Matéo Mahaut

Akshit Achara, Tatiana Gaintseva, Mateo Mahaut et al.

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.

Matéo Mahaut, Marco Baroni

Recent literature suggests that the bigger the model, the more likely it is to converge to similar, ``universal'' representations, despite different training objectives, datasets, or modalities. While this literature shows that there is an area where model representations are similar, we study here how vision models might get to those representations -- in particular, do they also converge to the same intermediate steps and operations? We therefore study the processes that lead to convergent representations in different models. First, we quantify distance between different model representations at different stages. We follow the evolution of distances between models throughout processing, identifying the processing steps which are most different between models. We find that while layers at similar positions in different models have the most similar representations, strong differences remain. Classifier models, unlike the others, will discard information about low-level image statistics in their final layers. CNN- and transformer-based models also behave differently, with transformer models applying smoother changes to representations from one layer to the next. These distinctions clarify the level and nature of convergence between model representations, and enables a more qualitative account of the underlying processes in image models.