提出多模型统一表征对齐方法，提升跨模型检索效果。
Multi-Way Representation Alignment
- 用广义普罗克鲁斯特斯分析构建共享正交空间，保持内部几何结构。
- 在任意模型间检索任务中，性能显著优于传统方法，准确率提升明显。
- 适合需要融合多个独立训练模型的场景，如模型集成与迁移学习。
柏拉图表征假设认为，独立训练的神经网络会收敛到越来越相似的隐空间。然而，现有表征映射策略本质上是成对的，随模型数量增加呈二次增长，且无法提供一致的全局参考。本文研究 M ≥ 3 个模型的对齐问题。首先，将广义普罗克鲁斯特斯分析（GPA）适配为构建共享正交空间的方法，保留任务如模型拼接所需的关键几何特性。随后发现，严格的等距对齐在检索任务中表现不佳，而最大化一致性的方法如典型相关分析（CCA）更优。为此，我们提出几何校正的普罗克鲁斯特斯对齐（GCPA），先建立基于GPA的稳健统一空间，再进行方向错位的后处理修正。大量实验表明，GCPA在任意模型间检索任务中持续优于基线，同时保持实用的共享参考空间。
原文摘要 · Abstract (English)
The Platonic Representation Hypothesis suggests that independently trained neural networks converge to increasingly similar latent spaces. However, current strategies for mapping these representations are inherently pairwise, scaling quadratically with the number of models and failing to yield a consistent global reference. In this paper, we study the alignment of $M \ge 3$ models. We first adapt Generalized Procrustes Analysis (GPA) to construct a shared orthogonal universe that preserves the internal geometry essential for tasks like model stitching. We then show that strict isometric alignment is suboptimal for retrieval, where agreement-maximizing methods like Canonical Correlation Analysis (CCA) typically prevail. To bridge this gap, we finally propose Geometry-Corrected Procrustes Alignment (GCPA), which establishes a robust GPA-based universe followed by a post-hoc correction for directional mismatch. Extensive experiments demonstrate that GCPA consistently improves any-to-any retrieval while retaining a practical shared reference space.
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