Prescriptive Scaling Reveals the Evolution of Language Model Capabilities

Abstract:Machine learning model performance improvements tend to arise from competition and application. For deployment, we consider 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 existing and 2k newly evaluated model checkpoints spanning 2022-2026 across six benchmarks, 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 temporal reliability by fitting on earlier model generations and evaluating on later releases: across four of six tasks, the out-of-distribution coverage error remains below 2%, while math reasoning exhibits a consistently advancing boundary over time. For instance, at a budget of 10^24 FLOPs, the estimated attainable accuracies are 0.83 on IFEval and 0.54 on MATH Lvl 5. We then extend our approach to analyze task-dependent saturation and to probe contamination-related shifts on math reasoning tasks. Finally, we introduce a balanced I-optimal sampling algorithm that recovers near-full-data frontiers using roughly 20% of the parameter-count-weighted evaluation budget, as low as 5% on some tasks, while maintaining comparable calibration. Together, our work releases 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.

ICML 2026 Oral. Blog Post: this https URL

Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computation and Language (cs.CL); Machine Learning (stat.ML)

arXiv:2602.15327 [cs.LG]

(or arXiv:2602.15327v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2602.15327 Focus to learn more arXiv-issued DOI via DataCite

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