Surface: Anisotropic Ravine
Step: 0 / 150
θ₀: [-2.60, 1.40]
2D Contour
Min: (0,0)
Updated starting point θ₀
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Landscape & Hyperparameters
0.035
Convergence Telemetry
Loss ℒ(θ)
| Optimiser | Loss | Dist to Min | Show |
|---|---|---|---|
| SGD | -- | -- | |
| Momentum (γ=0.9) | -- | -- | |
| RMSProp (β=0.99) | -- | -- | |
| Adam (β₁=0.9, β₂=0.999) | -- | -- |
Mathematical Mechanics
Anisotropic Ravine: The curvature in the $y$-direction is
25× higher than along the $x$-floor ($\lambda_1 \gg \lambda_2$). Vanilla SGD oscillates
violently between canyon walls. Momentum cancels perpendicular oscillations and accelerates
along the floor, while Adam dynamically normalises step sizes via $\sqrt{\hat{v}_t}$.