Configuration-to-Performance Scaling Law with Neural Ansatz

Researchers build scaling laws to forecast the training performance of expensive large-scale runs with larger model size $N$ and data size $D$. These laws assume that other training hyperparameters are optimally chosen, which can require significant effort and, in some cases, be impossible due to external hardware constraints. To improve predictability across a broader set of hyperparameters and enable simpler tuning at scale, we propose learning a \textit{Configuration-to-Performance Scaling Law} (CPL): a mapping from the \textit{full training configuration} to training performance. Because no simple functional form can express this mapping, we parameterize it with a large language model (LLM), and fit it with diverse open-source pretraining logs across multiple sources, yielding a \textit{Neural} Configuration-to-Performance Scaling Law (\predictor). \predictor\ accurately predicts how training configurations influence the final pretraining loss, achieving 20-40\% lower prediction error than the configuration-agnostic Chinchilla law and generalizing to runs using up to 10$\times$ more compute than any run in the training set. It further supports joint tuning of multiple hyperparameters with performance comparable to hyperparameter scaling law baselines. Finally, \predictor\ naturally and effectively extends to richer prediction targets such as loss-curve prediction.