CoSpaDi: Compressing LLMs via Calibration-Guided Sparse Dictionary Learning

Efficient deployment of large language models (LLMs) on mobile devices requires balancing performance with compute and memory constraints. Post-training compression is an effective approach to managing this trade-off, while requiring much less computation than in-training counterparts. We propose DictLLM, a dictionary-based compression scheme in which weight matrices within grouped layers are decomposed into a shared dictionary and layer-specific sparse coefficients, directly obtained from a pre-trained model without further training. Specifically, we cast DictLLM as a four-step post-training optimization. First, we obtain shared dictionaries via singular value decomposition (SVD) of input-scaled weight matrices, amortizing rank across grouped layers; second, we sparsify the layer-specific coefficients to the target compression ratio using a dictionary-aware Hessian; and third, we refine the dictionaries given the resulting sparse coefficients. Finally, we aggressively quantize both components using factor-specific Hessian information: input covariance for the dictionaries and the dictionary-aware Hessian for the coefficients. The resulting representation reduces memory footprint by storing a single shared dictionary per layer group, along with sparse layer-specific coefficients. On language modeling and zero-shot reasoning benchmarks, DictLLM consistently outperforms existing post-training low-rank compression methods and pushes the Pareto frontier between model size and performance. DictLLM compresses the original LLaMA-7B model by 5.1x with only a 2.9-point increase in WikiText-2 perplexity, achieving a 3.6x higher compression ratio than the state-of-the-art low-rank method.

Post-training compression of transformer models commonly relies on truncated singular value decomposition (SVD) strategies leading to low-rank approximations of the original model weights. However, the underlying single shared subspace modeling can degrade accuracy even at moderate compression. Sparse dictionary learning provides a more flexible union-of-subspaces representation, but existing approaches often suffer from costly iterative dictionary and coefficient updates. We propose $\textbf{COMPOT}$ ($\textbf{C}$alibration-$\textbf{O}$ptimized $\textbf{M}$atrix $\textbf{P}$rocrustes $\textbf{O}$rthogonalization for $\textbf{T}$ransformers), a training-free compression framework that uses a small calibration dataset to estimate a sparse weight factorization. COMPOT employs orthogonal dictionaries that enable closed-form Procrustes updates for the dictionary and analytical single-step sparse coding for the coefficients, reducing significantly the overall optimization cost. To handle heterogeneous layer sensitivity under a global compression budget, COMPOT further introduces a one-shot dynamic allocation strategy that adaptively redistributes layer-wise compression rates. Extensive experiments across diverse architectures and tasks show that COMPOT consistently delivers a superior quality-compression trade-off over strong low-rank and sparse baselines, while remaining fully compatible with post-training quantization for extreme compression.

This study presents an ensemble technique, SPQ (SVD-Pruning-Quantization), for large language model (LLM) compression that combines variance-retained singular value decomposition (SVD), activation-based pruning, and post-training linear quantization. Each component targets a different source of inefficiency: i) pruning removes redundant neurons in MLP layers, ii) SVD reduces attention projections into compact low-rank factors, iii) and 8-bit quantization uniformly compresses all linear layers. At matched compression ratios, SPQ outperforms individual methods (SVD-only, pruning-only, or quantization-only) in perplexity, demonstrating the benefit of combining complementary techniques. Applied to LLaMA-2-7B, SPQ achieves up to 75% memory reduction while maintaining or improving perplexity (e.g., WikiText-2 5.47 to 4.91) and preserving accuracy on downstream benchmarks such as C4, TruthfulQA, and GSM8K. Compared to strong baselines like GPTQ and SparseGPT, SPQ offers competitive perplexity and accuracy while using less memory (6.86 GB vs. 7.16 GB for GPTQ). Moreover, SPQ improves inference throughput over GPTQ, achieving up to a 1.9x speedup, which further enhances its practicality for real-world deployment. The effectiveness of SPQ's robust compression through layer-aware and complementary compression techniques may provide practical deployment of LLMs in memory-constrained environments. Code is available at: https://github.com/JiaminYao/SPQ_LLM_Compression/