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Research in human vision has shown that visual recognition is achieved through the interaction of a number of specialized brain areas in the ventral and dorsal visual stream. The most influential models of visual perception theorize a feedforward, unidirectional flow of information from low-level to high-level areas. However, growing evidence suggests, on the one hand, that lateral connections and connections from high- to low-level areas (i.e., top-down connections) may be crucially involved in more challenging object recognition tasks, and on the other hand that recurrent networks show higher correlation and have better predictivity of brain data. In this study, we explore the functional role of feedback connections in computational models of vision. To do so, we trained several Convolutional Neural Networks (CNNs) with and without recurrent connections (within layers, top-down, top-down + within) to perform object recognition tasks in relatively easy (e.g., normal stimuli) and more challenging (e.g., low/high partial occlusion, deletion, clutter, phase scrambling) conditions. Preliminary data shows an effect of the manipulation, where challenging tasks are indeed more problematic to solve, and, most importantly, are associated with higher average performance of the networks with recurrent processing. Across our recurrent networks, our data shows highest performance for the top-down + within network, and different -- but complementary -- advantages of the within and top-down networks over the feedforward ones. Overall, our results suggest that i) feedback processing in CNNs is critical to solve challenging visual tasks, and ii) that within layers and top-down signals have different functional roles -- i.e., different tasks are solved by different feedback connection types.