解构Scaling Law：优化、架构、数据的三重奏

TL;DR - A technical essay reframes scaling laws as the sum of optimization, architecture, and data errors, then uses power-law assumptions to derive relationships among learning rate, batch size, model scale, training data, and compute. The framework helps connect empirical laws such as Kaplan, Chinchilla, Step, and Microsoft while highlighting where their predictions diverge.

• Optimization error is modeled through training steps, batch size, and learning rate, yielding power-law expressions for their optimal settings.
• Under a fixed compute budget, the derivation predicts near-balanced scaling of model parameters and training data, broadly consistent with Chinchilla-style results.
• The architecture analysis extends beyond dense models to MoE and memory layers, distinguishing active, total, and compute-bearing parameters.
• Data error separates dataset size from the number of samples processed, enabling explicit analysis of multi-epoch training and overfitting.