Teach Old SAEs New Domain Tricks with Boosting

Sparse Autoencoders have emerged as powerful tools for interpreting the internal representations of Large Language Models, yet they often fail to capture domain-specific features not prevalent in their training corpora. This paper introduces a residual learning approach that addresses this feature blindness without requiring complete retraining. We propose training a secondary SAE specifically to model the reconstruction error of a pretrained SAE on domain-specific texts, effectively capturing features missed by the primary model. By summing the outputs of both models during inference, we demonstrate significant improvements in both LLM cross-entropy and explained variance metrics across multiple specialized domains. Our experiments show that this method efficiently incorporates new domain knowledge into existing SAEs while maintaining their performance on general tasks. This approach enables researchers to selectively enhance SAE interpretability for specific domains of interest, opening new possibilities for targeted mechanistic interpretability of LLMs.

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

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.

Train Sparse Autoencoders Efficiently by Utilizing Features Correlation

Sparse Autoencoders (SAEs) have demonstrated significant promise in interpreting the hidden states of language models by decomposing them into interpretable latent directions. However, training SAEs at scale remains challenging, especially when large dictionary sizes are used. While decoders can leverage sparse-aware kernels for efficiency, encoders still require computationally intensive linear operations with large output dimensions. To address this, we propose KronSAE, a novel architecture that factorizes the latent representation via Kronecker product decomposition, drastically reducing memory and computational overhead. Furthermore, we introduce mAND, a differentiable activation function approximating the binary AND operation, which improves interpretability and performance in our factorized framework.

Analyze Feature Flow to Enhance Interpretation and Steering in Language Models

We introduce a new approach to systematically map features discovered by sparse autoencoder across consecutive layers of large language models, extending earlier work that examined inter-layer feature links. By using a data-free cosine similarity technique, we trace how specific features persist, transform, or first appear at each stage. This method yields granular flow graphs of feature evolution, enabling fine-grained interpretability and mechanistic insights into model computations. Crucially, we demonstrate how these cross-layer feature maps facilitate direct steering of model behavior by amplifying or suppressing chosen features, achieving targeted thematic control in text generation. Together, our findings highlight the utility of a causal, cross-layer interpretability framework that not only clarifies how features develop through forward passes but also provides new means for transparent manipulation of large language models.