Sparse but Wrong: Incorrect L0 Leads to Incorrect Features in Sparse Autoencoders

Abstract: Sparse Autoencoders (SAEs) extract features from LLM internal activations, meant to correspond to single concepts. A core SAE training hyperparameter is L0: how many features should fire per token on average. Existing work compares SAE algorithms using sparsity--reconstruction tradeoff plots, implying L0 is a free parameter with no single correct value. In this work we study the effect of L0 on BatchTopK SAEs, and show that if L0 is not set precisely, the SAE fails to learn the underlying features of the LLM. If L0 is too low, the SAE will mix correlated features to improve reconstruction. If L0 is too high, the SAE finds degenerate solutions that also mix features. Further, we demonstrate a method to determine the correct L0 value for an SAE on a given training distribution, which finds the true L0 in toy models and coincides with peak sparse probing performance in LLMs. We find that most commonly used SAEs have an L0 that is too low. Our work shows that, to train SAEs with correct features, practitioners must set L0 correctly.