🌊 Fisher Geometry Curvature Explorer

Core idea:

1. Multi-head setup: Think of 3-5 different "expert" networks, each with their own weights
2. Smart blending: A gating function decides how much to trust each expert at different points in parameter space
3. Fisher geometry: Uses probability theory to measure how "curved" or "bumpy" the combined loss surface is at each point
4. Interactive exploration: You can adjust the experts and gating to see how it changes the landscape's geometry

🌈 The colors show:

• Red/Yellow: Very curved, difficult optimization (imagine steep hills)
• Blue/Purple: Flatter regions, easier optimization (imagine gentle valleys)

🎯 Why it matters:

This geometry tells you where gradient descent will struggle (high curvature) vs. where it will flow smoothly (low curvature). It's like having a topographical map of your neural network's optimization landscape.

The interactive controls let you see how different architectural choices (number of heads, gating strength, etc.) create completely different geometric landscapes for optimization.