Allowing each quantization group to select among multiple 4-bit grids improves accuracy over single-grid FP4 for both post-training and pre-training of LLMs.
Four Over Six: More Accurate NVFP4 Quantization with Adaptive Block Scaling
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abstract
As large language models have grown larger, interest has grown in low-precision numerical formats such as NVFP4 as a way to improve speed and reduce memory usage. However, quantizing models to NVFP4 remains challenging as the lack of precision generally degrades model performance. In this work, we address this issue with Four Over Six (4/6), a modification to the block-scaled NVFP4 quantization algorithm that yields reduced quantization error. Unlike integer formats, floating point formats have non-uniform step sizes which create larger quantization error on larger values. 4/6 takes advantage of this by adaptively scaling some blocks to smaller FP4 values, making the distribution of representable values more uniform and reducing quantization error for near-maximal values. We show that 4/6 can be implemented efficiently on modern hardware accelerators, resulting in performance gains during both pre-training and inference with minimal computational overhead. In pre-training experiments with the Nemotron 3 Nano 30B-A3B model architecture, we find that 4/6 brings training loss closer to BF16 compared to models trained with current state-of-the-art NVFP4 training recipes. Our code is available at https://github.com/mit-han-lab/fouroversix.
years
2026 7representative citing papers
SOAR improves NVFP4 post-training quantization accuracy for LLMs by analytically solving joint scale optimization and searching decoupled scales.
Finer block sizes strictly improve theoretical MSE in microscaling for LLMs when scaling is adjusted to handle heavy-tailed distributions and FP4 binning, allowing standard formats to match custom wider-exponent ones.
nGPT's hypersphere constraint makes dot-product signal accumulate constructively under 4-bit quantization while noise averages out, enabling native low-precision training.
QuantClaw dynamically routes precision in agent workflows to cut cost by up to 21.4% and latency by 15.7% while keeping or improving task performance.
DuQuant++ adapts outlier-aware fine-grained rotation to MXFP4 by matching block size to the 32-element microscaling group, enabling a single rotation that smooths distributions and achieves SOTA performance on LLaMA-3 with lower cost.
HiFloat4 FP4 with stabilization techniques trains dense and MoE language models on Ascend NPUs at relative error within 1% of full-precision baselines.
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Grid Games: The Power of Multiple Grids for Quantizing Large Language Models
Allowing each quantization group to select among multiple 4-bit grids improves accuracy over single-grid FP4 for both post-training and pre-training of LLMs.