Does a Shared Temperature Imply a Shared Angular Scale in Probabilistic Contrastive Learning?
In probabilistic contrastive learning, a shared temperature is commonly interpreted as a shared similarity scale, but this interpretation does not hold for high-dimensional distributional class representations. We study the exact von Mises-Fisher (vMF) probabilistic score used by ProCo when representation dimension and class concentration grow jointly. We prove that the score retains a class-dependent leading angular gain $g_c=A_c/τ$, where $A_c$ is the mean resultant length. This gain enters Softmax competition, pairwise decision boundaries, and feature gradients. On real CIFAR-LT, ImageNet-LT, and iNaturalist representations, the theory accurately predicts boundary movements and local g...
| Authors | Ningkang Peng, Qianfeng Yu, Jingyang Mao et al. |
|---|---|
| Primary category | cs.LG |
| Published | 30 September 2026 |
| Last updated at source | 30 September 2026 |
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