Information-Theoretic Lower Bounds for Bit-Constrained Stochastic Optimization via a Reduction to Compressed Gaussian Mean Estimation
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 family to interactively compressed Gaussian mean estimation -- under the B-bit oracle the query carries no information, so optimization collapses exact...
| Authors | Munsik Kim |
|---|---|
| Primary category | cs.IT |
| Published | 30 May 2026 |
| Last updated at source | 30 May 2026 |
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