When Pruning Meets Interpretability: Preserving Sparse Autoencoder Robustness in LLMs

Suchit Gupte; Xueru Zhang; Mohammad Mahdi Khalili

cs.LGAug 26, 2026

When Pruning Meets Interpretability: Preserving Sparse Autoencoder Robustness in LLMs

Authors: Suchit Gupte, Xueru Zhang, Mohammad Mahdi Khalili

Organizations: Department of Computer Science The Ohio State University Columbus, OH 43210, USA

Abstract

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.

Figures & tables

Layers	Method	Spar. (%)	Core					Absorption		SCR	TPP
Layers	Method	Spar. (%)	KL Score $\uparrow$	CE Score $\uparrow$	Expl. Var. $\uparrow$	Cos Sim $\uparrow$	MSE $\downarrow$	Abs. Frac. $\downarrow$	Full Abs. $\downarrow$	Top-10 $\uparrow$	Top-10 $\uparrow$
Early (0-8)	Baseline	0	0.9944	0.9941	0.8976	0.9497	0.4268	0.0674	0.0354	0.1714	0.0270
	Magnitude	50	0.9847	0.9818	0.8416	0.9175	0.6536	0.0764	0.0486	0.1130	0.0187
	Wanda	50	0.9935	0.9873	0.8793	0.9401	0.4648	0.0691	0.0353	0.1487	0.0188
	SparseGPT	50	0.9918	0.9906	0.8728	0.9353	0.4886	0.0717	0.0402	0.1329	0.0196
Middle (9-17)	Baseline	0	0.9887	0.9876	0.8763	0.9301	2.0582	0.0668	0.0586	0.3047	0.0424

Table 1: SAEBench metrics at 50% sparsity for gemma-2-2b , aggregated by layer group (Early: layers 0–8; Middle: 9–17; Late: 18–25). Each group reports the unpruned dense baseline (italicised) alongside all three pruning methods.

\uparrow

higher is better;

\downarrow

lower is better. Refer to App. A.3 for per-layer SAEBench metrics from which these values are aggregated.

Figure 1: Per-layer percentage degradation from the dense baseline across all eight SAEBench metric categories for gemma-2-2b at 50% sparsity. Each panel corresponds to one metric; Magnitude (red), SparseGpt (blue), and Wanda (green) across layers 0–25. These plots emphasize per-layer trends and direct cross-method comparison at each layer; see Figure 2 for the same data as a heatmap.

Figure 2: Heatmap of per-layer, per-method percentage degradation from the dense baseline for gemma-2-2b at 50% sparsity. Each row corresponds to a pruning method; each column to a layer; colour intensity encodes the magnitude of degradation (darker $=$ larger change). This heatmap presents the same underlying data as Figure 1 , reorganized to expose spatial patterns across the full method $\times$ layer grid simultaneously.

Figure 3: Layer sensitivity profile for gemma-2-2b , computed as the mean absolute percentage degradation averaged across all three pruning methods and all eight SAEBench metrics. (a) Sensitivity profiles at three sparsity levels (25%, 40%, 50%). (b) Sensitivity profile at 50% sparsity, coloured by layer group (Early: 0–8, Middle: 9–17, Late: 18–25).

Model	Method	Spar. (%)	Core					Absorption		SCR	TPP
Model	Method	Spar. (%)	KL Score $\uparrow$	CE Score $\uparrow$	Expl. Var. $\uparrow$	Cos Sim $\uparrow$	MSE $\downarrow$	Abs. Frac. $\downarrow$	Full Abs. $\downarrow$	Top-10 $\uparrow$	Top-10 $\uparrow$
gemma-2 2b	Baseline	0	0.9873	0.9864	0.8812	0.9370	5.2568	0.0836	0.0746	0.2843	0.0450
	Magnitude	50	0.9681	0.9624	0.7928	0.8893	10.4390	0.0795	0.0783	0.1824	0.0131
	Wanda	50	0.9873	0.9835	0.8625	0.9277	5.4659	0.0789	0.0680	0.2497	0.0330
	SparseGPT	50	0.9855	0.9874	0.8468	0.9193	6.4717	0.0826	0.0766	0.2297	0.0325
gemma-2 9b	Baseline	0	0.9914	0.9900	0.8882	0.9380	7.7362	0.0997	0.0654	0.3237	0.0603

Table 2: Cross-architecture generalisation at 50% sparsity. Each cell reports the metric value averaged across all evaluated layers of a given model.

\uparrow

higher is better;

\downarrow

lower is better.

		Wanda		SparseGPT
Model	Avg. Sparsity	Uniform	Layer-wise	Uniform	Layer-wise
gemma-2-2b	50%	212	148	141	98

Table 3: Perplexity on gemma-2-2b under uniform versus layer-wise sparsity allocation evaluated for Wanda and SparseGpt . The ramp schedule assigns 20% sparsity to early layers, increasing linearly to 60% at the middle-layer and holding at 60% until the last layer.

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 4: SCR/TPP metric stability across ablation thresholds for gemma-2-2b at

50\%

sparsity. Left column : mean raw metric values as a function of ablation threshold

k\in\{2,5,10,20,50,100,500\}

for SCR (top)/ TPP (bottom), alongside the dense baseline (dotted). Right column: corresponding mean percentage change from the dense baseline.

