# Low-Rank Adapting Models for Sparse Autoencoders

arXiv: https://arxiv.org/abs/2501.19406 · HTML: https://mlsanity.com/paper/2501.19406/

## Key facts

- Cited by 7 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 30 of its 50 references that are in the map.
- First posted on arXiv 31 Jan 2025.

## Placed in

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

## Builds on (most cited first, 30 of 30)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [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)
- [k-Sparse Autoencoders](https://mlsanity.com/paper/1312.5663/) (2013)
- [Improving Dictionary Learning with Gated Sparse Autoencoders](https://mlsanity.com/paper/2404.16014/) (2024)
- [A is for Absorption: Studying Feature Splitting and Absorption in Sparse Autoencoders](https://mlsanity.com/paper/2409.14507/) (2024)
- [The Remarkable Robustness of LLMs: Stages of Inference?](https://mlsanity.com/paper/2406.19384/) (2024)
- [Llama Scope: Extracting Millions of Features from Llama-3.1-8B with Sparse Autoencoders](https://mlsanity.com/paper/2410.20526/) (2024)
- [BatchTopK Sparse Autoencoders](https://mlsanity.com/paper/2412.06410/) (2024)
- [Identifying Functionally Important Features with End-to-End Sparse Dictionary Learning](https://mlsanity.com/paper/2405.12241/) (2024)
- [Recurrent Neural Networks Learn to Store and Generate Sequences using Non-Linear Representations](https://mlsanity.com/paper/2408.10920/) (2024)
- [Decomposing The Dark Matter of Sparse Autoencoders](https://mlsanity.com/paper/2410.14670/) (2024)
- [Efficient Dictionary Learning with Switch Sparse Autoencoders](https://mlsanity.com/paper/2410.08201/) (2024)
- [Seeing is Believing: Brain-Inspired Modular Training for Mechanistic Interpretability](https://mlsanity.com/paper/2305.08746/) (2023)
- [Towards Reliable Evaluation of Behavior Steering Interventions in LLMs](https://mlsanity.com/paper/2410.17245/) (2024)
- [Monotonic Representation of Numeric Properties in Language Models](https://mlsanity.com/paper/2403.10381/) (2024)
- [You can remove GPT2's LayerNorm by fine-tuning](https://mlsanity.com/paper/2409.13710/) (2024)
- [Features that Make a Difference: Leveraging Gradients for Improved Dictionary Learning](https://mlsanity.com/paper/2411.10397/) (2024)

## Built on by (most cited first, 7 of 7)

- [Resa: Transparent Reasoning Models via SAEs](https://mlsanity.com/paper/2506.09967/) (2025)
- [Revisiting End-To-End Sparse Autoencoder Training: A Short Finetune Is All You Need](https://mlsanity.com/paper/2503.17272/) (2025)
- [Sparse CLIP: Co-Optimizing Interpretability and Performance in Contrastive Learning](https://mlsanity.com/paper/2601.20075/) (2026)
- [Superposition Without Interference? Towards Isolated Interventions via Almost Orthogonal Features in Language Models](https://mlsanity.com/paper/2602.04718/) (2026)
- [Breaking the Block: Preserving Data Continuity to Train Superior SAEs for Instruct Models](https://mlsanity.com/paper/2506.07691/) (2025)
- [Weights Read and Write Features: Scalable Parameter Decomposition Grounded in Activation Space](https://mlsanity.com/paper/2609.37731/) (2026)
- [Confine to the Task, Anchor the Rest: Concept-Guided Retention Regularizer for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2610.17713/) (2026)

## Abstract (arXiv)

Sparse autoencoders (SAEs) decompose language model representations into a sparse set of linear latent vectors. Recent works have improved SAEs using language model gradients, but these techniques require many expensive backward passes during training and still cause a significant increase in cross entropy loss when SAE reconstructions are inserted into the model. In this work, we improve on these limitations by taking a fundamentally different approach: we use low-rank adaptation (LoRA) to finetune the textitlanguage model itself around a previously trained SAE. We analyze our method across SAE sparsity, SAE width, language model size, LoRA rank, and model layer on the Gemma Scope family of SAEs. In these settings, our method reduces the cross entropy loss gap by 30% to 55% when SAEs are inserted during the forward pass. We also find that compared to end-to-end (e2e) SAEs, our approach achieves the same downstream cross entropy loss 3× to 20× faster on gemma and 2× to 10× faster on llama. We further show that our technique improves downstream metrics and can adapt multiple SAEs at once without harming general language model capabilities. Our results demonstrate that improving model interpretability is not limited to post-hoc SAE training; Pareto improvements can also be achieved by directly optimizing the model itself.