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. We study a B-bit quantized stochastic first-order oracle: an optimizer interacts for T rounds and receives, each round, a B-bit adaptive public-coin description of its stochastic gradient. Our main contribution is an exact reduction from optimizing a strongly convex quadratic fami

Source: arXiv cs.LG — read the full report at the original publisher.

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