Beyond Single-Dimensional Compression: The Compound Sparsity Frontier of Large Language Models

Large language models (LLMs) are often compressed through static parameter pruning or dynamic token-level computation, yet aggressive sparsification can trigger rapid performance degradation beyond an essential sparsity boundary. This work asks whether combining these two mechanisms can delay such degradation by distributing the compression burden. We study a minimalist compound sparsity framework that first applies low-rank approximation and channel pruning to obtain a statically compressed backbone, and then introduces lightweight routers for per-token dynamic layer skipping. This design enables independent control of parameter sparsity and token-level computation sparsity. Experiments across language understanding and modeling benchmarks show that compound sparsity consistently outperforms single-mechanism compression under the same total sparsity, delaying the decay point on understanding tasks and preserving stronger modeling performance. Further analysis reveals cross-dimensional interference between parameter pruning and token skipping, and shows that near-balanced allocation is most effective under a fixed sparsity budget. These results demonstrate that compound compression provides a practical way to improve LLM compression, while revealing a broader cross-dimensional sparsity boundary that ultimately limits further compression. Code will be available at https://github.com/EIT-NLP/LLM-Pruning.