[2Yin-B] Poster 4

[2Yin-B-61] Center-Dominant Classes and Label Dependence in the Geometric Structure of Low-Dimensional Classifiers

〇Mizuki Dai¹, Kenya Jin’no¹ (1. Graduate School of Tokyo City University)

Keywords:

Image Classification,CNN,Neural Collapse,Geometric Structure

Recent studies on Neural Collapse have shown that feature representations and classifier weights at the final layer converge to a regular geometric structure. However, under low-dimensional conditions where the feature dimension ($d=2$) is insufficient relative to the number of classes, the ideal structure does not hold, and the geometric behavior remains unclear. This study focuses on the central-dominant class structure observed in low-dimensional classifiers and examines the hypothesis that its emergence depends not only on the number of classes but also on label properties. Using CIFAR-10, we designed two class sets: Set-H, composed of labels frequently appearing as central-dominant classes, and Set-L, composed of labels with low frequency. Experiments were conducted with class counts of 4, 5, and 6, with 100 trials per condition. The results showed that the occurrence of the central-dominant structure increased with the number of classes in Set-H, whereas it was rarely observed in Set-L. Moreover, bird, cat, and deer were more likely to be selected as central-dominant classes. Inter-class Fisher distance analysis further indicated that these labels tended to have smaller distances to multiple classes. These findings suggest that classifier geometry under low-dimensional conditions depends not only on class number but also on label-specific properties.