We present a greedy-based approach to construct an efficient single hidden layer neural network with the ReLU activation that approximates a target function. In our approach we obtain a shallow network by utilizing a greedy algorithm with the prescribed dictionary provided by the available training data and a set of possible inner weights. To facilitate the greedy selection process we employ an integral representation of the network, based on the ridgelet transform, that significantly reduces the cardinality of the dictionary and hence promotes feasibility of the greedy selection. Our approach allows for the construction of efficient architectures which can be treated either as improved initializations to be used in place of random-based alternatives, or as fully-trained networks in certain cases, thus potentially nullifying the need for backpropagation training. Numerical experiments demonstrate the tenability of the proposed concept and its advantages compared to the conventional techniques for selecting architectures and initializations for neural networks.
The dictionary reduction step in our approach heavily relies on neural network integral representations, particularly on the so called ridgelet transform. Other similar approaches include those in @cite_0 and @cite_2 .
@cite_0 @cite_2
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We propose a simple two-step approach for speeding up convolution layers within large convolutional neural networks based on tensor decomposition and discriminative fine-tuning. Given a layer, we use non-linear least squares to compute a low-rank CP-decomposition of the 4D convolution kernel tensor into a sum of a small number of rank-one tensors. At the second step, this decomposition is used to replace the original convolutional layer with a sequence of four convolutional layers with small kernels. After such replacement, the entire network is fine-tuned on the training data using standard backpropagation process. We evaluate this approach on two CNNs and show that it is competitive with previous approaches, leading to higher obtained CPU speedups at the cost of lower accuracy drops for the smaller of the two networks. Thus, for the 36-class character classification CNN, our approach obtains a 8.5x CPU speedup of the whole network with only minor accuracy drop (1 from 91 to 90 ). For the standard ImageNet architecture (AlexNet), the approach speeds up the second convolution layer by a factor of 4x at the cost of @math increase of the overall top-5 classification error. Abstract: We propose a simple two-step approach for speeding up convolution layers within large convolutional neural networks based on tensor decomposition and discriminative fine-tuning. Given a layer, we use non-linear least squares to compute a low-rank CP-decomposition of the 4D convolution kernel tensor into a sum of a small number of rank-one tensors. At the second step, this decomposition is used to replace the original convolutional layer with a sequence of four convolutional layers with small kernels. After such replacement, the entire network is fine-tuned on the training data using standard backpropagation process. We evaluate this approach on two CNNs and show that it is competitive with previous approaches, leading to higher obtained CPU speedups at the cost of lower accuracy drops for the smaller of the two networks. Thus, for the 36-class character classification CNN, our approach obtains a 8.5x CPU speedup of the whole network with only minor accuracy drop (1 from 91 to 90 ). For the standard ImageNet architecture (AlexNet), the approach speeds up the second convolution layer by a factor of 4x at the cost of @math increase of the overall top-5 classification error. Deep Neural Network has been applied to many Natural Language Processing tasks. Instead of building hand-craft features, DNN builds features by automatic learning, fitting different domains well. In this paper, we propose a novel convolution network, incorporating lexical features, applied to Relation Extraction. Since many current deep neural networks use word embedding by word table, which, however, neglects semantic meaning among words, we import a new coding method, which coding input words by synonym dictionary to integrate semantic knowledge into the neural network. We compared our Convolution Neural Network CNN on relation extraction with the state-of-art tree kernel approach, including Typed Dependency Path Kernel and Shortest Dependency Path Kernel and Context-Sensitive tree kernel, resulting in a 9 improvement competitive performance on ACE2005 data set. Also, we compared the synonym coding with the one-hot coding, and our approach got 1.6 improvement. Moreover, we also tried other coding method, such as hypernym coding, and give some discussion according the result. This paper presents methods to reduce the complexity of convolutional neural networks (CNN). These include: (1) A method to quickly and easily sparsify a given network. (2) Fine tune the sparse network to obtain the lost accuracy back (3) Quantize the network to be able to implement it using 8-bit fixed point multiplications efficiently. (4) We then show how an inference engine can be designed to take advantage of the sparsity. These techniques were applied to full frame semantic segmentation and the degradation due to the sparsity and quantization is found to be negligible. We show by analysis that the complexity reduction achieved is significant. Results of implementation on Texas Instruments TDA2x SoC [17] are presented. We have modified Caffe CNN framework to do the sparse, quantized training described in this paper. The source code for the training is made available at https: github.com tidsp caffe-jacinto