# MetaSAEs: Joint Training with a Decomposability Penalty Produces More Atomic Sparse Autoencoder Latents

arXiv: https://arxiv.org/abs/2604.03436 · HTML: https://mlsanity.com/paper/2604.03436/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Sparse autoencoder training and evaluation, one of 13 directions in Mechanistic interpretability.
- Builds on 6 of its 15 references that are in the map.
- First posted on arXiv 3 Apr 2026.

## Placed in

- Mechanistic interpretability / [Sparse autoencoder training and evaluation](https://mlsanity.com/mechinterp/sparse-autoencoder-training-and-evaluation/)

## Builds on (most cited first, 6 of 6)

- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2](https://mlsanity.com/paper/2408.05147/) (2024)
- [Automatically Interpreting Millions of Features in Large Language Models](https://mlsanity.com/paper/2410.13928/) (2024)

## Abstract (arXiv)

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 |varphi| 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% DeltaFuzz. 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.