The Experts below are selected from a list of 5235 Experts worldwide ranked by ideXlab platform
Ge Wang - One of the best experts on this subject based on the ideXlab platform.
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universal approximation with quadratic deep Networks
Neural Networks, 2020Co-Authors: Jinjun Xiong, Ge WangAbstract:Abstract Recently, deep learning has achieved huge successes in many important applications. In our previous studies, we proposed quadratic/second-order neurons and deep quadratic neural Networks. In a quadratic neuron, the inner product of a vector of data and the corresponding weights in a Conventional neuron is replaced with a quadratic function. The resultant quadratic neuron enjoys an enhanced expressive capability over the Conventional neuron. However, how quadratic neurons improve the expressing capability of a deep quadratic Network has not been studied up to now, preferably in relation to that of a Conventional neural Network. Specifically, we ask four basic questions in this paper: (1) for the one-hidden-layer Network structure, is there any function that a quadratic Network can approximate much more efficiently than a Conventional Network? (2) for the same multi-layer Network structure, is there any function that can be expressed by a quadratic Network but cannot be expressed with Conventional neurons in the same structure? (3) Does a quadratic Network give a new insight into universal approximation? (4) To approximate the same class of functions with the same error bound, could a quantized quadratic Network have a lower number of weights than a quantized Conventional Network? Our main contributions are the four interconnected theorems shedding light upon these four questions and demonstrating the merits of a quadratic Network in terms of expressive efficiency, unique capability, compact architecture and computational capacity respectively.
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Universal Approximation with Quadratic Deep Networks
2019Co-Authors: Fan Fenglei, Xiong Jinjun, Ge WangAbstract:Recently, deep learning has achieved huge successes in many important applications. In our previous studies, we proposed quadratic/second-order neurons and deep quadratic neural Networks. In a quadratic neuron, the inner product of a vector of data and the corresponding weights in a Conventional neuron is replaced with a quadratic function. The resultant quadratic neuron enjoys an enhanced expressive capability over the Conventional neuron. However, how quadratic neurons improve the expressing capability of a deep quadratic Network has not been studied up to now, preferably in relation to that of a Conventional neural Network. Regarding this, we ask four basic questions in this paper: (1) for the one-hidden-layer Network structure, is there any function that a quadratic Network can approximate much more efficiently than a Conventional Network? (2) for the same multi-layer Network structure, is there any function that can be expressed by a quadratic Network but cannot be expressed with Conventional neurons in the same structure? (3) Does a quadratic Network give a new insight into universal approximation? (4) To approximate the same class of functions with the same error bound, is a quantized quadratic Network able to enjoy a lower number of weights than a quantized Conventional Network? Our main contributions are the four interconnected theorems shedding light upon these four questions and demonstrating the merits of a quadratic Network in terms of expressive efficiency, unique capability, compact architecture and computational capacity respectively.Comment: 10 pages, 7 figure
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universal approximation with quadratic deep Networks
arXiv: Learning, 2018Co-Authors: Jinjun Xiong, Ge WangAbstract:Recently, deep learning has achieved huge successes in many important applications. In our previous studies, we proposed quadratic/second-order neurons and deep quadratic neural Networks. In a quadratic neuron, the inner product of a vector of data and the corresponding weights in a Conventional neuron is replaced with a quadratic function. The resultant quadratic neuron enjoys an enhanced expressive capability over the Conventional neuron. However, how quadratic neurons improve the expressing capability of a deep quadratic Network has not been studied up to now, preferably in relation to that of a Conventional neural Network. Regarding this, we ask four basic questions in this paper: (1) for the one-hidden-layer Network structure, is there any function that a quadratic Network can approximate much more efficiently than a Conventional Network? (2) for the same multi-layer Network structure, is there any function that can be expressed by a quadratic Network but cannot be expressed with Conventional neurons in the same structure? (3) Does a quadratic Network give a new insight into universal approximation? (4) To approximate the same class of functions with the same error bound, is a quantized quadratic Network able to enjoy a lower number of weights than a quantized Conventional Network? Our main contributions are the four interconnected theorems shedding light upon these four questions and demonstrating the merits of a quadratic Network in terms of expressive efficiency, unique capability, compact architecture and computational capacity respectively.
