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A Convergence Analysis of Adaptive Optimizers under Floating-point Quantization
🤖AI Summary
Researchers introduce the first theoretical framework analyzing convergence of adaptive optimizers like Adam and Muon under floating-point quantization in low-precision training. The study shows these algorithms maintain near full-precision performance when mantissa length scales logarithmically with iterations, with Muon proving more robust than Adam to quantization errors.
Key Takeaways
- →First theoretical framework developed for analyzing adaptive optimizer convergence under hardware-aware floating-point quantization
- →Both Adam and Muon maintain convergence rates close to full-precision versions with proper quantization parameters
- →Adam shows high sensitivity to weights and second-moment quantization due to its β₂ → 1 parameter dependency
- →Muon optimizer demonstrates superior robustness to quantization errors compared to Adam
- →Mantissa length needs to scale only logarithmically with iteration count to preserve performance
#ai#machine-learning#optimization#low-precision-training#adam-optimizer#convergence-analysis#quantization#llm#efficiency#research
Read Original →via arXiv – CS AI
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