Train One Sparse Autoencoder Across Multiple Sparsity Budgets to Preserve Interpretability and Accuracy

TL;DR

This paper introduces HierarchicalTopK, a novel training method for sparse autoencoders that enables a single model to optimize across multiple sparsity levels, balancing interpretability and accuracy efficiently.

Contribution

The paper proposes HierarchicalTopK, a new training objective allowing one SAE to handle multiple sparsity levels simultaneously, reducing computational costs and maintaining interpretability.

Findings

Achieves Pareto-optimal trade-offs between sparsity and explained variance.

Outperforms traditional SAEs trained at fixed sparsity levels.

Maintains high interpretability scores at increased sparsity.

Abstract

Sparse Autoencoders (SAEs) have proven to be powerful tools for interpreting neural networks by decomposing hidden representations into disentangled, interpretable features via sparsity constraints. However, conventional SAEs are constrained by the fixed sparsity level chosen during training; meeting different sparsity requirements therefore demands separate models and increases the computational footprint during both training and evaluation. We introduce a novel training objective, \emph{HierarchicalTopK}, which trains a single SAE to optimise reconstructions across multiple sparsity levels simultaneously. Experiments with Gemma-2 2B demonstrate that our approach achieves Pareto-optimal trade-offs between sparsity and explained variance, outperforming traditional SAEs trained at individual sparsity levels. Further analysis shows that HierarchicalTopK preserves high interpretability scores even at higher sparsity. The proposed objective thus closes an important gap between flexibility and interpretability in SAE design.