Optimal Learning-Rate Schedules under Functional Scaling Laws: Power Decay and Warmup-Stable-Decay
We study optimal learning-rate schedules (LRSs) under the functional scaling law (FSL) framework introduced in Li et al. (2025), which accurately models the loss dynamics of both linear regression and large language model (LLM) pre-training. Within FSL, loss dynamics are governed by two exponents: a source exponent $s>0$ controlling the rate of signal learning, and a capacity exponent $β>1$ determining the rate of noise forgetting. Focusing on a fixed training horizon $N$, we derive the optimal LRSs and […]