Information-Theoretic Lower Bounds for Bit-Constrained Stochastic Optimization via a Reduction to Compressed Gaussian Mean Estimation

arXiv:2606. 00703v1 Announce Type: cross Abstract: Low-precision pretraining (FP8, MXFP4, NVFP4) is now standard for frontier language models, yet the literature is almost entirely achievability -- algorithms and empirical scaling laws -- with no matching characterization of what is information-theoretically possible.

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• llms
• efficiency