A real ResNet-50 trained with hard-negative contrastive losses and unit-ball normalization converges to Neural-Collapse ETF geometry on CIFAR-100, while omitting either yields Dimensional-Collapse instead

A real ResNet-50 is trained from scratch for 400 epochs (Adam, batch size 512) on real CIFAR-100 (and CIFAR-10, TinyImageNet) with representation dimension set to d = C - 1 and unit-ball/unit-sphere feature normalization, under supervised and unsupervised hard-negative contrastive losses (HSCL, HUCL) [jiang-etal-2023-hard-negative-sampling-neural-dimensional-collapse] Under these conditions the trained representations converge to Neural-Collapse (NC) geometry -- class means forming an Equiangular Tight Frame, measured via the zero-sum, unit-norm, and equal-inner-product metrics matching their theoretical minima -- for a range of hardness levels and batch sizes from 64 to 512 [jiang-etal-2023-hard-negative-sampling-neural-dimensional-collapse] Without incorporating hard negatives or feature normalization, Adam optimization of the same losses on the same real ResNet-50/CIFAR-100 setup instead produces Dimensional-Collapse (DC), failing to attain the NC-ETF geometry [jiang-etal-2023-hard-negative-sampling-neural-dimensional-collapse]