ENTERPRISE AI ANALYSIS
Revisiting the Scaling Properties of Downstream Metrics in Large Language Model Training
While scaling laws for Large Language Models (LLMs) traditionally focus on proxy metrics like pretraining loss, predicting downstream task performance has been considered unreliable. This paper challenges that view by proposing a direct framework to model the scaling of benchmark performance from the training budget. We find that for a fixed token-to-parameter ratio, a simple power law can accurately describe the scaling behavior of log accuracy on multiple popular downstream tasks. Our results show that the direct approach extrapolates better than the previously proposed two-stage procedure, which is prone to compounding errors. Furthermore, we introduce functional forms that predict accuracy across token-to-parameter ratios and account for inference compute under repeated sampling. We validate our findings on models with up to 17B parameters trained on up to 350B tokens across two dataset mixtures. To support reproducibility and encourage future research, we release the complete set of pretraining losses and downstream evaluation results.
Executive Impact & Core Metrics
Our work demonstrates that directly modeling downstream performance offers significantly improved predictability and reliability for large language models. This shift from proxy metrics to direct, compute-budget-driven scaling laws translates into more efficient resource allocation and more accurate forecasting of LLM capabilities for enterprise applications.
0.0203
Avg. MAE (Power Law)
4.72%
Avg. MRE (%) (Power Law)
70.5%
MRE Improvement over Two-Stage Linear
Deep Analysis & Enterprise Applications
Select a topic to dive deeper, then explore the specific findings from the research, rebuilt as interactive, enterprise-focused modules.
Direct Scaling Law
Our research establishes a new, direct scaling law for downstream performance. Contrary to previous claims of unreliability, we show that for a fixed token-to-parameter ratio, a simple power law can accurately describe the scaling behavior of log accuracy on multiple popular downstream tasks. This direct approach extrapolates better than the previously proposed two-stage procedure, which is prone to compounding errors.
The functional form we use is: - log(Q) = A / C^a, where Q is accuracy, C is training budget (FLOPs), and A, a are benchmark-specific coefficients. To account for random choice in multiple-choice tasks, we normalize accuracy using Q' := (Q - Qrandom) / (1 - Qrandom).
Token-to-Parameter Ratios
We extend the direct scaling law to model downstream performance across different token-to-parameter ratios (TPRs). Building on analogies with pretraining loss scaling, we model the negative log accuracy as a function of model parameters (N) and dataset size (D).
The extended functional form for pretraining loss, adapted for accuracy, is: - log Q ≈ A / N^a + B / D^β, where A, a, B, β are fitted coefficients. This allows us to predict performance when varying model size and training data quantity, optimizing resource allocation effectively.
Pass@k with Inference Compute
For coding benchmarks, we study the effect of increasing the number of samples in pass@k. Our observations show that for a fixed training budget, the relationship between negative log pass rate and 'k' (number of trials) is approximately linear in log scale, indicating a power law behavior with respect to 'k'. The slope of this linear relationship depends on the training compute budget, becoming steeper for larger compute.
We propose an equation to model the pass@k rate Q based on training budget C and number of trials k: log(-log Q(C, k)) = log A + a log C + β log k + δ log C log k. This formula captures the nuanced interaction between compute, sampling, and performance, offering precise predictions for code generation tasks.
1.963%
Average MRE (%) for Power Law (across benchmarks)
Enterprise Process Flow
Fixed Token-to-Parameter Ratio
→
Simple Power Law Model (Eq. 2)
→
Log Accuracy Scaling
→
Predict Downstream Performance
| Strategy | MRE (mean %) | MAE (mean) | RMSE (mean) | R² (mean) |
|---|---|---|---|---|
| Power Law | 1.963 | 0.015 | 0.011 | 0.986 |
| BNSL | 2.713 | 0.020 | 0.013 | 0.993 |
| TwoStage-Linear | 6.667 | 0.044 | 0.023 | 0.943 |
| TwoStage-Logistic | 6.351 | 0.047 | 0.017 | 0.974 |
Direct Scaling Law Outperforms Two-Stage Approaches
Our findings unequivocally demonstrate that direct approaches to scaling downstream performance (both Power Law and BNSL) consistently outperform traditional two-stage methods. This holds true even when two-stage models exhibit superior goodness-of-fit on training data. The discrepancy is attributed to the compounding of errors in two-stage pipelines, where inaccuracies in the initial FLOPs-to-NLL stage are amplified by the subsequent NLL-to-Accuracy mapping. This highlights the practical benefits of a simpler, direct modeling strategy for predicting LLM capabilities, offering higher predictive power and reliability for enterprise applications.
Calculate Your Potential ROI
Estimate the potential efficiency gains and cost savings for your enterprise by leveraging advanced AI models with predictable scaling.
Estimated Annual Savings
$0
Hours Reclaimed Annually
0
Your Enterprise AI Implementation Roadmap
A structured approach to integrating predictable scaling laws into your AI strategy for maximum impact and efficiency.
Phase 1: Discovery & Strategy Alignment
Assess current LLM usage, identify key performance indicators (KPIs), and align AI strategy with business objectives. Leverage direct scaling laws to forecast initial compute requirements and expected performance thresholds.
Phase 2: Pilot Program & Scaling Law Validation
Implement small-scale experiments to validate scaling law predictions for your specific downstream tasks and data mixtures. Refine models for token-to-parameter ratios and pass@k metrics using our extended frameworks.
Phase 3: Full-Scale Deployment & Optimization
Roll out large-scale models, continuously monitoring performance against predicted scaling curves. Utilize insights from predictable scaling to optimize training budgets, model sizes, and inference strategies for maximum ROI.
Phase 4: Continuous Improvement & Innovation
Establish a feedback loop for ongoing model refinement. Explore new frontiers in AI capabilities, confident in the ability to predict and manage performance scaling for future advancements.
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Unlock the full potential of your large language models with a direct, predictable scaling strategy. Schedule a free consultation with our AI experts to tailor these insights to your enterprise needs.
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