# Replay the Curvature: Accurate and Scalable NVFP4 Quantization for Large Language Model Inference

arXiv: https://arxiv.org/abs/2609.36654 · HTML: https://mlsanity.com/paper/2609.36654/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 40 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 30 of 31)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [Language Models are Multilingual Chain-of-Thought Reasoners](https://mlsanity.com/paper/2210.03057/) (2022)
- [SpinQuant: LLM quantization with learned rotations](https://mlsanity.com/paper/2405.16406/) (2024)
- [OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Models](https://mlsanity.com/paper/2308.13137/) (2023)
- [QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebooks](https://mlsanity.com/paper/2402.04396/) (2024)
- [LLM-QAT: Data-Free Quantization Aware Training for Large Language Models](https://mlsanity.com/paper/2305.17888/) (2023)
- [Optimal Brain Compression: A Framework for Accurate Post-Training Quantization and Pruning](https://mlsanity.com/paper/2208.11580/) (2022)
- [Microscaling Data Formats for Deep Learning](https://mlsanity.com/paper/2310.10537/) (2023)
- [EfficientQAT: Efficient Quantization-Aware Training for Large Language Models](https://mlsanity.com/paper/2407.11062/) (2024)
- [CMATH: Can Your Language Model Pass Chinese Elementary School Math Test?](https://mlsanity.com/paper/2306.16636/) (2023)
- [Pretraining Large Language Models with NVFP4](https://mlsanity.com/paper/2509.25149/) (2025)
- [Low-Rank Quantization-Aware Training for LLMs](https://mlsanity.com/paper/2406.06385/) (2024)
- [Four Over Six: More Accurate NVFP4 Quantization with Adaptive Block Scaling](https://mlsanity.com/paper/2512.02010/) (2025)
- [LLMC: Benchmarking Large Language Model Quantization with a Versatile Compression Toolkit](https://mlsanity.com/paper/2405.06001/) (2024)
- [Bridging the Gap Between Promise and Performance for Microscaling FP4 Quantization](https://mlsanity.com/paper/2509.23202/) (2025)
- [TorchAO: PyTorch-Native Training-to-Serving Model Optimization](https://mlsanity.com/paper/2507.16099/) (2025)
- [Quantization-Aware Distillation for NVFP4 Inference Accuracy Recovery](https://mlsanity.com/paper/2601.20088/) (2026)
- [ARCQuant: Boosting NVFP4 Quantization with Augmented Residual Channels for LLMs](https://mlsanity.com/paper/2601.07475/) (2026)
- [Exploring the Trade-Offs: Quantization Methods, Task Difficulty, and Model Size in Large Language Models From Edge to Giant](https://mlsanity.com/paper/2409.11055/) (2024)
- [SOAR: Scale Optimization for Accurate Reconstruction in NVFP4 Quantization](https://mlsanity.com/paper/2605.12245/) (2026)

## Abstract (arXiv)

Large language models make weight storage and memory traffic major inference costs, motivating low-precision formats that represent each weight with only a few bits. Such formats use a scale to map floating-point values into a small codebook; NVFP4 improves local range utilization by letting every 16 E2M1 weights share an E4M3 block scale. Choosing that scale is difficult in GPTQ because quantizing one column updates those that follow, so evaluating a block independently can misestimate its final reconstruction error. Large models pose a second challenge: full-precision weights, calibration activations, and second-order state cannot all remain on one accelerator, while assigning complete layers to devices leaves each time-consuming layer solve serial. We introduce Schur Replay, a scale-selection algorithm that reproduces the GPTQ updates caused by each block scale and scores the resulting block error after accounting for compensation from unquantized columns. Separately, our execution infrastructure keeps only the active layer resident, tiers activations across device, host, and disk, retires full-precision layers after export, and distributes independent output rows across tensor-parallel ranks. Together, the algorithm and infrastructure attain 99.35% and 100.84% question-weighted recovery from BF16 across seven benchmarks on Qwen3.5-397B-A17B and Llama-3.3-70B-Instruct. On the 397B model, the infrastructure reduces measured per-layer time by 15.17× over ModelOpt and 23.14× over LLM Compressor, with lower memory used per GPU.