MetaSAEs: Joint Training with a Decomposability Penalty Produces More Atomic Sparse Autoencoder Latents
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914445171621888 |
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| author | Levinson, Matthew |
| author_facet | Levinson, Matthew |
| contents | Sparse autoencoders (SAEs) are increasingly used for safety-relevant applications including alignment detection and model steering. These use cases require SAE latents to be as atomic as possible. Each latent should represent a single coherent concept drawn from a single underlying representational subspace. In practice, SAE latents blend representational subspaces together. A single feature can activate across semantically distinct contexts that share no true common representation, muddying an already complex picture of model computation. We introduce a joint training objective that directly penalizes this subspace blending. A small meta SAE is trained alongside the primary SAE to sparsely reconstruct the primary SAE's decoder columns; the primary SAE is penalized whenever its decoder directions are easy to reconstruct from the meta dictionary. This occurs whenever latent directions lie in a subspace spanned by other primary directions. This creates gradient pressure toward more mutually independent decoder directions that resist sparse meta-compression.
On GPT-2 large (layer 20), the selected configuration reduces mean $|φ|$ by 7.5% relative to an identical solo SAE trained on the same data. Automated interpretability (fuzzing) scores improve by 7.6%, providing external validation of the atomicity gain independent of the training and co-occurrence metrics. Reconstruction overhead is modest. Results on Gemma 2 9B are directional. On not-fully-converged SAEs, the same parameterization yields the best results, a $+8.6\%$ $Δ$Fuzz. Though directional, this is an encouraging sign that the method transfers to a larger model. Qualitative analysis confirms that features firing on polysemantic tokens are split into semantically distinct sub-features, each specializing in a distinct representational subspace. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_03436 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | MetaSAEs: Joint Training with a Decomposability Penalty Produces More Atomic Sparse Autoencoder Latents Levinson, Matthew Machine Learning Artificial Intelligence I.2 Sparse autoencoders (SAEs) are increasingly used for safety-relevant applications including alignment detection and model steering. These use cases require SAE latents to be as atomic as possible. Each latent should represent a single coherent concept drawn from a single underlying representational subspace. In practice, SAE latents blend representational subspaces together. A single feature can activate across semantically distinct contexts that share no true common representation, muddying an already complex picture of model computation. We introduce a joint training objective that directly penalizes this subspace blending. A small meta SAE is trained alongside the primary SAE to sparsely reconstruct the primary SAE's decoder columns; the primary SAE is penalized whenever its decoder directions are easy to reconstruct from the meta dictionary. This occurs whenever latent directions lie in a subspace spanned by other primary directions. This creates gradient pressure toward more mutually independent decoder directions that resist sparse meta-compression. On GPT-2 large (layer 20), the selected configuration reduces mean $|φ|$ by 7.5% relative to an identical solo SAE trained on the same data. Automated interpretability (fuzzing) scores improve by 7.6%, providing external validation of the atomicity gain independent of the training and co-occurrence metrics. Reconstruction overhead is modest. Results on Gemma 2 9B are directional. On not-fully-converged SAEs, the same parameterization yields the best results, a $+8.6\%$ $Δ$Fuzz. Though directional, this is an encouraging sign that the method transfers to a larger model. Qualitative analysis confirms that features firing on polysemantic tokens are split into semantically distinct sub-features, each specializing in a distinct representational subspace. |
| title | MetaSAEs: Joint Training with a Decomposability Penalty Produces More Atomic Sparse Autoencoder Latents |
| topic | Machine Learning Artificial Intelligence I.2 |
| url | https://arxiv.org/abs/2604.03436 |