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arXiv · 2202.12404

Exploiting Problem Structure in Deep Declarative Networks: Two Case Studies

Stephen Gould·Dylan Campbell·Itzik Ben-Shabat·Chamin Hewa Koneputugodage·Zhiwei Xu
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Abstract

Deep declarative networks and other recent related works have shown how to differentiate the solution map of a (continuous) parametrized optimization problem, opening up the possibility of embedding mathematical optimization problems into end-to-end learnable models. These differentiability results can lead to significant memory savings by providing an expression for computing the derivative without needing to unroll the steps of the forward-pass optimization procedure during the backward pass. However, the results typically require inverting a large Hessian matrix, which is computationally expensive when implemented naively. In this work we study two applications of deep declarative networks -- robust vector pooling and optimal transport -- and show how problem structure can be exploited to obtain very efficient backward pass computations in terms of both time and memory. Our ideas can be used as a guide for improving the computational performance of other novel deep declarative nodes.

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Stephen Gould, Dylan Campbell, Itzik Ben-Shabat, Chamin Hewa Koneputugodage, Zhiwei Xu. 2022-02-24. Exploiting Problem Structure in Deep Declarative Networks: Two Case Studies. https://arxiv.org/abs/2202.12404

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