Bocheng Zhu - One of the best experts on this subject based on the ideXlab platform.
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Joint Network-Channel Design with Destination-Relay Feedback in Multiple-Access Relay Channel
2010 International Conference on Internet Technology and Applications, 2010Co-Authors: Jishun Wang, Yun Liu, Yunhua Tan, Bocheng ZhuAbstract:The multiple-access relay channel (MARC) based on Network coding, typically with two sources, one relay, and one destination, has been proposed in recent papers as an approach to achieve diversity gain in wireless Networks and reduce the number of transmissions by the relay node. However, Conventional Network-coding-based MARC scheme wastes the channel resource because the relay forwards the signal every time regardless of the channel conditions. Our new scheme is that, through using the feedback information from the destination to the relay, the relay can use Network coding, maximum ratio combining, or keep silent depending on the two source-destination channel link states. Then we derive the closed-form expressions for the outage probability and throughput of the system. Simulation results show that the new scheme improves the bit error rate(BER) and outage probability performance in contrast with direct transmission, and improves the throughput compared with Conventional Network coding scheme.
M.c. Bromberg - One of the best experts on this subject based on the ideXlab platform.
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WCNC - Using information theory to optimize wireless Networks
2003 IEEE Wireless Communications and Networking 2003. WCNC 2003., 1Co-Authors: M.c. BrombergAbstract:This paper shows how Network information theory can lead to practical algorithms for optimizing multipoint wireless Networks. An information theoretic Network objective function is formulated, which takes full advantage of channel reciprocity and multiple input multiple output (MIMO) channels. A numerical example is provided showing more than an order of magnitude performance improvement over a Conventional Network.
Seree Supharatid - One of the best experts on this subject based on the ideXlab platform.
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FIELD DATA RECOVERY OF TIDAL LEVEL USING A NEURO-GENETIC ALGORITHM
Coastal Engineering Journal, 2004Co-Authors: Seree SupharatidAbstract:This paper presents validation results of the neuro-genetic algorithm with Conventional Network structure and recursive implementation. The aim of the research is to recover the missing data of tidal level in the vicinity of the Chao Phraya river mouth, in Thailand. This data recovery system (DRS) is based on the use of transfer function approach where the system response is constructed by the concept of learning from experiences. The genetic algorithm (GA) was used to find the optimum number of units in the hidden layer. Sensitivity test of input units was performed by trials. A self recovery and a spatial recovery are investigated at two tidal stations. It is found that the obtained Network outperforms the harmonic analysis and can be used in real practice. In general, the efficiency index of the design Network is found more than 0.90. Overall, the NN model reproduces the time series tidal level data in the missing window. The use of Conventional Network structure with known data set at the neighboring station in the spatial recovery gives better results than the use of recursive architecture in the self recovery.
Jietao Zhang - One of the best experts on this subject based on the ideXlab platform.
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ICC - Network-Coded Cooperation for Multi-Unicast with Non-Ideal Source-Relay Channels
2010 IEEE International Conference on Communications, 2010Co-Authors: Yingbin Liu, Wen Chen, Jietao ZhangAbstract:Network coding is considered as a promising technique to improve diversity gain and Network throughput in multi-source relay systems. This paper presents an opportunistic Network coded cooperation scheme in wireless multi-unicast system with non-ideal source-relay channels. In the Conventional Network-coding-based cooperation schemes, the relay merges the messages received from multiple sources and always forwards them to the destinations without checking their reception status. The destinations recover the sources' messages either from the direct transmissions or from the relay forwarding. Such mode is easy to implement, but may lead to error propagation in the event of decoding failures at relay. In contrast to these works, the proposed scheme is opportunistic, where the relay forwarding is determined by the quality of $S\rightarrow R$ channels, that is, the relay does not assist transmission unless it has correctly decoded the received sources' messages. Systematic performance analysis in the form of outage probability and spectral efficiency is performed in this paper. Comparisons with the Conventional Network coded multi-unicast and Incremental Relaying protocol are made under a fixed system energy constraint. The outage results show that the proposed scheme performs better than the Conventional Network-coded schemes when source-relay links has poor quality. Comparing with Incremental Relaying protocol, the opportunistic scheme achieves a reduced system outage probability as well as a higher spectral efficiency. This scenario can be extended to general multi-user environment without much cost.