Human vision is foveated and active: resolution is highest at the fovea and falls off towards the periphery, and fixations are actively directed to locations of interest. Building a machine system that processes information in the same way lets us study gaze behavior in a controlled setting where the system's components and objectives are known. The emergence of gaze characteristics can therefore be examined systematically, which may in turn inform our understanding of biological vision. This requires a model that can sample like the fovea, handle various tasks from classification to dense prediction, and be trained concurrently with a fixation policy. In our study, we present such a system and study its capabilities and the fixation policies that emerge from it. Our system, FoAViS, samples visual input by adopting the established log-polar foveation and accumulates information in a 2D spatial memory. Due to its 2D structure, the same memory can be read out globally for classification or densely for semantic segmentation, without any architectural change. Fixations are drawn from a 2D map by a policy trained concurrently with the task. We find that learned fixation policies select more informative, task-specific locations than non-learned heuristics. These policies also shape the task representations in a beneficial way: for both classification and segmentation, models trained concurrently with a policy outperform models trained with random locations, even when the latter are provided with learned scanpaths. Moreover, these scanpaths exhibit similarities to human gaze behavior by capturing aspects of empirical scanpath characteristics. Our work marks an important step away from standard passive, single-pass architectures, towards biologically grounded models of vision. It opens a path for studying goal-directed gaze behavior and information representation in the visual system.

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