Unstable Features, Reproducible Subspaces: Understanding Seed Dependence in Sparse Autoencoders
Summary
This paper studies seed dependence in sparse autoencoders, finding that stable features carry most predictive signal while unstable features reflect reproducible low-dimensional subspaces.
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Paper page - Unstable Features, Reproducible Subspaces: Understanding Seed Dependence in Sparse Autoencoders
Source: https://huggingface.co/papers/2606.12138
Abstract
Sparse autoencoders exhibit feature stability patterns where stable features carry most predictive signal while unstable features reflect reproducible low-dimensional structure despite individual non-reproducibility.
Sparse autoencoders(SAEs) are widely used to interpret neural network representations, but their utility depends on whether the learned features are reproducible across training runs. We study this question throughfeature stability: for each SAE feature, we estimate the probability that a similar feature reappears in an independently trained SAE. This yields a scalable per-feature signal that separates stable from unstable features. In a large-scale study across seeds, models, layers, dictionary sizes, and SAE variants, we find a pronounced functional asymmetry: stable features carry most of the reconstruction- andprediction-relevant signal, while unstable features have weak marginal impact and are dominated by low-frequency surface-form triggers in bothactivation statisticsandautomatic explanations. Geometrically, unstable features are individually non-reproducible but concentrate in reproducible lower-rank subspaces, suggesting that seed dependence often reflectsbasis ambiguitywithin a shared region of activation space rather than pure noise. A controlled synthetic model makes this mechanism explicit, showing that low-rank ground-truth features can be recovered at the subspace level while remaining non-identifiable as individual SAE latents across seeds. Finally, by pooling uniquecross-seed features, we construct more stable SAEs while preservingexplained variancein this setting. Together, these results show that unstable features are not merely failed or noisy latents: they have weak individual functional impact, but reflect reproducible low-dimensional structure that standard SAEs resolve differently across seeds.
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