ND Optimizer Arena v2

Pre-runs every optimizer from several starts in the full N-D space, then picks one fixed 2-D plane (PCA of the trajectories, as in Li et al. 2018) and draws the true loss on that plane. Faded markers = far from the plane.

Presets

Landscape

Scene

Dimensions Roughness Gaussian bumps Gradient noise σ Landscape seed

Optimizers

Learning rate Steps Start points

2-D view

Plane Contour lines Fade points by distance from plane

Critical-point census (synthetic scene)

From random starts, Newton's method finds nearby critical points of any type; each is classified by the number of negative Hessian eigenvalues (its index). As dimension grows the fraction that are true minima collapses — saddles dominate.

Starts per dimension

Loss vs step (true full-batch loss)

Decision boundary