Title: Random Scaling of Emergent Capabilities
Primary area: foundation or frontier models, including LLMs
Keywords: random variation, emergence, length generalization, scaling

Abstract: Language models famously improve under a smooth scaling law, but some specific capabilities exhibit sudden breakthroughs in performance.
While advocates of ``emergence" view breakthroughs as unlocked capabilities, others attribute them to thresholding effects on noncontinuous metrics. We propose that breakthroughs are instead driven by continuous changes in the \textit{probability distribution} of training outcomes when performance is bimodally distributed across random seeds. In synthetic length generalization tasks, we show that different random seeds can produce either highly linear or emergent scaling trends. We reveal that sharp breakthroughs in metrics are produced by underlying continuous changes in their distribution across seeds. In a case study of inverse scaling, we  show that even as the probability of a successful run declines, the average performance of a successful run increases monotonically.
We validate our distributional scaling framework on realistic settings by measuring MMLU performance in LM populations. Our observations hold true even under continuous loss metrics, confirming that random variation must be considered when predicting a model's performance from its scale.