Learning Linearized Assignment Flows for Image Labeling
- URL: http://arxiv.org/abs/2108.02571v1
- Date: Mon, 2 Aug 2021 13:38:09 GMT
- Title: Learning Linearized Assignment Flows for Image Labeling
- Authors: Alexander Zeilmann, Stefania Petra, Christoph Schn\"orr
- Abstract summary: We introduce a novel algorithm for estimating optimal parameters of linearized assignment flows for image labeling.
We show how to efficiently evaluate this formula using a Krylov subspace and a low-rank approximation.
- Score: 70.540936204654
- License: http://creativecommons.org/licenses/by/4.0/
- 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, in less than 10 seconds for a
$512\times 512$ image using just about $0.5$ GB memory. 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 networks
work and perform that realize assignment flows and generalizations thereof.
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