Layers	Method	Spar. (%)	Core					Absorption		SCR	TPP
Layers	Method	Spar. (%)	KL Score $\uparrow$	CE Score $\uparrow$	Expl. Var. $\uparrow$	Cos Sim $\uparrow$	MSE $\downarrow$	Abs. Frac. $\downarrow$	Full Abs. $\downarrow$	Top-10 $\uparrow$	Top-10 $\uparrow$
Layer 0	Baseline	0	0.9966	0.9967	0.9453	0.9766	0.1396	0.0131	0.0324	0.1488	0.0272
	Magnitude	50	0.9915	0.9962	0.8984	0.9531	0.2754	0.0141	0.0432	0.1385	0.0327
	Wanda	50	0.9964	0.9932	0.9375	0.9727	0.1582	0.0127	0.0339	0.1605	0.0242
	SparseGPT	50	0.9953	0.9948	0.9375	0.9727	0.1611	0.0133	0.0346	0.1514	0.0206
Layer 1	Baseline	0	0.9958	0.9951	0.9219	0.9648	0.2402	0.0989	0.0913	0.1788	0.0336

Appendix

Table 4: Per-layer SAEBench metrics for gemma-2-2b at

50\%

sparsity, layers 0–8 (Early group). The dense baseline is italicised for each layer.

\uparrow

higher is better;

\downarrow

lower is better.

Layers	Method	Spar. (%)	Core					Absorption		SCR	TPP
Layers	Method	Spar. (%)	KL Score $\uparrow$	CE Score $\uparrow$	Expl. Var. $\uparrow$	Cos Sim $\uparrow$	MSE $\downarrow$	Abs. Frac. $\downarrow$	Full Abs. $\downarrow$	Top-10 $\uparrow$	Top-10 $\uparrow$
Layer 9	Baseline	0	0.9917	0.9901	0.8711	0.9297	0.9844	0.0555	0.0498	0.2386	0.0247
	Magnitude	50	0.9664	0.9544	0.7773	0.8789	1.3438	0.0555	0.0498	0.0858	0.0118
	Wanda	50	0.9915	0.9846	0.8438	0.9141	1.0234	0.0429	0.0310	0.1830	0.0170
	SparseGPT	50	0.9888	0.9880	0.8281	0.9062	1.0938	0.0527	0.0414	0.1565	0.0138
Layer 10	Baseline	0	0.9909	0.9901	0.8672	0.9258	1.1953	0.0708	0.0541	0.2430	0.0220

Appendix

Table 5: Per-layer SAEBench metrics for gemma-2-2b at

50\%

sparsity, layers 9–17 (Middle group). The dense baseline is italicised for each layer.

\uparrow

higher is better;

\downarrow

lower is better.

Layers	Method	Spar. (%)	Core					Absorption		SCR	TPP
Layers	Method	Spar. (%)	KL Score $\uparrow$	CE Score $\uparrow$	Expl. Var. $\uparrow$	Cos Sim $\uparrow$	MSE $\downarrow$	Abs. Frac. $\downarrow$	Full Abs. $\downarrow$	Top-10 $\uparrow$	Top-10 $\uparrow$
Layer 18	Baseline	0	0.9855	0.9852	0.8867	0.9375	4.4062	0.0951	0.1101	0.3244	0.0655
	Magnitude	50	0.9426	0.9278	0.7617	0.8672	6.9375	0.0795	0.1189	0.1193	0.0063
	Wanda	50	0.9854	0.9846	0.8672	0.9297	4.8750	0.0813	0.0921	0.2761	0.0511
	SparseGPT	50	0.9831	0.9880	0.8477	0.9180	5.5000	0.0815	0.1070	0.2658	0.0573
Layer 19	Baseline	0	0.9844	0.9835	0.8828	0.9375	5.5312	0.0823	0.0935	0.3398	0.0660

Appendix

Table 6: Per-layer SAEBench metrics for gemma-2-2b at

50\%

sparsity, layers 18–25 (Late group). The dense baseline is italicised for each layer.

\uparrow

higher is better;

\downarrow

lower is better.

Layer Group	Magnitude $\varepsilon^{2}$	Wanda $\varepsilon^{2}$	SparseGPT $\varepsilon^{2}$
Early (0–8)	57.36	31.87	26.66
Middle (9–17)	47.13	21.16	20.70
Late (18–25)	53.69	26.45	24.95

Appendix

Table 7: Empirical perturbation energy

\varepsilon^{2}

by layer group for gemma-2-2b at 50% sparsity. Lower is better; the ordering predicted by Corollary 3.3 holds in every group.

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LLM Pruning Representation Geometry in Language Models LLM Compression

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Weight pruning is a standard technique for compressing large language models, yet its effect on learned internal representations remains poorly understood. We present the first systematic study of how unstructured pruning reshapes the feature geometry of language models, using Sparse Autoencoders (SAEs) as interpretability probes. Across three model families (Gemma 3 1B, Gemma 2 2B, Llama 3.2 1B), two pruning methods (magnitude and Wanda), and six sparsity levels (0--60%), we investigate five research questions spanning seed stability, feature survival, SAE transferability, feature fragility, and causal relevance. Our most striking finding is that rare SAE features--those with low firing rates--survive pruning far better than frequent ones, with within-condition Spearman correlations of rho = -1.0 in 11 of 17 experimental conditions. This counter-intuitive result suggests that pruning acts as implicit feature selection, preferentially destroying high-frequency generic features while preserving specialized rare ones. We further show that Wanda pruning preserves feature structure up to 3.7x better than magnitude pruning, that pre-trained SAEs remain viable on Wanda-pruned models up to 50% sparsity, and that geometric feature survival does not predict causal importance--a dissociation with implications for interpretability under compression.

Abstract

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