Proto-EVFL: Enhanced Vertical Federated Learning via Dual Prototype with Extremely Unaligned Data

--In vertical federated learning (VFL), multiple enterprises address aligned sample scarcity by leveraging massive locally unaligned samples to facilitate collaborative learning. However, unaligned samples across different parties in VFL can be extremely class-imbalanced, leading to insufficient feature representation and limited model prediction space. Specifically, class-imbalanced problems consist of intra-party class imbalance and inter-party class imbalance, which can further cause local model bias and feature contribution inconsistency issues, respectively. T o address the above challenges, we propose Proto-EVFL, an enhanced VFL framework via dual prototypes. We first introduce class prototypes for each party to learn relationships between classes in the latent space, allowing the active party to predict unseen classes. We further design a probabilistic dual prototype learning scheme to dynamically select unaligned samples by conditional optimal transport cost with class prior probability. Moreover, a mixed prior guided module guides this selection process by combining local and global class prior probabilities. Finally, we adopt an adaptive gated feature aggregation strategy to mitigate feature contribution inconsistency by dynamically weighting and aggregating local features across different parties. We proved that Proto-EVFL, as the first bi-level optimization framework in VFL, has a convergence rate of 1 / T . Even in a zero-shot scenario with one unseen class, it outperforms baselines by at least 6.97%. NTRODUCTION indicates equal contribution, * represents the corresponding authors Wei Guo, Yiyang Duan and Fuzhen Zhuang are with the School of Artificial Intelligence, Beihang University, Beijing 100083, China (e-mail: { guowei, duanyiyang, zhuangfuzhen }@buaa.edu.cn). Xiao Zhang is with the School of Computer Science and Technology, Shan-dong University, Shandong 266237, China (e-mail: xiaozhang@sdu.edu.cn). Zhaojun Hu is with the Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing 100872, China (e-mail: huzhao-jun@ruc.edu.cn).