Studio · Computed loss landscape

Fig. 1

trajectory · newer loss ↑ update −η∇L gradient ∇L minimum

Computed example · two-parameter loss

Ready. Press Step once to separate the gradient from the update.

Drag or use arrow keys to rotate · switch to contours for a top-down path

Current state

6.542Loss L

3.174Gradient norm

0Update step

0.381Update norm

Ready

w = [2.500, 2.500]

Current parameter vector

w_{t + 1} = w_{t} - η \nabla L (w_{t})

next = [2.175, 2.301]

The violet arrow is the gradient. The brass arrow reverses it and scales it by η; that brass vector is the update actually applied.

\begin{array}{l} L (w_{1}, w_{2}) = \frac{1}{2} (w_{1}^{2} + w_{2}^{2}) \\ + 0.2 \sin (3 w_{1}) + 0.3 \cos (3 w_{2}) \end{array}

This is a computed teaching landscape, not a trace from a trained model. It has two equal global minima near [−0.330, ±0.731].