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:
- 10095863
- Journal Name:
- Joint Workshop on On-Device Machine Learning & Compact Deep Neural Network Representations (ODML-CDNNR) at ICML 2019
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Deep convolutional neural networks have revolutionized many machine learning and computer vision tasks, however, some remaining key challenges limit their wider use. These challenges include improving the network's robustness to perturbations of the input image and the limited ``field of view'' of convolution operators. We introduce the IMEXnet that addresses these challenges by adapting semi-implicit methods for partial differential equations. Compared to similar explicit networks, such as residual networks, our network is more stable, which has recently shown to reduce the sensitivity to small changes in the input features and improve generalization. The addition of an implicit step connects all pixels in each channel of the image and therefore addresses the field of view problem while still being comparable to standard convolutions in terms of the number of parameters and computational complexity. We also present a new dataset for semantic segmentation and demonstrate the effectiveness of our architecture using the NYU Depth dataset.
-
The high demand for computational and storage resources severely impedes the deployment of deep convolutional neural networks (CNNs) in limited resource devices. Recent CNN architectures have proposed reduced complexity versions (e.g,. SuffleNet and MobileNet) but at the cost of modest decreases in accuracy. This paper proposes pSConv, a pre-defined sparse 2D kernel based convolution, which promises significant improvements in the trade-off between complexity and accuracy for both CNN training and inference. To explore the potential of this approach, we have experimented with two widely accepted datasets, CIFAR-10 and Tiny ImageNet, in sparse variants of both the ResNet18 and VGG16 architectures. Our approach shows a parameter count reduction of up to 4.24× with modest degradation in classification accuracy relative to that of standard CNNs. Our approach outperforms a popular variant of ShuffleNet using a variant of ResNet18 with pSConv having 3 × 3 kernels with only four of nine elements not fixed at zero. In particular, the parameter count is reduced by 1.7× for CIFAR-10 and 2.29× for Tiny ImageNet with an increased accuracy of ~ 4%.
-
In this paper, we pave a novel way towards the concept of bit-wise In-Memory Convolution Engine (IMCE) that could implement the dominant convolution computation of Deep Convolutional Neural Networks (CNN) within memory. IMCE employs parallel computational memory sub-array as a fundamental unit based on our proposed Spin Orbit Torque Magnetic Random Access Memory (SOT-MRAM) design. Then, we propose an accelerator system architecture based on IMCE to efficiently process low bit-width CNNs. This architecture can be leveraged to greatly reduce energy consumption dealing with convolutional layers and also accelerate CNN inference. The device to architecture co-simulation results show that the proposed system architecture can process low bit-width AlexNet on ImageNet data-set favorably with 785.25μJ/img, which consumes ~3× less energy than that of recent RRAM based counterpart. Besides, the chip area is ~4× smaller.
-
In this paper, we propose a deep multimodal fusion network to fuse multiple modalities (face, iris, and fingerprint) for person identification. The proposed deep multimodal fusion algorithm consists of multiple streams of modality-specific Convolutional Neural Networks (CNNs), which are jointly optimized at multiple feature abstraction levels. Multiple features are extracted at several different convolutional layers from each modality-specific CNN for joint feature fusion, optimization, and classification. Features extracted at different convolutional layers of a modality-specific CNN represent the input at several different levels of abstract representations. We demonstrate that an efficient multimodal classification can be accomplished with a significant reduction in the number of network parameters by exploiting these multi-level abstract representations extracted from all the modality-specific CNNs. We demonstrate an increase in multimodal person identification performance by utilizing the proposed multi-level feature abstract representations in our multimodal fusion, rather than using only the features from the last layer of each modality-specific CNNs. We show that our deep multi-modal CNNs with multimodal fusion at several different feature level abstraction can significantly outperform the unimodal representation accuracy. We also demonstrate that the joint optimization of all the modality-specific CNNs excels the score and decision level fusions of independently optimized CNNs.
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Publisher's Version of Record
- The DOI is not currently available
