BATQuant: Outlier-resilient MXFP4 Quantization via Learnable Block-wise Optimization

The MXFP4 microscaling format, which partitions tensors into blocks of 32 elements sharing an E8M0 scaling factor, has emerged as a promising substrate for efficient LLM inference, backed by native hardware support on NVIDIA Blackwell Tensor Cores. However, activation outliers pose a unique challenge under this format: a single outlier inflates the shared block scale, compressing the effective dynamic range of the remaining elements and causing significant quantization error. Existing rotation-based remedies, including randomized Hadamard and learnable rotations, are data-agnostic and therefore unable to specifically target the channels where outliers concentrate. We propose DuQuant++, which adapts the outlier-aware fine-grained rotation of DuQuant to the MXFP4 format by aligning the rotation block size with the microscaling group size (B{=}32). Because each MXFP4 group possesses an independent scaling factor, the cross-block variance issue that necessitates dual rotations and a zigzag permutation in the original DuQuant becomes irrelevant, enabling DuQuant++ to replace the entire pipeline with a single outlier-aware rotation, which halves the online rotation cost while simultaneously smoothing the weight distribution. Extensive experiments on the LLaMA-3 family under MXFP4 W4A4 quantization show that DuQuant++ consistently achieves state-of-the-art performance. Our code is available at https://github.com/Hsu1023/DuQuant-v2.

As Large Language Models (LLMs) advance toward practical deployment, the Microscaling FP4 (MXFP4) format has emerged as a cornerstone for next-generation low-bit inference, owing to its ability to balance high dynamic range with hardware efficiency. However, directly applying MXFP4 to LLM activation quantization inevitably leads to significant accuracy degradation. In this paper, we theoretically analyze the error structure of MXFP4 activation quantization, revealing that the root cause of this performance drop lies in two structural imbalances between activation distributions and the MXFP4 block floating-point format: (1) extreme inter-block variance imbalance and (2) intra-block codebook utilization imbalance. To address these challenges, we propose TORQ (Two-level Orthogonal Rotation for MXFP4 Quantization), a training-free Post-Training Quantization (PTQ) framework designed to reshape the geometric properties of the activation space through optimal coordinate transformations. At the macroscopic level, TORQ leverages the Schur-Horn theorem to redistribute activation energy via inter-block orthogonal rotation, preventing high-variance blocks from driving up shared scaling factors and thereby preserving the precision of small-magnitude elements. At the microscopic level, TORQ employs maximum-entropy-guided intra-block rotation to alleviate codebook collapse and maximize the MXFP4 codebook's information capacity. Experiments on mainstream LLMs such as LLaMA3 and Qwen3 show that TORQ significantly improves the accuracy of MXFP4 activation quantization compared to existing methods: on Qwen3-32B, the perplexity on WikiText is reduced to 8.43 (vs. 7.61 for BF16), and the average accuracy increases from 38.40% with direct RTN to 73.63% (vs. 74.82% for BF16), substantially narrowing the gap between 4-bit floating-point quantization and full-precision inference.

Large language models (LLMs) achieve remarkable performance but are expensive to deploy due to their enormous size. FP4 quantization, with formats such as MXFP4 and NVFP4, offers an appealing solution with native hardware support on modern accelerators. However, maintaining accuracy under FP4 precision remains difficult. A key bottleneck lies in scale optimization: existing methods tightly couple the quantization and dequantization scales, forcing both to conform to the discrete low-precision format required by hardware, such as E8M0 in MXFP4. Yet the quantization scale is never stored and need not obey this constraint, suggesting a significant untapped optimization space. In this work, we propose FOCUS, a post-training quantization framework with end-to-end scale learning for FP4 Optimization via Coupled-Relaxation and Dual-Granularity Scaling. Coupled-Relaxation Scaling (CRS) relaxes the tight coupling between quantization and dequantization scales with a learnable full-precision coefficient, enabling more effective optimization without breaking hardware compliance. Dual-Granularity Scaling (DGS) further refines the quantization scale at a finer sub-block granularity, allowing more precise adaptation to local weight distributions. Experiments across multiple LLM families and benchmarks show that FOCUS achieves state-of-the-art FP4 accuracy under both MXFP4 and NVFP4 formats, while introducing no additional inference overhead. Code and quantized models will be released at https://github.com/tencent/AngelSlim.