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LeanQuant: Accurate and Scalable Large Language Model Quantization with Loss-error-aware Grid
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Proposes LeanQuant, a post-training weight quantization method that learns loss-error-aware affine and non-uniform grids inside the GPTQ/OBQ framework, enabling accurate and scalable quantization of models up to Llama-3.1 405B.
Problem
Iterative loss-error-based PTQ methods (OBQ/GPTQ) use min-max affine grids that fail to preserve precision for outliers in inverse Hessian diagonals, degrading quality at low bit widths; accurate methods also often need specialized kernels or heavy resources to scale to hundreds of billions of param
Approach
Replace the min-max affine grid with grids learned to minimize a Hessian-inverse-weighted quantization error (weights (H^-1_ii)^-p), using k-means with uniform initialization for non-uniform grids and a fused GPU kernel for enumerative search over affine scale/zero-point, so the result stays compatible with standard affine and non-uniform kernels.
Key results
- LeanQuant_aff improves 3-bit Llama-3-8B average zero-shot accuracy over OmniQuant by 17.18% and over GPTQ by 18.38%.
- LeanQuant quantizes Llama-3.1 405B on two 48GB GPUs in about 21 hours (20.7 hours reported for quantization), with 65.4 GB peak memory.
- 4-bit LeanQuant_nu achieves 81.13 average accuracy on Llama-3.1-405B-Instruct versus 80.83 for GPTQ.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a loss-error-aware affine grid instead of the standard affine grid | GPTQ-style quantization · Llama-3-8B, 3-bit affine zero-shot benchmarks | average accuracy: 37.75 -> 56.13 | Helped |
| Use a loss-error-aware affine grid instead of the standard affine grid | GPTQ-style quantization · Mistral-7B, 3-bit affine zero-shot benchmarks | average accuracy: 52.60 -> 61.00 | Helped |
| Use a loss-error-aware non-uniform grid instead of SqueezeLLM's grid | Llama-3-8B, 3.02-bit non-uniform quantization · zero-shot benchmarks | average accuracy: 59.70 -> 62.97 | Helped |
| Use a loss-error-aware non-uniform grid instead of SqueezeLLM's grid | Mistral-7B, 4.05-bit non-uniform quantization · zero-shot benchmarks | average accuracy: 65.73 -> 65.99 | Helped |
| Use loss-error-aware non-uniform rather than affine grids (ablation) | LeanQuant on Mistral-Large-Instruct-2407 · 4-bit zero-shot benchmarks | average accuracy: 79.28 -> 79.99 | Helped |
| Use loss-error-aware affine quantization | LeanQuant on Llama-3.1-405B-Instruct · 4.25-bit, group size 128 zero-shot benchmarks | average accuracy: 80.83 -> 80.95 | Helped |
| Use loss-error-aware non-uniform grids | LeanQuant on Llama-3.1-405B-Instruct · 4.05-bit zero-shot benchmarks | average accuracy | Helped |
| Use LeanQuant-nu-Exact instead of OBQ | BERT-3 · SQuAD test, approximately 4-bit quantization | F1: 84.40 -> 84.58 | Helped |
| Use LeanQuant-nu-Exact instead of OBQ | BERT · SQuAD test, approximately 4-bit quantization | F1: 87.96 -> 88.49 | Helped |
| Use LeanQuant-nu-Exact instead of OBQ | BERT-3 · SQuAD test, approximately 3-bit quantization | F1: 83.47 -> 84.20 | Helped |
| Use LeanQuant-nu-Exact instead of OBQ | BERT · SQuAD test, approximately 3-bit quantization | F1: 84.72 -> 86.21 | Helped |
| Add uniformly spaced grid initialization rather than k-means++ initialization (ablation) | LeanQuant-nu · 3-bit and 2-bit quantization across models | zero-shot accuracy | Helped |
Surprising findings
- Perplexity does not always reflect zero-shot accuracy differences; LeanQuant matches OmniQuant/SqueezeLLM perplexity while showing larger gains in accuracy.
- The fused kernel for affine grid learning speeds end-to-end quantization of Llama-3-8B by over 50x (e.g., 15.1 hrs to 0.27 hrs).
Limitations
- Affine grid search relies on enumerating candidates with a shrinkage hyperparameter t set per bit width, which needs tuning.
- Fixed grids computed before iterative quantization may misalign as weights shift, though the authors argue this is rare in practice.
- Perplexity may be an unrepresentative metric for quantized model quality.
Experimental setup
Datasets: C4 WikiText2 SQuAD
Benchmarks: ARC LAMBADA MMLU HellaSwag PIQA WinoGrande WikiText2 C4 MT-Bench SQuAD
Metrics: zero-shot accuracy perplexity win rate F1 peak GPU memory quantization time
Baselines: GPTQ OmniQuant AWQ SqueezeLLM QuaRot
Builds on: GPTQ Optimal Brain Quantization SqueezeLLM OmniQuant
Closest papers by meaning
- OSTQuant: Refining Large Language Model Quantization with Orthogonal and Scaling Transformations for Better Distribution Fitting (ICLR 2025 · similarity 0.92)
- AffineQuant: Affine Transformation Quantization for Large Language Models (ICLR 2024 · similarity 0.92)
- CBQ: Cross-Block Quantization for Large Language Models (ICLR 2025 · similarity 0.92)
- SliM-LLM: Salience-Driven Mixed-Precision Quantization for Large Language Models (ICML 2025 · similarity 0.91)
- Norm Tweaking: High-Performance Low-Bit Quantization of Large Language Models (AAAI 2024 · similarity 0.91)
- OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Models (ICLR 2024 · similarity 0.91)
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