# When Pruning Meets Interpretability: Preserving Sparse Autoencoder Robustness in LLMs

arXiv: https://arxiv.org/abs/2608.25941 · HTML: https://mlsanity.com/paper/2608.25941/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in SAE features and their applications, one of 13 directions in Mechanistic interpretability.
- Builds on 19 of its 26 references that are in the map.
- First posted on arXiv 26 Aug 2026.

## Placed in

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

## Builds on (most cited first, 19 of 19)

- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [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)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2](https://mlsanity.com/paper/2408.05147/) (2024)
- [Scaling Monosemanticity: Extracting Interpretable Features from Claude 3 Sonnet](https://mlsanity.com/paper/2605.29358/) (2026)
- [Outlier Weighed Layerwise Sparsity (OWL): A Missing Secret Sauce for Pruning LLMs to High Sparsity](https://mlsanity.com/paper/2310.05175/) (2023)
- [A is for Absorption: Studying Feature Splitting and Absorption in Sparse Autoencoders](https://mlsanity.com/paper/2409.14507/) (2024)
- [SAEBench: A Comprehensive Benchmark for Sparse Autoencoders in Language Model Interpretability](https://mlsanity.com/paper/2503.09532/) (2025)
- [A Survey on Sparse Autoencoders: Interpreting the Internal Mechanisms of Large Language Models](https://mlsanity.com/paper/2503.05613/) (2025)
- [SlimLLM: Accurate Structured Pruning for Large Language Models](https://mlsanity.com/paper/2505.22689/) (2025)
- [Evaluating Sparse Autoencoders on Targeted Concept Erasure Tasks](https://mlsanity.com/paper/2411.18895/) (2024)
- [Fewer Weights, More Problems: A Practical Attack on LLM Pruning](https://mlsanity.com/paper/2510.07985/) (2025)
- [Stable and Steerable Sparse Autoencoders with Weight Regularization](https://mlsanity.com/paper/2603.04198/) (2026)
- [An Efficient Training Algorithm for Models with Block-wise Sparsity](https://mlsanity.com/paper/2503.21928/) (2025)
- [Privacy-Aware Randomized Quantization via Linear Programming](https://mlsanity.com/paper/2406.02599/) (2024)

## Abstract (arXiv)

Sparse autoencoders (SAEs) are widely used to interpret the internal representations of large language models (LLMs), yet their reliability under post-hoc model compression remains poorly understood. We present a systematic study of how pruning affects SAE behavior and theoretically show that, for a fixed SAE, its impact is governed by perturbation energy, a covariance-weighted norm. This perspective exposes a key limitation of magnitude pruning: by ignoring activation geometry, it distorts the learned representation space and degrades SAE functionality. Activation-aware methods such as Wanda and SparseGPT, in contrast, implicitly control perturbation energy and are therefore substantially more robust at preserving SAE behavior. We further reveal a consistent structural vulnerability across all pruning methods: middle layers are significantly more sensitive to pruning than early or late layers. Guided by this insight, we propose a layer-wise sparsity allocation strategy, achieving lower perplexity under the same average pruning sparsity. Experiments across four model architectures validate our theoretical findings. Code is publicly available at https://github.com/osu-srml/sae-robustness-under-pruning/tree/main.