# Prescriptive Scaling Reveals the Evolution of Language Model Capabilities

arXiv: https://arxiv.org/abs/2602.15327 · HTML: https://mlsanity.com/paper/2602.15327/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 63 references that are in the map.
- First posted on arXiv 17 Feb 2026.

## Builds on (most cited first, 30 of 48)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [Yi: Open Foundation Models by 01.AI](https://mlsanity.com/paper/2403.04652/) (2024)
- [Deep Learning Scaling is Predictable, Empirically](https://mlsanity.com/paper/1712.00409/) (2017)
- [Dynabench: Rethinking Benchmarking in NLP](https://mlsanity.com/paper/2104.14337/) (2021)
- [An Empirical Model of Large-Batch Training](https://mlsanity.com/paper/1812.06162/) (2018)
- [Scaling Laws for Transfer](https://mlsanity.com/paper/2102.01293/) (2021)
- [LiveBench: A Challenging, Contamination-Limited LLM Benchmark](https://mlsanity.com/paper/2406.19314/) (2024)
- [Artificial Hivemind: The Open-Ended Homogeneity of Language Models (and Beyond)](https://mlsanity.com/paper/2510.22954/) (2025)
- [Observational Scaling Laws and the Predictability of Language Model Performance](https://mlsanity.com/paper/2405.10938/) (2024)
- [Language models scale reliably with over-training and on downstream tasks](https://mlsanity.com/paper/2403.08540/) (2024)
- [Broken Neural Scaling Laws](https://mlsanity.com/paper/2210.14891/) (2022)
- [Nemotron 3 Nano: Open, Efficient Mixture-of-Experts Hybrid Mamba-Transformer Model for Agentic Reasoning](https://mlsanity.com/paper/2512.20848/) (2025)

## Built on by (most cited first, 1 of 1)

- [Tokens-per-Parameter Coverage Is Critical for Robust LLM Scaling Law Extrapolation](https://mlsanity.com/paper/2605.08541/) (2026)

## Abstract (arXiv)

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.