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

Sparse Autoencoders (SAEs) extract features from LLM internal activations, meant to correspond to interpretable concepts. A core SAE training hyperparameter is L0: how many SAE 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 inherently correct value aside from its effect on reconstruction. In this work we study the effect of L0 on SAEs, and show that if L0 is not set correctly, the SAE fails to disentangle 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 present a proxy metric that can help guide the search for the correct L0 for an SAE on a given training distribution. We show that our method finds the correct L0 in toy models and coincides with peak sparse probing performance in LLM SAEs. We find that most commonly used SAEs have an L0 that is too low. Our work shows that practitioners must set L0 correctly to train SAEs with monosemantic features.

Large language models (LLMs) are black boxes, and we struggle to understand what LLMs are thinking about. One popular technique to try to read the mind of a LLM is called a Sparse Autoencoder (SAE). However, when you use a sparse autoencoder, you need to set a parameter called L0 that determines how many concepts you think the model is thinking about at a time on average. Most people think that you can set any number for L0 and it is fine. However, this paper shows that is not the case: if you set L0 incorrectly, the sparse autoencoder can become corrupted. We show how this happens, and we introduce a metric you can use to tell if you are setting L0 too low.