# Barycentric alignment for instance-level comparison of neural representations

arXiv: https://arxiv.org/abs/2602.09225 · HTML: https://mlsanity.com/paper/2602.09225/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 32 references that are in the map.
- First posted on arXiv 9 Feb 2026.

## Builds on (most cited first, 16 of 16)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [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)
- [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)
- [The Platonic Representation Hypothesis](https://mlsanity.com/paper/2405.07987/) (2024)
- [Insights on representational similarity in neural networks with canonical correlation](https://mlsanity.com/paper/1806.05759/) (2018)
- [Re-evaluating Automatic Metrics for Image Captioning](https://mlsanity.com/paper/1612.07600/) (2016)
- [Investigating the Effects of Fairness Interventions Using Pointwise Representational Similarity](https://mlsanity.com/paper/2305.19294/) (2023)

## Abstract (arXiv)

Comparing representations across neural networks is challenging because representations admit symmetries, such as arbitrary reordering of units or rotations of activation space, that obscure underlying equivalence between models. We introduce a barycentric alignment framework that quotients out these nuisance symmetries to construct a universal embedding space across many models. Unlike existing similarity measures, which summarize relationships over entire stimulus sets, this framework enables similarity to be defined at the level of individual stimuli, revealing inputs that elicit convergent versus divergent representations across models. Using this instance-level notion of similarity, we identify systematic input properties that predict representational convergence versus divergence across vision and language model families. We also construct universal embedding spaces for brain representations across individuals and cortical regions, enabling instance-level comparison of representational agreement across stages of the human visual hierarchy. Finally, we apply the same barycentric alignment framework to purely unimodal vision and language models and find that post-hoc alignment into a shared space yields image text similarity scores that closely track human cross-modal judgments and approach the performance of contrastively trained vision-language models. This strikingly suggests that independently learned representations already share sufficient geometric structure for human-aligned cross-modal comparison. Together, these results show that resolving representational similarity at the level of individual stimuli reveals phenomena that cannot be detected by set-level comparison metrics.