# Multi-Way Representation Alignment

arXiv: https://arxiv.org/abs/2602.06205 · HTML: https://mlsanity.com/paper/2602.06205/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 56 references that are in the map.
- First posted on arXiv 5 Feb 2026.

## Builds on (most cited first, 30 of 39)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [wav2vec 2.0: A Framework for Self-Supervised Learning of Speech Representations](https://mlsanity.com/paper/2006.11477/) (2020)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [ALBERT: A Lite BERT for Self-supervised Learning of Language Representations](https://mlsanity.com/paper/1909.11942/) (2019)
- [HuBERT: Self-Supervised Speech Representation Learning by Masked Prediction of Hidden Units](https://mlsanity.com/paper/2106.07447/) (2021)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [MiniLM: Deep Self-Attention Distillation for Task-Agnostic Compression of Pre-Trained Transformers](https://mlsanity.com/paper/2002.10957/) (2020)
- [MPNet: Masked and Permuted Pre-training for Language Understanding](https://mlsanity.com/paper/2004.09297/) (2020)
- [Large Dual Encoders Are Generalizable Retrievers](https://mlsanity.com/paper/2112.07899/) (2021)
- [The Platonic Representation Hypothesis](https://mlsanity.com/paper/2405.07987/) (2024)
- [Relative representations enable zero-shot latent space communication](https://mlsanity.com/paper/2209.15430/) (2022)
- [MASSIVE: A 1M-Example Multilingual Natural Language Understanding Dataset with 51 Typologically-Diverse Languages](https://mlsanity.com/paper/2204.08582/) (2022)
- [Similarity of Neural Network Models: A Survey of Functional and Representational Measures](https://mlsanity.com/paper/2305.06329/) (2023)
- [A Survey of Multi-View Representation Learning](https://mlsanity.com/paper/1610.01206/) (2016)
- [Unsupervised Alignment of Embeddings with Wasserstein Procrustes](https://mlsanity.com/paper/1805.11222/) (2018)
- [Towards Backward-Compatible Representation Learning](https://mlsanity.com/paper/2003.11942/) (2020)
- [Deep Multimodal Semantic Embeddings for Speech and Images](https://mlsanity.com/paper/1511.03690/) (2015)
- [Harnessing the Universal Geometry of Embeddings](https://mlsanity.com/paper/2505.12540/) (2025)
- [Latent Space Translation via Semantic Alignment](https://mlsanity.com/paper/2311.00664/) (2023)
- [ASIF: Coupled Data Turns Unimodal Models to Multimodal Without Training](https://mlsanity.com/paper/2210.01738/) (2022)
- [Learning Multilingual Word Embeddings in Latent Metric Space: A Geometric Approach](https://mlsanity.com/paper/1808.08773/) (2018)
- [Ranking the information content of distance measures](https://mlsanity.com/paper/2104.15079/) (2021)
- [Towards Universal Backward-Compatible Representation Learning](https://mlsanity.com/paper/2203.01583/) (2022)

## Built on by (most cited first, 5 of 5)

- [Evidence for Shared Routing Geometry and Dynamics in Sparse Mixture-of-Experts](https://mlsanity.com/paper/2609.02404/) (2026)
- [Model Merging: Foundations and Algorithms](https://mlsanity.com/paper/2605.01580/) (2026)
- [Spherical Interpolation for Backward-Compatible Multimodal Representations](https://mlsanity.com/paper/2609.39836/) (2026)
- [SuperAI: Merging Capabilities Across Heterogeneous Foundation Models](https://mlsanity.com/paper/2610.15322/) (2026)
- [What Makes a Latent Space Shared? Direct and Recoverable Compatibility in Motion VAEs](https://mlsanity.com/paper/2610.17376/) (2026)

## Abstract (arXiv)

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 ≥ 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.