Learning Linearized Assignment Flows for Image Labeling

TL;DR

This paper presents a new algorithm for optimizing parameters in linearized assignment flows for image labeling, enabling efficient learning and better understanding of neural network dynamics.

Contribution

It introduces an exact gradient formula and an efficient evaluation method, allowing parameter learning without backpropagation or adjoint equations.

Findings

Performs comparably to automatic differentiation-based methods.

Provides a low-dimensional insight into assignment flow parameters.

Enables efficient parameter optimization via Riemannian gradient descent.

Abstract

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