Ask what should change under a concrete input, then trace that expectation through the equation.
Foundation Lab
Weight Initialization: Xavier, He & µP
Bad initialization → vanishing/exploding activations → training fails immediately
#48InitOptimization
key equation
Selected Foundation Object
Keep the equation fixed; move through the evidence.
Concept 48 of 100InitOptimization / Phase 3: Optimization & generalization
Current question
The "1/√n" scaling keeps variance constant through layers: Var(output) ≈ Var(input)
Use the key equation and canonical papers as the available witnesses, without implying that a runnable panel exists.
The useful learning product is the reusable mechanism you can carry into another model, paper, or engineering tradeoff.
Use prerequisites, dependents, and semantic links to repair the next gap without leaving the object behind.
Why It Matters for Modern Models
- Bad initialization → vanishing/exploding activations → training fails immediately
- µP is how labs scale hyperparameters: tune on small proxy, apply to full-scale training
- Connects to NTK theory: at infinite width with proper scaling, training becomes deterministic
What Tutorials Skip
What is still poorly explained in textbooks and papers:
- The "1/√n" scaling keeps variance constant through layers: Var(output) ≈ Var(input)
- ReLU kills half the activations, so He init uses 2× variance to compensate
- µP insight: learning rate should scale with layer width to keep update magnitudes constant
Visualization Status
Core Math (Optional Deep Dive)
If you want intuition first, start with the key equation and cited sources. Come back here for the full walkthrough.
Key Equation
Xavier/Glorot (for tanh/sigmoid):
He/Kaiming (for ReLU):
µP (Maximal Update Parameterization): Scales init AND learning rate by width:
This enables hyperparameter transfer: tune on small model, scale to large.