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 comparing 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. We evaluate the trained models on classification accuracy, robustness to weight perturbations and input degradation, the spatial organization of learned representations, and development of category-selective "expert units" in the penultimate layer. Both losses changed inter-unit correlation structure, but in qualitatively different ways. WS produced smooth topographies, with correlated neighborhoods. In contrast, AS produced a bimodal inter-unit correlation structure that lacked spatial smoothness. AS and WS training increased robustness relative to control (non-topographic) models: AS improved robustness to image degradation on CIFAR-10, WS did so on MNIST, and both improved robustness to weight perturbations. WS was also associated with greater input sensitivity at the unit level and stronger functional localization. In addition, as compared to control models, both AS and WS produced differences in orientation tuning, symmetry sensitivity, and eccentricity profiles of units. Together, these results show that local topographic regularization can improve robustness during end-to-end training while systematically reshaping representational structure.

翻译：地形卷积神经网络（TCNNs）是一种能够模拟大脑空间与功能组织特征的计算模型。然而，目前尚不清楚不同类型的地形正则化在端到端训练过程中如何影响鲁棒性、表征结构及功能组织。本研究通过比较两种应用于倒数第二层地形网格的局部空间损失函数训练的TCNNs来探讨该问题：i）权重相似性（WS），其目标函数惩罚相邻单元输入权重向量之间的差异；ii）激活相似性（AS），其目标函数惩罚相邻单元在刺激响应中激活模式的差异。我们从分类准确率、权重扰动与输入退化的鲁棒性、学习表征的空间组织，以及倒数第二层中类别选择性“专家单元”的形成等方面评估训练模型。两种损失函数均改变了单元间相关结构，但方式存在质的不同：WS产生具有空间相关邻域的光滑地形，而AS则产生缺乏空间平滑性的双峰型单元间相关结构。相较于对照（非地形）模型，AS与WS训练均提升了鲁棒性：AS在CIFAR-10数据集上增强了对图像退化的鲁棒性，WS在MNIST数据集上表现更优，两者均有效提升了权重扰动鲁棒性。WS还表现出单元层面更高的输入敏感性及更强的功能局部化特征。此外，与对照模型相比，AS和WS均导致单元在方向调谐、对称敏感性和离心率分布等方面产生系统性差异。这些结果表明，局部地形正则化能在端到端训练过程中提升鲁棒性，同时系统性地重塑神经网络的表征结构。