If the Hessian is simply a local quadratic, why can't we approximate it with a spline model?

37 Views Asked by At

The Hessian describes the curvature of the loss landscape that we're optimizing on. In particular, it describes the local quadratic of the loss landscape.

My question is: this seems like we could compute the Hessian much more efficently if we just modelled a local spline model. Why not do that?