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SLiM: One-shot Quantization and Sparsity with Low-rank Approximation for LLM Weight Compression

ICML 2025 · Architectures and efficiency › Quantization · approach: KV cache quantization · 0 citations (OpenAlex)

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Proposes SLiM, a one-shot LLM compression pipeline combining SLiM-Quant (probabilistic uniform quantization), Wanda pruning to 2:4 or unstructured sparsity, and saliency-based low-rank adapters, with an optional PEFT recovery step.

Problem

One-shot compression of LLMs typically loses substantial accuracy when combining sparsity (especially semi-structured 2:4) with low-bit quantization, and retraining-based recovery is expensive.

Approach

Quantize uniformly with a data-driven MSE-minimizing clipping scale (SLiM-Quant), prune with Wanda, then compute low-rank adapters in closed form via SVD of a saliency-weighted compression error, where the saliency diag(x) is invertible and additive so adapters can be recovered exactly without iterative optimization.

Key results

Measured effects reported in the paper

What was changedWhereMeasuredEffect
use saliency-based adapters instead of norm-based Naive-LoRA adapters (ablation)SLiM compression · LLaMA-2-7B, 50% 2:4 sparsity and 4-bit weight quantizationaverage zero-shot accuracy: 48.45 -> 51.15Helped
quantize the low-rank adapters (ablation)SLiM-LoRA · LLaMA-2-7B, 50% 2:4 sparsity and 4-bit weight quantizationaverage zero-shot accuracy: 51.15 -> 51.02Hurt
use saliency-based adapters instead of norm-based Naive-LoRA adapters (ablation)SLiM compression · LLaMA-2-7B, 50% unstructured sparsity and 4-bit weight quantizationaverage zero-shot accuracy: 51.52 -> 54.26Helped
quantize the low-rank adapters (ablation)SLiM-LoRA · LLaMA-2-7B, 50% unstructured sparsity and 4-bit weight quantizationaverage zero-shot accuracy: 54.26 -> 54.18Hurt
fine-tune the adapters after compression (ablation)SLiM-LoRA · LLaMA-2-7B, 50% 2:4 sparsity and 4-bit weight quantizationaverage zero-shot accuracy: 51.15 -> 52.12Helped
fine-tune the adapters after compression (ablation)SLiM-LoRA · LLaMA-2-7B, 50% unstructured sparsity and 4-bit weight quantizationaverage zero-shot accuracy: 54.26 -> 54.69Helped
use activation-aware output-error quantization instead of weight-error quantization (ablation)SLiM-Quant · LLaMA-2-7B, 50% 2:4 sparsity and 4-bit weight quantizationaverage zero-shot accuracy: 51.15 -> 51.22Helped
use activation-aware output-error quantization instead of weight-error quantization (ablation)SLiM-Quant · LLaMA-2-7B, 50% unstructured sparsity and 4-bit weight quantizationaverage zero-shot accuracy: 54.26 -> 54.46Helped
add 8-bit input quantization (ablation)SLiM-LoRA · LLaMA-2-7B, 50% 2:4 sparsity and 4-bit weight quantizationaverage zero-shot accuracy: 51.15 -> 50.99Hurt

Surprising findings

Limitations

Experimental setup

Datasets: C4 WikiText2

Benchmarks: MMLU PIQA ARC-Easy ARC-Challenge WinoGrande OpenBookQA WikiText2 perplexity

Metrics: zero-shot accuracy perplexity layer-wise speedup memory reduction

Baselines: Wanda SparseGPT Magnitude Pruning OPTQ OmniQuant AffineQuant AWQ L2QER JSQ MaskLLM

Builds on: Wanda AWQ L2QER SparseGPT Optimal Brain Surgeon

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