Semantic Optimal Transport for Sparse Autoencoder Feature Matching and Circuit Compression

• URL: http://arxiv.org/abs/2605.28567v1
• Date: Wed, 27 May 2026 14:54:58 GMT
• Title: Semantic Optimal Transport for Sparse Autoencoder Feature Matching and Circuit Compression
• Abstract summary: Two key SAE analyses that remain difficult to scale are matching semantically similar features across multi-layers and compressing large feature circuits into interpretable supernodes.<n>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.<n>We prove that our representation is invariant to activation rescaling, stable under perturbations, and recovers true matches under finite-sample margin conditions.
• Score: 11.444432919120173
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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