Hierarchical Sparse Plus Low Rank Compression of LLM

• URL: http://arxiv.org/abs/2601.07839v1
• Date: Fri, 19 Dec 2025 04:28:30 GMT
• Title: Hierarchical Sparse Plus Low Rank Compression of LLM
• Authors: Pawan Kumar, Aditi Gupta,
• Abstract summary: We present Hierarchical Sparse Plus Low-Rank (HSS) compression, a two-stage scheme that removes the largest-magnitude weights into a sparse matrix S.<n>HSS is hardware-friendly: its matrix-vector multiply reduces to one sparse and a sequence of thin-matrix multiplications.<n>Experiments on LLaMA-7B show that targeting only the self-attention projections suffices to yield large memory savings.
• Score: 2.4311207322523023
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Modern large language models (LLMs) place extraordinary pressure on memory and compute budgets, making principled compression indispensable for both deployment and continued training. We present Hierarchical Sparse Plus Low-Rank (HSS) compression, a two-stage scheme that (i) removes the largest-magnitude weights into a sparse matrix S and (ii) applies a recursive Hierarchically Sparse Separable (HSS) low-rank factorisation to the dense residual matrix. A recursive rank-reducing strategy and a reverse Cuthill-Mckee (RCM) permutation are introduced to align high weights towards the diagonal with the block-diagonal hierarchy, maximising off-diagonal compressibility (because they are touched only once). HSS is hardware-friendly: its matrix-vector multiply reduces to one sparse and a sequence of thin-matrix multiplications and can be trained end-to-end with standard optimisers. Experiments on LLaMA-7B show that targeting only the self-attention projections (1.6 B parameters of Q, K, and V matrices out of a total 7B parameters) suffices to yield large memory savings while retaining comparable state-of-the-art perplexity scores on test samples of the WikiText dataset. For example, with a 30\% sparsity budget and an outer rank of 512, sHSS-RCM achieves a perplexity of 1.64, outperforming dense baselines and classical sparse-plus-SVD variants, while also achieving significant memory savings.

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