Similar Accuracy but Different Topographies under Cross-Entropy and Contrastive Learning

The brain’s topographic organization has motivated topographic deep neural networks (TDNNs) as models of perceptual and conceptual representation. However, prior TDNN studies largely paired topography with cross-entropy (CE). They have not examined whether contrastive objectives are generally compatible with topographic training, how topographic strength affects run-to-run representational consistency, or what failure modes limit the effect of the topographic constraint. We addressed these issues by training TDNNs on CIFAR-10 with a local topographic loss that minimized the average l2 distance between afferent weight vectors of neighboring units. We compared four objectives: CE, supervised contrastive, self-supervised SimCLR, and a label-aware contrastive margin loss reflecting an animacy hierarchy. Across topographic strengths, label-supervised objectives maintained high accuracy, produced smooth activation maps, and increased within-class similarity relative to CE. Two factors limited the impact of the topographic loss: 1) dropout was required to obtain smooth maps rather than sparse activations; 2) under strong penalties, networks reduced the topographic loss by shrinking weight norms rather than aligning weight directions. We also found that stronger topographic constraints reduced cross-seed representational consistency, indicating multiple comparably good topographic solutions. Nonetheless, ensembles built from sets of less-consistent models only slightly outperformed ensembles without topographic constraints. Our results indicate that contrastive objectives are a robust option for training topographic networks, producing good accuracy and high within-class similarity. The findings also identify boundary conditions for afferent-weight similarity as a topographic prior.