arXiv:2507.21184v1 Announce Type: cross Abstract: Scaling laws are fundamental mathematical relationships that predict how neural network performance evolves with changes in variables such as model size, dataset size, and computational resources. Traditionally, discovering these laws requires extensive human expertise and manual experimentation. We introduce EvoSLD, an automated framework for Scaling Law Discovery (SLD) that leverages evolutionary algorithms guided by Large Language Models (LLMs) to co-evolve symbolic expressions and their optimization routines. Formulated to handle scaling variables, control variables, and response metrics across diverse experimental settings, EvoSLD searches for parsimonious, universal functional forms that minimize fitting errors on grouped data subsets. Evaluated on five real-world scenarios from recent literature, EvoSLD rediscovers exact human-derived laws in two cases and surpasses them in others, achieving up to orders-of-magnitude reductions in normalized mean squared error on held-out test sets. Compared to baselines like symbolic regression and ablated variants, EvoSLD demonstrates superior accuracy, interpretability, and efficiency, highlighting its potential to accelerate AI research. Code is available at https://github.com/linhaowei1/SLD.