Residual neural networks can be viewed as the forward Euler discretization of an Ordinary Differential Equation (ODE) with a unit time step. This has recently motivated researchers to explore other discretization approaches and train ODE based networks. However, an important challenge of neural ODEs is their prohibitive memory cost during gradient backpropogation. Recently a method proposed in arXiv:1806.07366, claimed that this memory overhead can be reduced from LNt, where Nt is the number of time steps, down to O(L) by solving forward ODE backwards in time, where L is the depth of the network. However, we will show that this approach may lead to several problems: (i) it may be numerically unstable for ReLU/non-ReLU activations and general convolution operators, and (ii) the proposed optimize-then-discretize approach may lead to divergent training due to inconsistent gradients for small time step sizes. We discuss the underlying problems, and to address them we propose ANODE, a neural ODE framework which avoids the numerical instability related problems noted above. ANODE has a memory footprint of O(L) + O(Nt), with the same computational cost as reversing ODE solve. We furthermore, discuss a memory efficient algorithm which can further reduce this footprint with a tradeoff of additionalmore »
LeanResNet: A Low-cost Yet Effective Convolutional Residual Networks
Convolutional Neural Networks (CNNs) filter the input data using spatial convolution operators with compact stencils. Commonly, the convolution operators couple features from all channels, which leads to immense computational cost in the training of and prediction with CNNs. To improve the efficiency of CNNs, we introduce lean convolution operators that reduce the number of parameters and computational complexity, and can be used in a wide range of existing CNNs. Here, we exemplify their use in residual networks (ResNets), which have been very reliable for a few years now and analyzed intensively. In our experiments on three image classification problems, the proposed LeanResNet yields results that are comparable to other recently proposed reduced architectures using similar number of parameters.
- Publication Date:
- NSF-PAR ID:
- Journal Name:
- Joint Workshop on On-Device Machine Learning & Compact Deep Neural Network Representations (ODML-CDNNR) at ICML 2019
- Sponsoring Org:
- National Science Foundation
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