Beyond topography: Topographic regularization improves robustness and reshapes representations in convolutional neural networks

Topographic convolutional neural networks (TCNNs) are computational models that can simulate aspects of the brain’s spatial and functional organization. However, it is unclear whether and how different types of topographic regularization shape robustness, representational structure, and functional organization during end-to-end training. We address this question by studying TCNNs trained with two local spatial losses applied to a penultimate-layer topographic grid: i ) Weight Similarity (WS), whose objective penalizes differences between neighboring units’ incoming weight vectors, and ii ) Activation Similarity (AS), whose objective penalizes differences between neighboring units’ activation patterns over stimuli. Relative to matched non-topographic controls, both regularizers generally improved robustness to input perturbations, reduced activation sparsity, and altered unit-level tuning profiles. In a larger-scale setting, topographic regularization also improved robustness to adversarial attacks. WS, but not AS, consistently increased robustness to weight perturbations and produced stronger signatures of functional localization. Both AS and WS also changed orientation tuning, symmetry sensitivity, and eccentricity profiles relative to control models. These findings show that local topographic regularization can improve robustness during end-to-end training while systematically reshaping representational structure, and that these effects depend strongly on how similarity is imposed.