Researchers demonstrate that the scaling exponent in neural scaling laws varies systematically based on optimizer choice, with preconditioned optimizers achieving 2.6x larger exponents than standard gradient descent in controlled experiments. The findings suggest scaling-law forecasts must account for optimizer selection, though the practical impact on large-scale LLM training remains uncertain.
This research challenges a foundational assumption in deep learning: that neural scaling laws follow fixed, architecture-determined patterns. The study uses random-feature regression—a theoretically tractable framework—to isolate optimizer effects from confounding variables, finding that preconditioned optimizers consistently produce steeper learning curves across different spectral conditions. At spectral indices near s ≈ 1.0, characteristic of natural language processing, the gap widens dramatically: full natural gradient achieves α ≈ 0.31 versus α ≈ 0.12 for vanilla gradient descent. This 2.6x difference compounds exponentially with model-size scaling, suggesting optimizer choice could significantly impact sample efficiency and training costs.
The research addresses a critical gap in scaling-law literature, which typically treats the exponent α as fixed despite widespread practitioner knowledge that different optimizers behave differently. By providing spectral diagnostics that predict when advanced optimizers prove worthwhile, the authors offer practitioners a principled way to select optimization methods based on data properties.
For AI development, the implications are substantial: accurately forecasting scaling behaviors requires optimizer-aware models, potentially reshaping compute allocation decisions and training budget planning. However, the authors acknowledge a crucial limitation—whether these laboratory findings transfer to billion-parameter LLM training remains unresolved, with emerging evidence suggesting advantages may diminish at scale. This uncertainty prevents definitive claims about production impact, but the theoretical insight validates the importance of optimizer selection in scaling discussions.
- →Neural scaling exponents depend systematically on optimizer choice, contradicting prior assumptions of fixed values
- →Preconditioned optimizers achieve 2.6x larger scaling exponents than gradient descent in controlled experiments
- →Optimizer advantages concentrate at spectral indices characteristic of natural language processing (s ≈ 1.0)
- →Scaling-law forecasts must incorporate optimizer selection for accuracy, especially in compute-intensive training scenarios
- →Transferability to large-scale LLM training remains uncertain, requiring further investigation at production scales