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arXiv 1705.03341cs.LGcs.NAmath.NAmath.OC
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深度神经网络的稳定结构

Stable Architectures for Deep Neural Networks

The University of British Columbia(英属哥伦比亚大学);Xtract Technologies Inc.(Xtract技术公司);Emory University(埃默里大学)

Eldad Haber, Lars Ruthotto

摘要:

深度神经网络已经成为监督机器学习的宝贵工具,例如,文本或图像的分类。虽然深度架构通常提供优于传统技术的结果并成功地表达数据中的复杂模式,但众所周知,深度架构在设计和训练方面具有挑战性,以便它们很好地推广到新数据。深度架构的重要问题是基于导数的学习算法中的数值不稳定性,通常称为爆炸或消失梯度。在本文中,我们提出了受常微分方程(ODE)系统启发的新的前向传播技术,这些技术克服了这一挑战,并为任意深度的网络带来了适定的学习问题。我们方法的核心是将深度学习解释为非线性动力系统的参数估计问题。鉴于这种提法,我们分析了深度学习的稳定性和适定性,并使用这种新的理解来开发新的网络架构。我们将爆炸和消失梯度现象与离散常微分方程的稳定性联系起来,并提出了几种稳定深度网络深度学习的策略。虽然我们的新架构限制了解决方案空间,但几个数值实验显示了它们与最先进网络的竞争力。

英文摘要:

Deep neural networks have become invaluable tools for supervised machine learning, e.g., classification of text or images. While often offering superior results over traditional techniques and successfully expressing complicated patterns in data, deep architectures are known to be challenging to design and train such that they generalize well to new data. Important issues with deep architectures are numerical instabilities in derivative-based learning algorithms commonly called exploding or vanishing gradients. In this paper we propose new forward propagation techniques inspired by systems of Ordinary Differential Equations (ODE) that overcome this challenge and lead to well-posed learning problems for arbitrarily deep networks. The backbone of our approach is our interpretation of deep learning as a parameter estimation problem of nonlinear dynamical systems. Given this formulation, we analyze stability and well-posedness of deep learning and use this new understanding to develop new network architectures. We relate the exploding and vanishing gradient phenomenon to the stability of the discrete ODE and present several strategies for stabilizing deep learning for very deep networks. While our new architectures restrict the solution space, several numerical experiments show their competitiveness with state-of-the-art networks.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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