发表机构
Nanjing Normal University; Nanjing University of Chinese Medicine; Tohoku University（南京师范大学; 南京中医药大学; 东北大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究证明在概率对比学习中，共享温度并不直接对应共享角度尺度，并提出了vMF得分的前导角度增益理论，通过实验验证了其在多种数据集上的预测准确性，并展示了纯角度编辑对表示学习的改善作用。
AI 中文摘要
在概率对比学习中，共享温度通常被解释为共享相似度尺度，但这种解释对于高维分布类表示并不成立。我们研究了当表示维度和类浓度共同增长时，ProCo所使用的精确von Mises-Fisher（vMF）概率得分。我们证明了该得分保留了一个类依赖的前导角度增益$g_c=A_c/\ au$，其中$A_c$是平均合成长度。该增益进入Softmax竞争、成对决策边界和特征梯度。在真实的CIFAR-LT、ImageNet-LT和iNaturalist表示上，该理论准确预测了完整vMF得分下的边界移动和局部梯度变化。类级温度调整也改变了余弦零截距和有限维响应。我们构建了保持截距和纯角度控制，以将前导增益与这些伴随变化分开。完全增益均衡在首阶产生共享尺度余弦原型规则；有限维边际条件保证两个分类器的一致性。在16个冻结表示设置中，预测一致性为98.43%-99.99%，不一致集中在小的余弦边际处。在受控的仅对比训练中，使用训练频率先验，纯角度编辑在所有测试的CIFAR-10/100不平衡因子下改善了两种学习表示，并在ImageNet-LT上保持积极变化。因此，vMF浓度不仅描述了类分布，还在高维概率对比学习中形成了决策和学习尺度。
英文摘要
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 gradient changes under the full vMF score. Classwise temperature adjustment also changes the cosine-zero intercept and finite-dimensional response. We construct intercept-preserving and Pure Angular controls to separate the leading gain from these accompanying changes. Complete gain equalization yields a shared-scale cosine prototype rule at leading order; a finite-dimensional margin condition guarantees agreement of the two classifiers. Across 16 frozen representation settings, prediction agreement is 98.43-99.99%, with disagreements concentrated at small cosine margins. In controlled contrastive-only training with the training-frequency prior, Pure Angular editing improves both learned representations at all tested CIFAR-10/100 imbalance factors and retains positive changes on ImageNet-LT. Thus vMF concentration not only describes class distributions, but also forms a decision and learning scale in high-dimensional probabilistic contrastive learning.
Comments59 pages, including supplementary material
