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We reformulated this problem in the context of hierarchical convolutional neural networks (CNNs)\u2014whose architectures have been inspired by the hierarchical signal processing of the mammalian visual system\u2014and examined perceptual stability as an optimization process that identifies image-defining features for accurate image classification in the presence of movements. Movement signals, multiplexed with visual inputs along overlapping convolutional layers, aided classification invariance of shifted images by making the classification faster to learn and more robust relative to input noise. Classification invariance was reflected in activity manifolds associated with image categories emerging in late CNN layers and with network units acquiring movement-associated activity modulations as observed experimentally during saccadic eye movements. 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