# Group-SAE: Efficient Training of Sparse Autoencoders for Large Language Models via Layer Groups

arXiv: https://arxiv.org/abs/2410.21508 · HTML: https://mlsanity.com/paper/2410.21508/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Placed in SAE features and their applications, one of 13 directions in Mechanistic interpretability.
- Builds on 14 of its 34 references that are in the map.
- First posted on arXiv 28 Oct 2024.

## Placed in

- Mechanistic interpretability / [SAE features and their applications](https://mlsanity.com/mechinterp/sae-features-and-their-applications/)

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2](https://mlsanity.com/paper/2408.05147/) (2024)
- [Emergent Linear Representations in World Models of Self-Supervised Sequence Models](https://mlsanity.com/paper/2309.00941/) (2023)
- [Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoders](https://mlsanity.com/paper/2407.14435/) (2024)
- [Hierarchical Clustering: Objective Functions and Algorithms](https://mlsanity.com/paper/1704.02147/) (2017)
- [Fine-Tuned Transformers Show Clusters of Similar Representations Across Layers](https://mlsanity.com/paper/2109.08406/) (2021)
- [Residual Stream Analysis with Multi-Layer SAEs](https://mlsanity.com/paper/2409.04185/) (2024)

## Built on by (most cited first, 11 of 11)

- [A Survey on Sparse Autoencoders: Interpreting the Internal Mechanisms of Large Language Models](https://mlsanity.com/paper/2503.05613/) (2025)
- [Evaluate Bias without Manual Test Sets: A Concept Representation Perspective for LLMs](https://mlsanity.com/paper/2505.15524/) (2025)
- [LLM Interpretability with Identifiable Temporal-Instantaneous Representation](https://mlsanity.com/paper/2509.23323/) (2025)
- [Beyond Input Activations: Identifying Influential Latents by Gradient Sparse Autoencoders](https://mlsanity.com/paper/2505.08080/) (2025)
- [A Comparative Analysis of Sparse Autoencoder and Activation Difference in Language Model Steering](https://mlsanity.com/paper/2510.01246/) (2025)
- [Time-Aware Feature Selection: Adaptive Temporal Masking for Stable Sparse Autoencoder Training](https://mlsanity.com/paper/2510.08855/) (2025)
- [LouvreSAE: Sparse Autoencoders for Interpretable and Controllable Style Transfer](https://mlsanity.com/paper/2512.18930/) (2025)
- [Sparsification and Reconstruction from the Perspective of Representation Geometry](https://mlsanity.com/paper/2505.22506/) (2025)
- [Identifying Temporal Features within Transcoders for Time Sensitive Factual Recall](https://mlsanity.com/paper/2609.33183/) (2026)
- [The System Prompt Illusion: How Instruction Preambles Modify Computation in Language Models](https://mlsanity.com/paper/2609.38205/) (2026)
- [Sparse Autoencoders for Mechanistic Interpretability in NLP: A Critical Survey of Recoverability, Interpretability, and Utility](https://mlsanity.com/paper/2610.20139/) (2026)

## Abstract (arXiv)

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 textitGroup-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 textitAMAD (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.