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

TY - JOUR

T1 - Beyond topography

T2 - Topographic regularization improves robustness and reshapes representations in convolutional neural networks

AU - Truong, Nhut

AU - Hasson, Uri

N1 - Publisher Copyright: © 2026 The Author(s)

PY - 2026/11/7

Y1 - 2026/11/7

N2 - 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.

AB - 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.

KW - Representation learning

KW - Robustness

KW - Spatial regularization

KW - Topographic neural networks

UR - https://www.scopus.com/pages/publications/105045225951

UR - https://www.scopus.com/pages/publications/105045225951#tab=citedBy

U2 - 10.1016/j.neucom.2026.134496

DO - 10.1016/j.neucom.2026.134496

M3 - Article

SN - 0925-2312

VL - 701

JO - Neurocomputing

JF - Neurocomputing

M1 - 134496

ER -