Labs

Calculus · Follow the steepest slope

Gradient descent on a loss

Place a starting point on an elongated bowl and step downhill. See why learning rate is a length, not a vibe.

Loss is an elongated bowl, f(x, y) = 0.25 x² + y². Click the field to place a start. Each step subtracts η ∇f. The bowl is stretched, so a naive step zigzags in y while crawling in x.

x
2.200
y
1.600
f(x,y)
3.770
‖∇f‖
3.384

Small η crawls. Feature scaling is equivalent to making this bowl rounder.