Scaling Laws Revisited: Non-Monotonic Emergence in Foundation Models

Abstract

Recent empirical investigations of transformer-based language models have revealed systematic relationships between model size, dataset size, and computational budget. We extend these findings by identifying critical transition points where qualitative capabilities emerge discontinuously despite smooth quantitative scaling. Through comprehensive experiments spanning 100M to 100B parameters across diverse architectures and training regimes, we demonstrate that emergence patterns exhibit non-monotonic behavior across different task categories. Our analysis reveals that standard power-law formulations inadequately capture these transition dynamics, particularly for tasks requiring multi-step reasoning and compositional generalization. We propose a refined theoretical framework incorporating phase transitions and discrete capacity thresholds, providing experimental validation across multiple benchmarks including BIG-Bench, MMLU, and custom evaluation suites. These findings have significant implications for efficient model development, capability prediction, and resource allocation in foundation model research, suggesting that linear extrapolation of scaling trends systematically underestimates capability jumps at critical thresholds.