Learning Linearized Assignment Flows for Image Labeling

Abstract We introduce a novel algorithm for estimating optimal parameters of linearized assignment flows image labeling. An exact formula is derived the parameter gradient any loss function that constrained by linear system ODEs determining flow. show how to efficiently evaluate this using Krylov subspace and low-rank approximation. This enables us perform learning Riemannian descent in space, without need backpropagate errors or solve an adjoint equation. Experiments demonstrate our method performs as good highly-tuned machine software automatic differentiation. Unlike methods employing differentiation, approach yields low-dimensional representation internal their dynamics which helps understand more generally neural networks work perform.