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Behavioral studies suggest that recurrence in the visual system is important for processing degraded stimuli. There are two broad anatomical forms this recurrence can take, lateral or feedback, each with different assumed functions. Here we add four different kinds of recurrence—two of each anatomical form—to a feedforward convolutional neural network and find all forms capable of increasing the ability of the network to classify noisy digit images. Specifically, we take inspiration from findings in biology by adding predictive feedback and lateral surround suppression. To compare these forms of recurrence to anatomically-matched counterparts we also train feedback and lateral connections directly to classify degraded images. Counter-intuitively, we find that the anatomy of the recurrence is not related to its function: both forms of task-trained recurrence change neural activity and behavior similarly to each other and differently from their bio-inspired anatomical counterparts. By using several analysis tools frequently applied to neural data, we identified the distinct strategies used by the predictive versus task-trained networks. Specifically, predictive feedback de-noises the representation of noisy images at the first layer of the network and decreases its dimensionality, leading to an expected increase in classification performance. Surprisingly, in the task-trained networks, representations are not de-noised over time at the first layer (in fact, they become ‘noiser’ and dimensionality increases) yet these dynamics do lead to de-noising at later layers. The analyses used here can be applied to real neural recordings to identify the strategies at play in the …