Summary

Context: Sparse Autoencoders (SAEs) reveal interpretable features in the activation spaces of language models. They achieve sparse, interpretable features by minimizing a loss function which includes an $ℓ_{1}$ penalty on the SAE hidden layer activations.
Problem & Hypothesis: While the SAE $ℓ_{1}$ penalty achieves sparsity, it has been argued that it can also cause SAEs to learn commonly-composed features rather than the “true” features in the underlying data.
Experiment: We propose a modified setup of Anthropic’s ReLU Output Toy Model where data vectors are made up of sets of composed features. We study the simplest possible version of this toy model with two hidden dimensions for ease of comparison to many of Anthropic’s visualizations.
- Features in a given set in our data are anticorrelated, and features are stored in antipodal pairs. Perhaps it’s a bit surprising that features are stored in superposition at all, because the features in the very small models we studied here are not sparse (they occur every-other data draw so have S ~ 0.5 in the language of Anthropic’s Toy Models paper)^[1].
Result: SAEs trained on the activations of these small toy models find composed features rather than the true features, regardless of learning rate or $ℓ_{1}$ coefficient used in SAE training.
- This finding largely persists even when we allow the SAE to see one-hot vectors of true features 75% of the time.
Future work: We see these models as a simple testing ground for proposed SAE training modifications. We share our code in the hopes that we can figure out, as a community, how to train SAEs that aren’t susceptible to this failure mode.

The diagram below gives a quick overview of what we studied and learned in this post:

Introduction

Last year, Anthropic and EleutherAI/Lee Sharkey's MATS stream showed that sparse autoencoders (SAEs) find human-interpretable “features” in language model activations. They achieve this interpretability by having sparse activations in the SAE hidden layer, such that only a small number of SAE features are active for any given token in the input data. While the objective of SAEs is, schematically, to “reconstruct model activations perfectly and do so while only having a few true features active on any given token,” the loss function used to train SAEs is a combinat...

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