Recent study shows that a wide deep network can obtain accuracy comparable to a deeper but narrower network. Compared to narrower and deeper networks, wide networks employ relatively less number of layers and have various important benefits, such that they have less running time on parallel computing devices, and they are less affected by gradient vanishing problems. However, the parameter size of a wide network can be very large due to use of large width of each layer in the network. In order to keep the benefits of wide networks meanwhile improve the parameter size and accuracy trade-off of wide networks, we propose a binary tree architecture to truncate architecture of wide networks by reducing the width of the networks. More precisely, in the proposed architecture, the width is continuously reduced from lower layers to higher layers in order to increase the expressive capacity of network with a less increase on parameter size. Also, to ease the gradient vanishing problem, features obtained at different layers are concatenated to form the output of our architecture. By employing the proposed architecture on a baseline wide network, we can construct and train a new network with same depth but considerably less number of parameters. In our experimental analyses, we observe that the proposed architecture enables us to obtain better parameter size and accuracy trade-off compared to baseline networks using various benchmark image classification datasets. The results show that our model can decrease the classification error of baseline from 20.43 to 19.22 on Cifar-100 using only 28 of parameters that baseline has. Code is available at this https URL.
Recently, various architectures of convolutional neural networks (CNNs) have been proposed @cite_1 @cite_4 @cite_25 @cite_18 @cite_21 @cite_6 . @cite_13 , connections between random forest @cite_12 and CNNs are investigated. Inspired by random forest, they embedded routing functions to CNNs and obtain Conditional CNNs. As shown in their experiments, Conditional CNNs with highly branched tree architectures can improve the accuracy-efficiency trade-off. Conditional CNNs can be considered as symmetric full tree architectures. On the other hand, we use an asymmetric tree architecture and concatenate features from different layers. Another related work, a used by FractalNet was proposed in @cite_17 . Fractal architecture can also be considered as a tree architecture. Fractal architecture is different from ours in several aspects. First, the output of a fractal architecture is element-wise mean of features obtained at different layers. Also, all convolutional layers used in fractal architecture use the same width, which may result in a large parameter size if the width is large.
@cite_18 @cite_4 @cite_21 @cite_1 @cite_6 @cite_13 @cite_25 @cite_12 @cite_17
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Deep Convolutional Neural Networks (CNNs) offer remarkable performance of classifications and regressions in many high-dimensional problems and have been widely utilized in real-word cognitive applications. However, high computational cost of CNNs greatly hinder their deployment in resource-constrained applications, real-time systems and edge computing platforms. To overcome this challenge, we propose a novel filter-pruning framework, two-phase filter pruning based on conditional entropy, namely , to compress the CNN models and reduce the inference time with marginal performance degradation. In our proposed method, we formulate filter pruning process as an optimization problem and propose a novel filter selection criteria measured by conditional entropy. Based on the assumption that the representation of neurons shall be evenly distributed, we also develop a maximum-entropy filter freeze technique that can reduce over fitting. Two filter pruning strategies -- global and layer-wise strategies, are compared. Our experiment result shows that combining these two strategies can achieve a higher neural network compression ratio than applying only one of them under the same accuracy drop threshold. Two-phase pruning, that is, combining both global and layer-wise strategies, achieves 10 X FLOPs reduction and 46 inference time reduction on VGG-16, with 2 accuracy drop. Recent advances in Convolutional Neural Networks (CNNs) have obtained promising results in difficult deep learning tasks. However, the success of a CNN depends on finding an architecture to fit a given problem. A hand-crafted architecture is a challenging, time-consuming process that requires expert knowledge and effort, due to a large number of architectural design choices. In this article, we present an efficient framework that automatically designs a high-performing CNN architecture for a given problem. In this framework, we introduce a new optimization objective function that combines the error rate and the information learnt by a set of feature maps using deconvolutional networks (deconvnet). The new objective function allows the hyperparameters of the CNN architecture to be optimized in a way that enhances the performance by guiding the CNN through better visualization of learnt features via deconvnet. The actual optimization of the objective function is carried out via the Nelder-Mead Method (NMM). Further, our new objective function results in much faster convergence towards a better architecture. The proposed framework has the ability to explore a CNN architecture’s numerous design choices in an efficient way and also allows effective, distributed execution and synchronization via web services. Empirically, we demonstrate that the CNN architecture designed with our approach outperforms several existing approaches in terms of its error rate. Our results are also competitive with state-of-the-art results on the MNIST dataset and perform reasonably against the state-of-the-art results on CIFAR-10 and CIFAR-100 datasets. Our approach has a significant role in increasing the depth, reducing the size of strides, and constraining some convolutional layers not followed by pooling layers in order to find a CNN architecture that produces a high recognition performance. Convolutional neural networks (CNNs) have become the dominant neural network architecture for solving many state-of-the-art (SOA) visual processing tasks. Even though graphical processing units are most often used in training and deploying CNNs, their power efficiency is less than 10 GOp s W for single-frame runtime inference. We propose a flexible and efficient CNN accelerator architecture called NullHop that implements SOA CNNs useful for low-power and low-latency application scenarios. NullHop exploits the sparsity of neuron activations in CNNs to accelerate the computation and reduce memory requirements. The flexible architecture allows high utilization of available computing resources across kernel sizes ranging from @math to @math . NullHop can process up to 128 input and 128 output feature maps per layer in a single pass. We implemented the proposed architecture on a Xilinx Zynq field-programmable gate array (FPGA) platform and presented the results showing how our implementation reduces external memory transfers and compute time in five different CNNs ranging from small ones up to the widely known large VGG16 and VGG19 CNNs. Postsynthesis simulations using Mentor Modelsim in a 28-nm process with a clock frequency of 500 MHz show that the VGG19 network achieves over 450 GOp s. By exploiting sparsity, NullHop achieves an efficiency of 368 , maintains over 98 utilization of the multiply–accumulate units, and achieves a power efficiency of over 3 TOp s W in a core area of 6.3 mm2. As further proof of NullHop’s usability, we interfaced its FPGA implementation with a neuromorphic event camera for real-time interactive demonstrations. Two architectures that generalize convolutional neural networks (CNNs) for the processing of signals supported on graphs are introduced. We start with the selection graph neural network (GNN), which replaces linear time invariant filters with linear shift invariant graph filters to generate convolutional features and reinterprets pooling as a possibly nonlinear subsampling stage where nearby nodes pool their information in a set of preselected sample nodes. A key component of the architecture is to remember the position of sampled nodes to permit computation of convolutional features at deeper layers. The second architecture, dubbed aggregation GNN, diffuses the signal through the graph and stores the sequence of diffused components observed by a designated node. This procedure effectively aggregates all components into a stream of information having temporal structure to which the convolution and pooling stages of regular CNNs can be applied. A multinode version of aggregation GNNs is further introduced for operation in large-scale graphs. An important property of selection and aggregation GNNs is that they reduce to conventional CNNs when particularized to time signals reinterpreted as graph signals in a circulant graph. Comparative numerical analyses are performed in a source localization application over synthetic and real-world networks. Performance is also evaluated for an authorship attribution problem and text category classification. Multinode aggregation GNNs are consistently the best-performing GNN architecture.