Compressed-Sensing-Guided, Inference-Aware Structured Reduction for Large Language Models

The memory-bound nature of the decoding stage of large language model (LLM) inference incurs significant latency. Layer-wise training-free network pruning approaches guided by the Hessian have been a prominent solution to this problem, as pruning reduces the number of nonzero parameters read from memory during decoding. Nevertheless, typical methods in this line compute the Hessian using pre-collected natural sequences, whereas the model is fed self-generated tokens during decoding, creating a distribution shift between the two sequences. The Hessian calculated on the natural sequence is different from that calculated on the generated sequence. We observe that this discrepancy causes the activation distribution during generation to deviate from that used for pruning, further hurting the pruned model performance. Moreover, most existing LLM pruning methods that bring actual speedup primarily target the sparse matrix-matrix (SpMM) multiplication, providing limited support for the sparse matrix-vector (SpMV) operations, which dominate decoding. To solve these problems, we introduce SparseDecoding, a principled decoding-aware pruning framework tailored for accurate and efficient LLM decoding. Specifically, at the algorithmic axis, SparseDecoding constructs calibration matrices from layer-wise activations collected during the dense-model autoregressive generation, excluding prefill, thereby aligning the pruning objective with the decoding activations. At the system axis, we develop an optimized N:M sparse matrix-vector kernel with bitmask indexing and fixed-step traversal. Substantial empirical results on representative LLMs (Llama-3.1-8B, Llama-3.3-70B, Qwen3-14B / 32B) demonstrate that our method consistently outperforms standard fixed-text calibration on the long-form generation benchmarks while achieving up to 1.48x end-to-end wall-clock decoding speedup on A100 GPUs.

Structured pruning of large language models (LLMs) offers hardware-efficient compression, yet existing methods require calibration data, gradient computation, or large auxiliary policy networks at pruning time. LILA (Latent-Informed Layer Analysis) scores neuron importance via the Kolmogorov--Smirnov (KS) distance between empirical singular value distributions of the full and neuron-ablated feed-forward network (FFN) weight matrix, providing a closed-form spectral rule requiring no training, calibration data, or auxiliary network. Without any fine-tuning, LILA surpasses PruneNet (45M-parameter RL policy) by 1.57pp in zero-shot accuracy on LLaMA-2-7B at 25% sparsity, and outperforms WikiText-2-calibrated SliceGPT by up to 6.0pp across all sparsity levels, while preserving the original architecture. After one epoch of LoRA recovery fine-tuning, LILA achieves highly competitive performance, matching the heavily calibrated SliceGPT baseline to within a 0.48~pp margin across LLaMA-2-7B and Phi-2, despite using zero calibration data. A Neural Tangent Kernel analysis confirms a 22$\times$ reduction in functional distortion versus random pruning, providing theoretical grounding for the spectral importance criterion. Finally, extending LILA to dynamically allocate sparsity budgets via KS-scores yields state-of-the-art generative preservation at moderate compression, while uncovering fundamental single-layer architectural bottlenecks at higher compression regimes.

Large language models (LLMs) have demonstrated impressive capabilities across various tasks, but the billion-scale parameters pose deployment challenges. Although existing methods attempt to reduce the scale of LLMs, they require either special hardware support or expensive post-training to maintain model quality. To facilitate efficient and affordable model slimming, we propose a novel training-free compression method for LLMs, named "SoLA", which leverages Soft activation sparsity and Low-rAnk decomposition. SoLA can identify and retain a minority of components significantly contributing to inference, while compressing the majority through low-rank decomposition, based on our analysis of the activation pattern in the feed-forward network (FFN) of modern LLMs. To alleviate the decomposition loss, SoLA is equipped with an adaptive component-wise low-rank allocation strategy to assign appropriate truncation positions for different weight matrices. We conduct extensive experiments on LLaMA-2-7B/13B/70B and Mistral-7B models across a variety of benchmarks. SoLA exhibits remarkable improvement in both language modeling and downstream task accuracy without post-training. For example, with a 30% compression rate on the LLaMA-2-70B model, SoLA surpasses the state-of-the-art method by reducing perplexity from 6.95 to 4.44 and enhancing downstream task accuracy by 10%.