The method of ellipcenters with momentum and relaxation for convex quadratic minimization

What the math gives to ML

The paper introduces an optimizer geometry that uses two points on the same objective level set and the intersection of their normal directions as an ellipcenter. For a strictly convex quadratic, the equal-value second point can be obtained exactly along the negative-gradient ray, and the two endpoint gradients define a two-dimensional subspace that captures local anisotropy. This suggests a minibatch optimizer that replaces part of a conventional gradient step with a curvature-aware secant construction, optionally mixed with momentum and relaxation. The main transferable asset is not the ellipse itself but the cheap use of two equal-loss gradient evaluations to infer a local two-dimensional geometry without forming a Hessian.