Year: 2026
Type: preprint
Abstract: Large language models are increasingly trained in continual or open-ended settings, where the total training horizon is not known in advance. Despite this, most existing pretraining recipes are not anytime: they rely on horizon-dependent learning rate schedules and extensive tuning under a fixed compute budget. In this work, we provide a theoretical analysis demonstrating the existence of anytime learning schedules for overparameterized linear regression, and we highlight the central role of weight averaging - also known as model merging - in achieving the minimax convergence rates of stochastic gradient descent. We show that these anytime schedules polynomially decay with time, with the decay rate determined by the source and capacity conditions of the problem. Empirically, we evaluate 150M and 300M parameter language models trained for up to 32x Chinchilla scale, comparing constant and $1/\sqrt{t}$ schedules with weight averaging against a well-tuned cosine schedule. Across the full training range, the anytime schedules achieve comparable final loss to cosine decay. Taken together, our results suggest that weight averaging combined with simple, horizon-free step sizes offers a practical and effective anytime alternative to cosine learning rate schedules for large language model pretraining.
Source: arXiv (Cornell University)
Institution: Harvard University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G1264789558, A Theory of Learned Representations in Artificial and Natural Neural Networks, CAREER: Developing Neural Network Theory for Uncovering How the Brain Learns, G4523241894, G5877837315, MACHINE LEARNING FOR ACCELERATED UNDERSTANDING OF DYNAMIC CATALYSIS, G6671297155, AI Institute for Societal Decision Making (AI-SDM)
OpenAlex ID: W7127646912