Optimal attentional allocation in the presence of capacity constraints in uncued and cued visual search

The vision sciences literature contains a large diversity of experimental and theoretical approaches to the study of visual attention. We argue that this diversity arises, at least in part, from the field's inability to unify differing theoretical perspectives. In particular, the field has been hindered by a lack of a principled formal framework for simultaneously thinking about both optimal attentional processing and capacity-limited attentional processing, where capacity is limited in a general, task-independent manner. Here, we supply such a framework based on rate-distortion theory (RDT) and optimal lossy compression. Our approach defines Bayes-optimal performance when an upper limit on information processing rate is imposed. In this article, we compare Bayesian and RDT accounts in both uncued and cued visual search tasks. We start by highlighting a typical shortcoming of unlimited-capacity Bayesian models that is not shared by RDT models, namely, that they often overestimate task performance when information-processing demands are increased. Next, we reexamine data from two cued-search experiments that have previously been modeled as the result of unlimited-capacity Bayesian inference and demonstrate that they can just as easily be explained as the result of optimal lossy compression. To model cued visual search, we introduce the concept of a "conditional communication channel." This simple extension generalizes the lossy-compression framework such that it can, in principle, predict optimal attentional-shift behavior in any kind of perceptual task, even when inputs to the model are raw sensory data such as image pixels. To demonstrate this idea's viability, we compare our idealized model of cued search, which operates on a simplified abstraction of the stimulus, to a deep neural network version that performs approximately optimal lossy compression on the real (pixel-level) experimental stimuli.