Open access
Date
2022-04-01Type
- Journal Article
Abstract
Most stochastic gradient descent algorithms can optimize neural networks that are sub-differentiable in their parameters; however, this implies that the neural network's activation function must exhibit a degree of continuity which limits the neural network model's uniform approximation capacity to continuous functions. This paper focuses on the case where the discontinuities arise from distinct sub-patterns, each defined on different parts of the input space. We propose a new discontinuous deep neural network model trainable via a decoupled two-step procedure that avoids passing gradient updates through the network's only and strategically placed, discontinuous unit. We provide approximation guarantees for our architecture in the space of bounded continuous functions and universal approximation guarantees in the space of piecewise continuous functions which we introduced herein. We present a novel semi-supervised two-step training procedure for our discontinuous deep learning model, tailored to its structure, and we provide theoretical support for its effectiveness. The performance of our model and trained with the propose procedure is evaluated experimentally on both real-world financial datasets and synthetic datasets. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000530954Publication status
publishedExternal links
Journal / series
NeurocomputingVolume
Pages / Article No.
Publisher
ElsevierSubject
Piecewise continuous functions; Universal approximation; Discontinuous feedforward networks; Discontinuous functions; Deep zero-sets; Set-valued universal approximation; Quantitative financeRelated publications and datasets
Is new version of: https://doi.org/10.3929/ethz-b-000522028
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