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Training LLMs with MXFP4
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Training LLMs with MXFP4
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Low precision (LP) datatypes such as MXFP4 can accelerate matrix multiplications (GEMMs) and reduce training costs. However, directly using MXFP4 instead of BF16 during training significantly degrades model quality. In this work, we present the first near-lossless training recipe that uses MXFP4 GEMMs, which are $2\times$ faster than FP8 on supported hardware. Our key insight is to compute unbiased gradient estimates with stochastic rounding (SR), resulting in more accurate model updates. However, directly applying SR to MXFP4 can result in high variance from block-level outliers, harming convergence. To overcome this, we use the random Hadamard tranform to theoretically bound the variance of SR. We train GPT models up to 6.7B parameters and find that our method induces minimal degradation over mixed-precision BF16 training. Our recipe computes $>1/2$ the training FLOPs in MXFP4, enabling an estimated speedup of $>1.3\times$ over FP8 and $>1.7\times$ over BF16 during backpropagation.
Forward citations
Cited by 17 Pith papers
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Grid Games: The Power of Multiple Grids for Quantizing Large Language Models
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.
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HiFloat4 Format for End-To-End Reinforcement Learning Post-Training of Large Language Models
In end-to-end 4-bit RL post-training, rollout activation underflow, not training quantization, is the main accuracy killer; a sparse residual correction closes most of the gap to BF16.
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Full-Stack FP4: Stable LLM Pretraining with Quantized Projections, Optimizers, and Attention
Full-stack NVFP4 LLM pretraining is stable with a 1.47% loss gap to BF16 via LoRA-SVD projections, transformed AdamW/Root optimizers, and mixed-precision attention.
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Information-Theoretic Lower Bounds for Bit-Constrained Stochastic Optimization via a Reduction to Compressed Gaussian Mean Estimation
Exact reduction yields unconditional lower bounds TB = Omega(d) and T = Omega((sigma^2 d / eps^2) max{1, d/B}) for B-bit stochastic first-order oracles.
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Four Over Six: More Accurate NVFP4 Quantization with Adaptive Block Scaling
Four Over Six adaptively scales blocks in NVFP4 quantization to smaller FP4 values, making representable value distributions more uniform and reducing quantization error especially for near-maximal values.
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Why Low-Precision Transformer Training Fails: An Analysis on Flash Attention
Low-precision Flash Attention fails due to similar low-rank attention representations combined with biased rounding errors that accumulate and corrupt weight updates; a minimal fix to reduce rounding bias stabilizes training.
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Weight updates that fall below half a ULP freeze coordinates deterministically, and freeze time is predictable a priori from a high-precision trajectory and mantissa length alone.
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Stable FP4 Training via Transposition-Invariant Block Quantization
Transposition-invariant 2D block FP4 quantization plus truncation-free scaling and stochastic rounding enables stable end-to-end FP4 LLM training within ~1% of BF16.
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CANN Bench: Benchmarking Agent Generated Kernels against Real NPU and Algorithmic Limits
CANN Bench is an Ascend-NPU benchmark with 53 operators and 1,060 released test cases that scores agent-generated kernels on compilation, correctness, and hardware-anchored performance.
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Decomposing MXFP4 quantization error for LLM reinforcement learning: reducible bias, recoverable deadzone, and an irreducible floor
MXFP4 quantization error decomposes into scale bias, deadzone truncation, and grid noise; macro-block scaling, outlier fallback, and adaptive quantization noise recover BF16 accuracy to within 0.7% and 3.0% on tested models.
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Decomposing MXFP4 quantization error for LLM reinforcement learning: reducible bias, recoverable deadzone, and an irreducible floor
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.
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Decomposing MXFP4 quantization error for LLM reinforcement learning: reducible bias, recoverable deadzone, and an irreducible floor
MXFP4 error decomposes into scale bias, deadzone truncation, and grid noise that each dominate distinct RL failure modes, with macro-block scaling, outlier fallback, and adaptive noise recovering or exceeding BF16 per...
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Search Your Block Floating Point Scales!
ScaleSearch optimizes block floating point scales via fine-grained search to cut quantization error by 27% for NVFP4, improving PTQ by up to 15 points on MATH500 for Qwen3-8B and attention PPL by 0.77 on Llama 3.1 70B.
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Reference Traces for Auditing Invisible Weight Updates and Guiding Exact-Budget Protection
A matched high-precision reference trace forecasts invisible weight-update events in controlled low-precision runs, and a pre-frozen 10% fp32-master mask recovers ~61% of the RNE-vs-fp32 loss gap on three unseen targets.
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Stochastic Rounding Increases Small Singular Values
Stochastic rounding lifts clusters of small singular values even in constant aspect ratio matrices, extending its role as a spectral regularizer.
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VFA: Relieving Vector Operations in Flash Attention with Global Maximum Pre-computation
VFA optimizes Flash Attention by pre-computing global max approximations from key blocks and reordering traversal to reduce vector bottlenecks while preserving exact computation.
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What is New in Stochastic Rounding: a Survey on Theory, Hardware, and Applications
An update survey of stochastic rounding (2022–2026) that centers limited-precision SR, commercial hardware, probabilistic error bounds, and applications in ML and scientific computing.
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