# Representational Alignment Across Model Layers and Brain Regions with Multi-Level Optimal Transport

arXiv: https://arxiv.org/abs/2510.01706 · HTML: https://mlsanity.com/paper/2510.01706/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 32 references that are in the map.
- First posted on arXiv 2 Oct 2025.

## Builds on (most cited first, 11 of 11)

- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [MTEB: Massive Text Embedding Benchmark](https://mlsanity.com/paper/2210.07316/) (2022)
- [The Platonic Representation Hypothesis](https://mlsanity.com/paper/2405.07987/) (2024)
- [Revisiting Model Stitching to Compare Neural Representations](https://mlsanity.com/paper/2106.07682/) (2021)
- [Generalized Shape Metrics on Neural Representations](https://mlsanity.com/paper/2110.14739/) (2021)
- [Deep Neural Networks Reveal a Gradient in the Complexity of Neural Representations across the Brain's Ventral Visual Pathway](https://mlsanity.com/paper/1411.6422/) (2014)
- [Rosetta Neurons: Mining the Common Units in a Model Zoo](https://mlsanity.com/paper/2306.09346/) (2023)
- [Soft Matching Distance: A metric on neural representations that captures single-neuron tuning](https://mlsanity.com/paper/2311.09466/) (2023)
- [Universal dimensions of visual representation](https://mlsanity.com/paper/2408.12804/) (2024)

## Built on by (most cited first, 3 of 3)

- [Programs-of-Layers in LLMs through the Lens of Cortical Areas](https://mlsanity.com/paper/2609.31360/) (2026)
- [From Layers to Networks: Comparing Neural Representations via Diffusion Geometry](https://mlsanity.com/paper/2605.15901/) (2026)
- [Heterogeneous Ranking in Industrial-Scale Recommender Systems: A Case Study](https://mlsanity.com/paper/2607.27577/) (2026)

## Abstract (arXiv)

Standard representational similarity methods align each layer of a network to its best match in another independently, producing asymmetric results, lacking a global alignment score, and struggling with networks of different depths. These limitations arise from ignoring global activation structure and restricting mappings to rigid one-to-one layer correspondences. We propose Multi-Level Optimal Transport (MOT), a unified framework that jointly infers soft, globally consistent layer-to-layer couplings and neuron-level transport plans. MOT allows source neurons to distribute mass across multiple target layers while minimizing total transport cost under marginal constraints. This yields both a single alignment score for the entire network comparison and a soft transport plan that naturally handles depth mismatches through mass distribution. We evaluate MOT on vision models, large language models, and human visual cortex recordings. Across all domains, MOT matches or surpasses standard pairwise matching in alignment quality. Moreover, it reveals smooth, fine-grained hierarchical correspondences: early layers map to early layers, deeper layers maintain relative positions, and depth mismatches are resolved by distributing representations across multiple layers. These structured patterns emerge naturally from global optimization without being imposed, yet are absent in greedy layer-wise methods. MOT thus enables richer, more interpretable comparisons between representations, particularly when networks differ in architecture or depth. We further extend our method to a three-level MOT framework, providing a proof-of-concept alignment of two networks across their training trajectories and demonstrating that MOT uncovers checkpoint-wise correspondences missed by greedy layer-wise matching.