Quartet II: Accurate LLM Pre-Training in NVFP4 by Improved Unbiased Gradient Estimation

Wed, 25 Feb 2026 00:00:00 +0000

The Core Problem

The introduction of the NVFP4 lower-precision format (natively supported by NVIDIA Blackwell GPUs) opens the door for end-to-end fully-quantized pre-training of massive Large Language Models (LLMs). However, existing quantized training methods compromise the format’s representation capacity. Specifically, to achieve unbiased gradient estimation via stochastic rounding (SR), these methods sacrifice noticeable accuracy compared to standard FP16 and FP8 training.

Key Observations

To solve this, the authors introduce MS-EDEN, a novel unbiased quantization routine specifically designed for micro-scaled formats.

Reduced Error: MS-EDEN provides more than 2x lower quantization error than traditional stochastic rounding (SR).
Quartet II Integration: MS-EDEN is seamlessly integrated into a new fully-NVFP4 quantization scheme for linear layers, aptly named Quartet II.

Analytically, Quartet II achieves consistently better gradient estimation across all major matrix multiplications—in both forward and backward passes. Furthermore, the proposal pairs exceptionally well with other recent performance enhancements aimed at NVFP4.

Results

The authors validated Quartet II on end-to-end LLM training runs with up to 1.9 Billion parameters on 38 Billion tokens.

Supplied kernels for execution on NVIDIA Blackwell GPUs demonstrate an impressive up to 4.2x speedup over equivalent BF16 implementations.

NVIDIA Blackwell | Andrei Panferov

Quartet II: Accurate LLM Pre-Training in NVFP4 by Improved Unbiased Gradient Estimation

The Core Problem

Key Observations

Results

Links