A real ResNet-18 trained on multi-label CIFAR-10 obeys a class-frequency-weighted prototype synthesis rule rather than uniform averaging, with collapse metrics tracking label imbalance

A real ResNet-18 is trained from scratch (SGD, batch 128, momentum 0.9, cosine-annealed learning rate 0.1 to 0.001, 200 epochs) on a real trained multi-label construction built from CIFAR-10 images (MLab-CIFAR10, 40,000 samples with per-sample label multiplicity up to 2) [ma-etal-2026-multi-label-neural-collapse-spectral-analysis] Testing whether higher-multiplicity class prototypes are the uniform average of their constituent single-label means, a Gram-residual alignment test shows the residual drops from 36.14 to 0.116 when the last-layer weight matrix is rescaled by the class-count-aware factor D^(-1/2) predicted by the paper's class-frequency-weighted synthesis rule, versus 2.33x10^5 under the wrong-direction D^(1/2) scaling [ma-etal-2026-multi-label-neural-collapse-spectral-analysis] As the class-imbalance ratio is reduced from 1.0 to 0.2 to 0.1 (epoch 200), the NC2 and NC3 Neural-Collapse collapse metrics increase monotonically, showing label imbalance systematically distorts the classical (balanced) Neural-Collapse geometry away from a symmetric Equiangular Tight Frame [ma-etal-2026-multi-label-neural-collapse-spectral-analysis]