Semantic Optimal Transport for Sparse Autoencoder Feature Matching and Circuit Compression
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913168287072256 |
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| author | Cao, Tue M. Do, Nguyen Thai, My T. |
| author_facet | Cao, Tue M. Do, Nguyen Thai, My T. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28567 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Semantic Optimal Transport for Sparse Autoencoder Feature Matching and Circuit Compression Cao, Tue M. Do, Nguyen Thai, My T. Machine Learning Artificial Intelligence 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. |
| title | Semantic Optimal Transport for Sparse Autoencoder Feature Matching and Circuit Compression |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2605.28567 |