Section 1 — What you will learn
✓ By the end you will understand
- Learning rate (α) = the hiker’s step size.
- Gradient (slope) = which direction is downhill, and how steep.
- Convergence = when the hiker reaches the bottom and stops.
- Overshooting = when α is too big and the hiker jumps past the valley.
- Momentum = extra “speed memory” that can help (or cause chaos).
- Local minimum = a small dip that can trap the hiker on bumpy landscapes.
Section 2 — Controls
Low α: tiny steps (safe but slow). High α: huge jumps (fast… or explosive).
This is your initial parameter value θ (think: a weight).
Momentum can help roll through tiny bumps, but can overshoot if too high.
Bumpy valley is where “getting stuck” becomes real.
Tip: If you see “Divergence”, reduce α (move slider left).
Section 3 — Live Stats
Current Loss (Altitude)
—
Slope (Gradient)
—
Step Count
0
Status
Ready
Section 4 — Math (The Engine)
How the hiker moves (every step)
Hover words + canvas for hints
θnew =
θold
− α ·
∂J/∂θ
With momentum: v = m·v − α·(∂J/∂θ), θ = θ + v
Meaning: If slope is positive → move left. If slope is negative → move right.
With momentum: v = m·v − α·(∂J/∂θ), θ = θ + v
Meaning: If slope is positive → move left. If slope is negative → move right.
🎮 Kid Coach
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Hover the ball, arrows, and beams on the canvas.
Section 5 — The Valley Playground
hiker (ball)
loss curve J(θ)
gradient arrow (slope)
step jump (Δθ)
trail (path)
minimum zone
Live explanation
Move α and momentum. Press START. Watch the hiker learn to reach the minimum.
Game HUD
Mission: reach the bottom without bouncing forever.
Stability Meter
Stable: not moving yet.
Quick Actions
Hover the canvas: ball, arrows, and beams will explain themselves.