QuantForge: Discovering Residual Decompositions for MXFP4 Post-Training Quantization

Post-training quantization (PTQ) is widely used to reduce the memory and computational cost of large language models. Existing PTQ methods typically obtain an initial quantized model through heuristic rules or greedy optimization, and once quantization is completed the resulting integer assignments are usually treated as final. This observation motivates a complementary optimization stage within PTQ that keeps quantized weights improvable after an executable quantized model has been produced, while preserving the quantized format. We introduce ReQuant, a backpropagation-free fixed-grid refinement procedure for this stage. Agnostic to the PTQ initializer, ReQuant takes an existing quantized model as a feasible starting point and iteratively revisits its discrete weight assignments on the fixed quantization grid. Accepted updates strictly reduce the mean squared reconstruction error and remain on the original grid. In this way, ReQuant turns the initially fixed PTQ output into an iteratively optimizable discrete solution and serves as a plug-and-play post-processing stage for existing PTQ pipelines. Experiments across diverse model families, bit-widths, and downstream tasks show that ReQuant consistently improves quantized models from heterogeneous PTQ initializers, with especially large gains on simple initializers and lower bit-widths. Notably, ReQuant can refine a simple round-to-nearest initialization across multiple sweeps until it approaches or surpasses GPTAQ under the same quantization format. These results establish ReQuant as a practical complementary stage for further improving existing PTQ pipelines.

Why does full-pipeline FP4 training of large language models often diverge, even when forward activations and activation gradients remain stable? We address this question through a controlled study of MXFP4 quantization in transformer training, progressively enabling FP4 across forward propagation (Fprop), activation gradients (Dgrad), and weight gradients (Wgrad) while holding all other factors fixed. In full pretraining of Llama 3.1-8B on the C4 dataset, we observe that quantizing Wgrad is the primary driver of convergence degradation, whereas FP4 in Fprop and Dgrad alone introduces only modest additional token requirements. To interpret this behavior, we evaluate both structured and stochastic interventions under a controlled experimental setting. We find that stochastic rounding and randomized Hadamard rotations fail to stabilize training once Wgrad is quantized, whereas deterministic Hadamard rotations consistently restore stable optimization. These results suggest that FP4 training instability is driven by structured micro-scaling errors along sensitive gradient paths, rather than by insufficient stochasticity. We run experiments with native MXFP4 support on AMD Instinct MI355X GPUs, enabling controlled investigation of these effects without reliance on software emulation.

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.