scaling-design
ResearchDesign scaling experiments to characterize performance-resource relationships
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Strategy: Scaling Design
Question: How does performance scale with resources?
Methodology
- Neural Scaling Laws (Kaplan 2020, Hoffmann 2022): Power-law relationships between compute/data/parameters and loss.
- Compute-Optimal Scaling (Chinchilla): Find optimal allocation between model size and data.
- Data Scaling: Characterize learning curves as function of dataset size.
- Model Scaling: Performance vs. parameter count at fixed data.
- Inference Scaling: Throughput/latency vs. batch size, sequence length, model size.
Execution Flow
- factor-identification → Identify scaling axes (data, compute, parameters, time)
- level-specification → Define scale points (geometric progression, typically 4-8 points)
- metric-specification → Define metrics at each scale (loss, downstream task, efficiency)
- design-matrix-construction → Build scaling experiment grid
- sample-size-estimation → Determine replicates needed for reliable curve fitting
- budget-constrained-design (tactic) → Optimize which scale points to run given budget
Budget Gate
| Scaling Type | Scale Points | Replicates | Min Runs | Typical Cost |
|---|---|---|---|---|
| Data scaling | 4-6 | 3 | 12-18 | Low (same model, subset data) |
| Model scaling | 4-8 | 2-3 | 8-24 | High (different model sizes) |
| Compute-optimal | 6-10 per iso-FLOP | 1-2 | 12-20 | Very high |
| Inference scaling | 5-10 | 5 | 25-50 | Low (inference only) |
Available Tactics
Optional, no fixed order; the final leaf is always a sop.
| Tactic | When to use |
|---|---|
| budget-constrained-design | Optimize experiment design under compute and time budget constraints |
| statistical-method-selection | Select appropriate statistical methods for experiment analysis |
Available SOPs
Optional, no fixed order; the final leaf is always a sop.
| SOP | When to use |
|---|---|
| design-matrix-construction | Build the experiment design matrix with proper orthogonality and balance |
| factor-identification | Identify independent, dependent, and control variables for an experiment |
| level-specification | Determine appropriate levels for each experimental factor |
| metric-specification | Define experiment metrics and significance standards |
| sample-size-estimation | SOP: power analysis and required experiment count estimation |