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Prescriptive Scaling Reveals the Evolution of Language Model Capabilities

Hanlin Zhang, Jikai Jin, Vasilis Syrgkanis, Sham Kakade · Feb 17, 2026 · Citations: 0

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How to use this page

Coverage: Stale

Use this page to decide whether the paper is strong enough to influence an eval design. If the signals below are thin, treat it as background context and compare it against the stronger hub pages before making protocol choices.

Paper metadata checked

Feb 17, 2026, 3:13 AM

Stale

Protocol signals checked

Feb 17, 2026, 3:13 AM

Stale

Signal strength

Low

Model confidence 0.35

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.

Use caution before copying this protocol

Use this page for context, then validate protocol choices against stronger HFEPX references before implementation decisions.

  • Extraction flags indicate low-signal or possible false-positive protocol mapping.
  • Extraction confidence is 0.35 (below strong-reference threshold).
Human Eval Hub LLM-as-Judge Hub Pairwise Preference Hub

HFEPX Relevance Assessment

This paper is adjacent to HFEPX scope and is best used for background context, not as a primary protocol reference.

Best use

Background context only

Use if you need

A secondary eval reference to pair with stronger protocol papers.

Main weakness

Extraction flags indicate low-signal or possible false-positive protocol mapping.

Trust level

Low

Eval-Fit Score

0/100 • Low

Treat as adjacent context, not a core eval-method reference.

Human Feedback Signal

Not explicit in abstract metadata

Evaluation Signal

Detected

HFEPX Fit

Adjacent candidate

Extraction confidence: Low

If you are doing eval pipeline work, start here:

Human Eval Hub LLM-as-Judge Hub Pairwise Preference Hub Tool-Use Eval Hub

What We Could Reliably Extract

Each protocol field below shows whether the signal looked explicit, partial, or missing in the available metadata. Use this to judge what is safe to trust directly and what still needs full-paper validation.

Human Feedback Types

missing

None explicit

Confidence: Low Source: Persisted extraction missing

No explicit feedback protocol extracted.

Evidence snippet: 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?

Evaluation Modes

partial

Automatic Metrics

Confidence: Low Source: Persisted extraction evidenced

Includes extracted eval setup.

Evidence snippet: 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?

Quality Controls

missing

Not reported

Confidence: Low Source: Persisted extraction missing

No explicit QC controls found.

Evidence snippet: 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?

Benchmarks / Datasets

missing

Not extracted

Confidence: Low Source: Persisted extraction missing

No benchmark anchors detected.

Evidence snippet: 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?

Reported Metrics

partial

Accuracy

Confidence: Low Source: Persisted extraction evidenced

Useful for evaluation criteria comparison.

Evidence snippet: 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?

Rater Population

missing

Unknown

Confidence: Low Source: Persisted extraction missing

Rater source not explicitly reported.

Evidence snippet: 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?

Human Data Lens

  • Uses human feedback: No
  • Feedback types: None
  • Rater population: Unknown
  • Unit of annotation: Unknown
  • Expertise required: Math, Law
  • Extraction source: Persisted extraction

Evaluation Lens

  • Evaluation modes: Automatic Metrics
  • Agentic eval: None
  • Quality controls: Not reported
  • Confidence: 0.35
  • Flags: low_signal, possible_false_positive

Protocol And Measurement Signals

Benchmarks / Datasets

No benchmark or dataset names were extracted from the available abstract.

Reported Metrics

accuracy

Research Brief

Deterministic synthesis

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?

Generated Feb 17, 2026, 3:13 AM · Grounded in abstract + metadata only

Key Takeaways

  • 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.

Researcher Actions

  • Compare this paper against others mentioning MATH.
  • Validate inferred eval signals (Automatic metrics) against the full paper.
  • Use related-paper links to find stronger protocol-specific references.

Caveats

  • Generated from abstract + metadata only; no PDF parsing.
  • Signals below are heuristic and may miss details reported outside the abstract.

Recommended Queries

MATH Accuracy

Research Summary

Contribution Summary

  • 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…
  • 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…

Why It Matters For Eval

  • 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…
  • Finally, we introduce an efficient algorithm that recovers near full data frontiers using roughly 20% of evaluation budget.

Researcher Checklist

  • Gap: Human feedback protocol is explicit

    No explicit human feedback protocol detected.

  • Pass: Evaluation mode is explicit

    Detected: Automatic Metrics

  • Gap: Quality control reporting appears

    No calibration/adjudication/IAA control explicitly detected.

  • Gap: Benchmark or dataset anchors are present

    No benchmark/dataset anchor extracted from abstract.

  • Pass: Metric reporting is present

    Detected: accuracy

Related Papers

Papers are ranked by protocol overlap, extraction signal alignment, and semantic proximity.

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