Large language models (LLMs) exhibit significant layer-wise redundancy, motivating non-uniform pruning for efficient compression. However, existing sparsity allocation methods rely on indirect statistical heuristics derived from weight magnitudes or activation distributions, without directly assessing how robustly each layer preserves semantic information under input variation. We propose PerturbPrune, a framework that allocates layer-wise sparsity by probing the intrinsic stability of hidden representations. PerturbPrune estimates the principal subspace of each layer’s activations via PCA and injects structured perturbations along these directions. Layer sensitivity is quantified through matrix difference entropy (DiME): stable layers are identified as encoding compact, essential features and thus preserved, while highly sensitive layers are deemed over-parameterized and pruned more aggressively. Extensive experiments across diverse LLM families (LLaMA, LLaMA-2, Qwen, OPT) demonstrate that PerturbPrune broadly matches or outperforms existing non-uniform methods. Compared to uniform pruning, it prevents catastrophic collapse, reducing perplexity by up to 99.7% and improving zero-shot accuracy by up to 22.7%. The method is also highly efficient, completing sparsity allocation on Qwen3.5-9B in 7 minutes—achieving 24× and 17.4× speedups over AlphaPruning and MRP. Finally, PerturbPrune generalizes to Mixture-of-Experts architectures, achieving up to 19.3% perplexity reduction on Qwen3.5-35B-A3B.