Prescriptive Scaling Reveals the Evolution of Language Model Capabilities

TL;DR

This paper develops a methodology to predict language model performance based on compute resources, analyzing capability boundaries over time and across tasks, and introduces a new dataset and efficient evaluation algorithm.

Contribution

It presents a novel prescriptive scaling law approach for estimating language model capabilities and stability over time, along with a new dataset and an efficient evaluation algorithm.

Findings

Capability boundaries are mostly stable over time.

Math reasoning capabilities are steadily improving.

The proposed method accurately predicts performance with limited evaluation data.

Abstract

For deploying foundation models, practitioners increasingly need prescriptive scaling laws: given a pre training compute budget, what downstream accuracy is attainable with contemporary post training practice, and how stable is that mapping as the field evolves? Using large scale observational evaluations with 5k observational and 2k newly sampled data on model performance, we estimate capability boundaries, high conditional quantiles of benchmark scores as a function of log pre training FLOPs, via smoothed quantile regression with a monotone, saturating sigmoid parameterization. We validate the temporal reliability by fitting on earlier model generations and evaluating on later releases. Across various tasks, the estimated boundaries are mostly stable, with the exception of math reasoning that exhibits a consistently advancing boundary over time. We then extend our approach to analyze task dependent saturation and to probe contamination related shifts on math reasoning tasks. Finally, we introduce an efficient algorithm that recovers near full data frontiers using roughly 20% of evaluation budget. Together, our work releases the Proteus 2k, the latest model performance evaluation dataset, and introduces a practical methodology for translating compute budgets into reliable performance expectations and for monitoring when capability boundaries shift across time.