Multi-Way Representation Alignment
This addresses a scalability issue in multi-model representation alignment for researchers and practitioners in machine learning, though it is incremental as it builds on existing alignment methods.
The paper tackles the problem of aligning latent spaces of multiple neural networks, which scales quadratically with pairwise methods, by proposing Geometry-Corrected Procrustes Alignment (GCPA) to create a consistent global reference space, improving any-to-any retrieval performance.
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.