compose the environment? Should a given set of items be encoded as a collection of instances or as a set of rules? Restricted formulations of these questions are addressed by analysis within a new mathematical framework that describes stochastic parallel computation. An algorithm is given for simulating this computation once schemas encoding the modules of the environment have been seIected. The concept of computational temperature is introduced. As this temperature is Iowered, the system appears to display a dramatic tendency to interpret input, even if the evidence for any particular interpretation is very weak. IIltrodoction Our sensory systems are capabIe of representing a vast number of possible stimuli. Our environment presents us with only a smaI1 fraction of the possibilities; this se&ted subset is characterized by many regularities. Our minds encode these regularities, and this gives us some ability to infer the probable current condition of unknown portions of the environment given some Iimited information about the current state. What kind of regularities exist in the environment, and how should they be encoded? This paper presents preliminary results of research founded on the hypothesis that in real environments there exist reguIarities that can be idealized as mathematical structures that are simpIe enough to be anaIyxabIe. Only the simpIest kind of reguhuity is considered here: I will assume that the environment contains modules (objects) that recur exactly, with various states of the environment being comprised of various combinations of these modules. Even this simplest kind of environmental regularity offers interesting Iearning problems and results. It also serves to introduce a general framework capable of treating more subtle types of regularities. And the probIem considered is an important one, for the delineation of moduIes at one level of conceptual representation is a major step in the construction of higher Ievel representations.