Sparse Autoencoder Robustness in LLMs
When Pruning Meets Interpretability: Preserving Sparse Autoencoder Robustness in LLMs
The layer-wise sparsity strategy reduces perplexity under same pruning rates, benefiting developers optimizing compressed LLMs.
Sparse autoencoders (SAEs) interpret LLM internal representations but their reliability under model compression is poorly understood. The study shows pruning affects SAE behavior through perturbation energy, a covariance-weighted norm. Magnitude pruning distorts representation space while activation-aware methods like Wanda and SparseGPT preserve SAE functionality better. Middle layers are more sensitive to pruning than early or late layers across all methods.
When Pruning Meets Interpretability: Preserving Sparse Autoencoder Robustness in LLMs
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.
