# What Converges in the Platonic Representation Hypothesis? Structure over Geometry

arXiv: https://arxiv.org/abs/2609.27252 · HTML: https://mlsanity.com/paper/2609.27252/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 44 references that are in the map.
- First posted on arXiv 23 Sep 2026.

## Builds on (most cited first, 28 of 28)

- [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)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [VideoMAE: Masked Autoencoders are Data-Efficient Learners for Self-Supervised Video Pre-Training](https://mlsanity.com/paper/2203.12602/) (2022)
- [Reproducible scaling laws for contrastive language-image learning](https://mlsanity.com/paper/2212.07143/) (2022)
- [How to train your ViT? Data, Augmentation, and Regularization in Vision Transformers](https://mlsanity.com/paper/2106.10270/) (2021)
- [Perception Encoder: The best visual embeddings are not at the output of the network](https://mlsanity.com/paper/2504.13181/) (2025)
- [Insights on representational similarity in neural networks with canonical correlation](https://mlsanity.com/paper/1806.05759/) (2018)
- [WIT: Wikipedia-based Image Text Dataset for Multimodal Multilingual Machine Learning](https://mlsanity.com/paper/2103.01913/) (2021)
- [Convergent Learning: Do different neural networks learn the same representations?](https://mlsanity.com/paper/1511.07543/) (2015)
- [Revisiting Model Stitching to Compare Neural Representations](https://mlsanity.com/paper/2106.07682/) (2021)
- [Getting aligned on representational alignment](https://mlsanity.com/paper/2310.13018/) (2023)
- [Similarity of Neural Network Models: A Survey of Functional and Representational Measures](https://mlsanity.com/paper/2305.06329/) (2023)
- [Topological Autoencoders](https://mlsanity.com/paper/1906.00722/) (2019)
- [Generalized Shape Metrics on Neural Representations](https://mlsanity.com/paper/2110.14739/) (2021)
- [PerceptionLM: Open-Access Data and Models for Detailed Visual Understanding](https://mlsanity.com/paper/2504.13180/) (2025)
- [Representation Topology Divergence: A Method for Comparing Neural Network Representations](https://mlsanity.com/paper/2201.00058/) (2021)
- [Towards Understanding Learning Representations: To What Extent Do Different Neural Networks Learn the Same Representation](https://mlsanity.com/paper/1810.11750/) (2018)
- [Revisiting the Platonic Representation Hypothesis: An Aristotelian View](https://mlsanity.com/paper/2602.14486/) (2026)
- [Understanding the Emergence of Multimodal Representation Alignment](https://mlsanity.com/paper/2502.16282/) (2025)
- [RTD-Lite: Scalable Topological Analysis for Comparing Weighted Graphs in Learning Tasks](https://mlsanity.com/paper/2503.11910/) (2025)
- [Topological Alignment of Shared Vision-Language Embedding Space](https://mlsanity.com/paper/2510.10889/) (2025)
- [Topology-Aware Representation Alignment for Semi-Supervised Vision-Language Learning](https://mlsanity.com/paper/2604.26370/) (2026)
- [Scalable and Interpretable Representation Alignment with Ordinal Similarity](https://mlsanity.com/paper/2606.16379/) (2026)

## Built on by (most cited first, 1 of 1)

- [Shared Geometry As A Rosetta Stone: Cross-Modal Alignment Without Paired Data](https://mlsanity.com/paper/2610.09411/) (2026)

## Abstract (arXiv)

The Platonic Representation Hypothesis suggests that increasingly capable models converge toward shared representations. Recent work narrows this claim to shared local neighborhood relationships, finding that capacity-dependent trends in several global similarity measures largely disappear after calibration. We challenge this interpretation by showing that prior local-global comparisons confound structural scale (local versus global) with what is compared: relational structure, defined by which samples are related, versus metric geometry, characterized by quantitative relations such as distances, similarities, or correlations. To disentangle these factors, we construct a controlled 2×2 framework that evaluates both relational structure and metric geometry at local and global scales. We introduce H0 skeleton overlap as a global counterpart to mutual k-nearest neighbors, together with matched distance-aware variants. Across vision-language models, relational structure exhibits robust representational convergence at both scales after calibration, whereas increasingly stringent distance agreement substantially weakens alignment and progressively flattens the capacity-dependent trend. We further extend the analysis beyond ambient Euclidean geometry by evaluating distance agreement under a Riemannian metric approximation and recover the same structure-geometry pattern. The pattern is also reproduced in video-text representations. Together, these results show that relational convergence extends beyond local neighborhoods to global spanning structure, whereas metric geometry exhibits substantially weaker convergence.