Fractional Deep Neural Network via Constrained Optimization

• URL: http://arxiv.org/abs/2004.00719v1
• Date: Wed, 1 Apr 2020 21:58:21 GMT
• Title: Fractional Deep Neural Network via Constrained Optimization
• Authors: Harbir Antil, Ratna Khatri, Rainald L\"ohner, and Deepanshu Verma
• Abstract summary: This paper introduces a novel algorithmic framework for a deep neural network (DNN) Fractional-DNN can be viewed as a time-discretization of a fractional in time nonlinear ordinary differential equation (ODE)
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper introduces a novel algorithmic framework for a deep neural network (DNN), which in a mathematically rigorous manner, allows us to incorporate history (or memory) into the network -- it ensures all layers are connected to one another. This DNN, called Fractional-DNN, can be viewed as a time-discretization of a fractional in time nonlinear ordinary differential equation (ODE). The learning problem then is a minimization problem subject to that fractional ODE as constraints. We emphasize that an analogy between the existing DNN and ODEs, with standard time derivative, is well-known by now. The focus of our work is the Fractional-DNN. Using the Lagrangian approach, we provide a derivation of the backward propagation and the design equations. We test our network on several datasets for classification problems. Fractional-DNN offers various advantages over the existing DNN. The key benefits are a significant improvement to the vanishing gradient issue due to the memory effect, and better handling of nonsmooth data due to the network's ability to approximate non-smooth functions.

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