Sparse AutoEncoders (SAEs) have recently been employed as a promising unsupervised approach for understanding the representations of layers of Large Language Models (LLMs). However, with the growth in model size and complexity, training SAEs is computationally intensive, as typically one SAE is trained for each model layer. To address such limitation, we propose Group-SAE, a novel strategy to train SAEs. Our method considers the similarity of the residual stream representations between contiguous layers to group similar layers and train a single SAE per group. To balance the trade-off between efficiency and performance, we further introduce AMAD (Average Maximum Angular Distance), an empirical metric that guides the selection of an optimal number of groups based on representational similarity across layers. Experiments on models from the Pythia family show that our approach significantly accelerates training with minimal impact on reconstruction quality and comparable downstream task performance and interpretability over baseline SAEs trained layer by layer. This method provides an efficient and scalable strategy for training SAEs in modern LLMs.

Sparse AutoEncoders (SAEs) have gained popularity as a tool for enhancing the interpretability of Large Language Models (LLMs). However, training SAEs can be computationally intensive, especially as model complexity grows. In this study, the potential of transfer learning to accelerate SAEs training is explored by capitalizing on the shared representations found across adjacent layers of LLMs. Our experimental results demonstrate that fine-tuning SAEs using pre-trained models from nearby layers not only maintains but often improves the quality of learned representations, while significantly accelerating convergence. These findings indicate that the strategic reuse of pretrained SAEs is a promising approach, particularly in settings where computational resources are constrained.