# Semantic Optimal Transport for Sparse Autoencoder Feature Matching and Circuit Compression

arXiv: https://arxiv.org/abs/2605.28567 · HTML: https://mlsanity.com/paper/2605.28567/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in SAE features and their applications, one of 13 directions in Mechanistic interpretability.
- Builds on 14 of its 38 references that are in the map.
- First posted on arXiv 27 May 2026.

## Placed in

- Mechanistic interpretability / [SAE features and their applications](https://mlsanity.com/mechinterp/sae-features-and-their-applications/)

## Builds on (most cited first, 14 of 14)

- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2](https://mlsanity.com/paper/2408.05147/) (2024)
- [Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoders](https://mlsanity.com/paper/2407.14435/) (2024)
- [Attribution Patching Outperforms Automated Circuit Discovery](https://mlsanity.com/paper/2310.10348/) (2023)
- [BatchTopK Sparse Autoencoders](https://mlsanity.com/paper/2412.06410/) (2024)
- [Do I Know This Entity? Knowledge Awareness and Hallucinations in Language Models](https://mlsanity.com/paper/2411.14257/) (2024)
- [I Have Covered All the Bases Here: Interpreting Reasoning Features in Large Language Models via Sparse Autoencoders](https://mlsanity.com/paper/2503.18878/) (2025)
- [Overcoming Sparsity Artifacts in Crosscoders to Interpret Chat-Tuning](https://mlsanity.com/paper/2504.02922/) (2025)
- [Mechanistic Permutability: Match Features Across Layers](https://mlsanity.com/paper/2410.07656/) (2024)
- [Analyze Feature Flow to Enhance Interpretation and Steering in Language Models](https://mlsanity.com/paper/2502.03032/) (2025)

## Built on by (most cited first, 2 of 2)

- [Weights Read and Write Features: Scalable Parameter Decomposition Grounded in Activation Space](https://mlsanity.com/paper/2609.37731/) (2026)
- [Sparse Autoencoders for Mechanistic Interpretability in NLP: A Critical Survey of Recoverability, Interpretability, and Utility](https://mlsanity.com/paper/2610.20139/) (2026)

## Abstract (arXiv)

Sparse autoencoders (SAEs) have become a central tool for interpreting language models. However, two key SAE analyses that remain difficult to scale are (1) matching semantically similar features across multi-layers and (2) compressing large feature circuits into interpretable supernodes. Although these have been treated as separate problems, we show that both are instances of a more fundamental challenge, which we frame as the estimation of semantic distances between SAE features that lie on different activation manifolds. We introduce a distributional framework for this problem, in which each feature is represented not by a single decoder vector like in the literature, but by an activation-weighted distribution over the hidden states that express it. By projecting these distributions into a shared reference space and comparing them with Wasserstein distance, our method provides a unified semantic metric for cross-layer feature comparison. We prove that our representation is invariant to activation rescaling, stable under perturbations, and recovers true matches under finite-sample margin conditions. Empirically, our method outperforms decoder-vector and LLM-based baselines and captures subtle functional distinctions between related features. Notably, our method compresses large feature circuits into interpretable supernodes automatically.