One Kernel, Fitted Twice

Kernel methods gave us the theory everyone still wants back, and the field abandoned them over one procedure: the O(n³) solve over an n by n Gram matrix, which cannot minibatch, cannot scale, and cannot sit under other layers. So we took one Mercer kernel and fitted it twice: once by the classical exact solve, once by plain gradient descent on a bank of prototypes. The two machines agree, to a…