Distributional Scaling for Emergent Capabilities (2502.17356v3)

Abstract: This paper explores the nature of sudden breakthroughs in LLM performance at scale, which stand in contrast to smooth improvements governed by scaling laws. 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 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. Furthermore, we provide a case study of inverse scaling. We validate our distributional scaling framework on realistic settings by measuring MMLU performance in LM populations. These insights emphasize the role of random variation in the effect of scale on LM capabilities.