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.
Quartet II : Accurate LLM pre-training in NVFP4 by improved unbiased gradient estimation
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abstract
The NVFP4 lower-precision format, supported in hardware by NVIDIA Blackwell GPUs, promises to allow, for the first time, end-to-end fully-quantized pre-training of massive models such as LLMs. Yet, existing quantized training methods still sacrifice some of the representation capacity of this format in favor of more accurate unbiased quantized gradient estimation by stochastic rounding (SR), losing noticeable accuracy relative to standard FP16 and FP8 training. In this paper, improve the state of the art for quantized training in NVFP4 via a novel unbiased quantization routine for micro-scaled formats, called MS-EDEN, that has more than 2x lower quantization error than SR. We integrate it into a novel fully-NVFP4 quantization scheme for linear layers, called Quartet II. We show analytically that Quartet II achieves consistently better gradient estimation across all major matrix multiplications, both on the forward and on the backward passes. In addition, our proposal synergizes well with recent training improvements aimed specifically at NVFP4. We further validate Quartet II on end-to-end LLM training with up to 1.9B parameters on 38B tokens. We provide kernels for execution on NVIDIA Blackwell GPUs with up to 4.2x speedup over BF16. Our code is available at https://github.com/IST-DASLab/Quartet-II .
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Two randomized Hadamard transforms suffice to make coordinate marginals O(d^{-1/2})-close to Gaussian for most quantization methods, with three needed for vector quantization to match uniform random rotations asymptotically.
MXFP4 quantization error decomposes into scale bias, deadzone truncation, and grid noise; mode-targeted corrections recover BF16 accuracy within 0.7% on Qwen2.5-3B and exceed it by 1.0% on Qwen3-30B-A3B.
nGPT's hypersphere constraint makes dot-product signal accumulate constructively under 4-bit quantization while noise averages out, enabling native low-precision training.
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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Normalized Architectures are Natively 4-Bit
nGPT's hypersphere constraint makes dot-product signal accumulate constructively under 4-bit quantization while noise averages out, enabling native low-precision training.