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
The rapid adoption of low-precision pretraining in frontier language models necessitates a deeper theoretical understanding of its limits and information trade-offs.
This research provides crucial information-theoretic lower bounds for bit-constrained stochastic optimization, which is fundamental to scaling AI by optimizing compute and memory usage.
The focus shifts from purely empirical scaling laws to a theoretical understanding of what is information-theoretically possible in low-precision AI training, guiding future hardware and algorithm design.
- · AI algorithm designers
- · Semiconductor manufacturers
- · Cloud providers
- · Companies with inefficient AI training pipelines
- · Developers ignoring theoretical limits
More efficient and performant AI models due to a clearer understanding of optimization limits in low-precision settings.
Acceleration in the development of specialized AI hardware tailored to these theoretical optimization constraints.
Potentially democratized access to advanced AI training due to reduced computational requirements, broadening the base of AI innovators.
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Read at arXiv cs.LG