Under class imbalance, class embeddings and classifier weights in the unconstrained-features model interpolate a simplex-encoded label matrix whose SVD factors set their geometry, and convergence to this geometry worsens as imbalance grows

- Thrampoulidis, Kini, Vakilian and Behnia introduce Simplex-Encoded-Labels Interpolation (SELI) as an imbalance-invariant characterization of neural collapse: in the unconstrained-features model with cross-entropy and vanishing regularization, embeddings and classifiers interpolate a simplex-encoded label matrix and their geometries are set by its SVD factors; experiments on synthetic UFM data and on ResNet-18 and VGG-13 trained from scratch for 350 epochs on (R, 1/2)-step-imbalanced MNIST, Fashion-MNIST and CIFAR10 (R = 1, 5, 10, 100) show the distance to SELI decreasing during training and consistently smaller than to ETF, but convergence slows as imbalance grows (R = 100) and is worse for embeddings than for classifiers. The proof is for the UFM (a theoretical model); that deep nets approach SELI is stated as a conjecture supported by experiments, so directional wording. [thrampoulidis-etal-2022-imbalance-trouble-revisiting-neural-collapse-geometry]