Ask what should change when the equation is manipulated, then let the visualization test that expectation.
Foundation Lab
Scaling Laws & Emergent Abilities
GPT-3.5/4, Claude, Gemini, Llama were all designed with these scaling behaviors in mind
#14ScalingScaling & Alignment
key equation
L(N, D, C) \approx L_\infty + a N^{-\alpha} + b D^{-\beta}Selected Foundation Object
Keep the equation fixed; move through the evidence.
Concept 14 of 100ScalingScaling & Alignment / Phase 8: Scaling, theory & multimodal
Current question
Why power-law scaling happens (statistical physics analogies, information-theoretic arguments)
L(N, D, C) \approx L_\infty + a N^{-\alpha} + b D^{-\beta}Use the runnable panel, the key equation, and canonical papers as separate forms of evidence for the same object.
The useful learning product is the reusable mechanism you can carry into another model, paper, or engineering tradeoff.
This atlas page keeps the working demo; the domain notebook carries the fuller Intuition -> Math -> Code -> Demo sequence.
Why It Matters for Modern Models
- GPT-3.5/4, Claude, Gemini, Llama were all designed with these scaling behaviors in mind
- Sora & SDXL apply similar scaling-law reasoning for image/video diffusion backbones
What Tutorials Skip
What is still poorly explained in textbooks and papers:
- Why power-law scaling happens (statistical physics analogies, information-theoretic arguments)
- Visual, interactive plots showing evolving task-specific performance vs scale
Interactive Visualization
Core Math (Optional Deep Dive)
If you want intuition first, start with the key equation and the visualization. Come back here for the full walkthrough.
Key Equation
Test loss obeys approximate power laws:
where = parameters, = data, = compute; are exponents.
Chinchilla rule: for fixed compute, optimal frontier scales roughly as — don't over-scale parameters without matching data.
Some capabilities (chain-of-thought, few-shot reasoning) appear suddenly once scale crosses a threshold — "emergent abilities."