Learning linearized assignment flows for image labeling
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...
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| Main Authors: | , , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
2 Aug 2021
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| In: |
Arxiv
Year: 2021, Pages: 1-26 |
| DOI: | 10.48550/arXiv.2108.02571 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.48550/arXiv.2108.02571 Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/2108.02571 
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| Author Notes: | Alexander Zeilmann, Stefania Petra, Christoph Schnörr |
| Summary: | 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. |
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| Item Description: | Identifizierung der Ressource nach: 4 Apr 2022 Gesehen am 22.09.2022 |
| Physical Description: | Online Resource |
| DOI: | 10.48550/arXiv.2108.02571 |