Read slope. Choose distance. Measure again.

Can your next step lower the loss?

Place the probe on the terrain or use the exact start. Predict before moving: gradient gives a local direction, not a safe jump size.

Loading Three.js 0.160.0

WebGL is unavailable. The exact equations, controls, loss trace, assessment, and export remain active as a numeric fallback.

Current loss16.50

Position (x,y)3.00, 2.00

Gradient ∇L4.00, 10.00

Update count0

Surface A · Convex bowlMastery 0/3

Predict the next loss

L=(x−1)²+2(y+0.5)²
∇L=(2(x−1), 4(y+0.5))

Learning rate α0.10

Momentum β0.00

Commit a prediction.The gradient here is (4,10). The update subtracts a scaled version of it; your learning rate decides how far.

Diagnose the dangerous jump

Set α to 0.60 from the Surface A start, predict, and step. Why can loss rise even though the local direction was correct?

Run the counterexample, then diagnose it.

Transfer to a shifted valley

Surface B starts at (2,−2) with ∇L=(7,−3). If descent subtracts the gradient, which way does each coordinate move?

Transfer mastery is still open.

Teaching model: two analytic convex surfaces, not a live neural network. Real training can add stochastic batches, noise, saddles, constraints, and millions of parameters. The source video and speaker biography are not reproduced.