Fast Matrix Multiplication in fp8: Certified Coefficient Optimization and Measured Error

arXiv:2609.26077 · cs.LG, cs.NA, math.NA · Submitted 2026-08-04 · Read on arXiv

cs.LG, cs.NA, math.NA

Submitted: 2026-08-04

Updated: 2026-08-04

Comments: 25 pages, 4 figures. Reproducibility artifact: https://github.com/xieTwim/fast-matmul-fp8-artifact

Code: https://github.com/xieTwim/fast-matmul-fp8-artifact

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Calibration — 11× in this paper · explained in 7 episodes
• Quantization — 7× in this paper · explained in 12 episodes
• Accuracy — 6× in this paper · explained in 1 episode
• Fidelity — 6× in this paper · explained in 2 episodes
• Aggregation — 3× in this paper · explained in 1 episode
• Exchangeability — 3× in this paper · explained in 2 episodes
• Robustness — 3× in this paper · explained in 5 episodes
• Core — 2× in this paper · explained in 2 episodes
• Decode — 2× in this paper · explained in 2 episodes
• Trace — 2× in this paper · explained in 2 episodes
• Ablation — 1× in this paper · explained in 1 episode
• Annual Symposium on Foundations of Computer Science — 1× in this paper
• Benchmark — 1× in this paper · explained in 2 episodes
• Foundation Model — 1× in this paper · explained in 3 episodes
• Foundation Models — 1× in this paper · explained in 7 episodes
• Pairwise Comparisons — 1× in this paper · explained in 2 episodes
• Provenance — 1× in this paper · explained in 4 episodes
• Transformer — 1× in this paper · explained in 2 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• The geometry of rank decompositions of matrix multiplication I: 2x2 matrices
• Strassen's algorithm is not optimally accurate
• Towards automated generation of fast and accurate algorithms for recursive matrix multiplication
• A catalog of fast matrix multiplication algorithms with frontier-closure search
• FP8 Formats for Deep Learning
• Optimal Quantization for Matrix Multiplication
• High-Rate Quantized Matrix Multiplication I
• Fast Matrix Multiplication in Small Formats: Discovering New Schemes with an Open-Source Flip Graph Framework
• Stability Improvements for Fast Matrix Multiplication
• FalconGEMM: Surpassing Hardware Peaks with Lower-Complexity Matrix Multiplication

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