The last few years have witnessed a tremendous growth of the demand for wireless services and a significant increase of the number of mobile subscribers. A recent data traffic forecast from Cisco reported that the global mobile data traffic reached 1.2 zettabytes per year in 2016, and the global IP traffic will increase nearly threefold over the next 5 years. Based on these predictions, a 127-fold increase of the IP traffic is expected from 2005 to 2021. It is also anticipated that the mobile data traffic will reach 3.3 zettabytes per year by 2021, and that the number of mobile-connected devices will reach 3.5 per capita.
With such demands for higher data rates and for better quality of service (QoS), fifth generation (5G) standardization initiatives, whose initial phase was specified in June 2018 under the umbrella of Long Term Evolution (LTE) Release 15, have been under vibrant investigation. In particular, the International Telecommunication Union (ITU) has identified three usage scenarios (service categories) for 5G wireless networks: (i) enhanced mobile broadband (eMBB), (ii) ultra-reliable and low latency communications (uRLLC), and (iii) massive machine type communications (mMTC). The vast variety of applications for beyond 5G wireless networks has motivated the necessity of novel and more flexible physical layer (PHY) technologies, which are capable of providing higher spectral and energy efficiencies, as well as reduced transceiver implementations.
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Neural networks with rectified linear unit (ReLU) activation functions (a.k.a. ReLU networks) have achieved great empirical success in various domains. Nonetheless, existing results for learning ReLU networks either pose assumptions on the underlying data distribution being, e.g., Gaussian, or require the network size and/or training size to be sufficiently large. In this context, the problem of learning a two-layer ReLU network is approached in a binary classification setting, where the data are linearly separable and a hinge loss criterion is adopted. Leveraging the power of random noise perturbation, the paper entitled Learning ReLU Networks on Linearly Separable Data: Algorithm, Optimality, and Generalization by Gang Wang, Georgios Giannakis and Jie Chen published in IEEE Transactions on Signal Processing in May 2019 presents a novel stochastic gradient descent (SGD) algorithm, which can provably train any single-hidden-layer ReLU network to attain global optimality, despite the presence of infinitely many bad local minima, maxima, and saddle points in general. This result is the first of its kind, requiring no assumptions on the data distribution, raining/network size, or initialization. Convergence of the resultant iterative algorithm to a global minimum is analyzed by establishing both an upper bound and a lower bound on the number of non-zero updates to be performed. Moreover, generalization guarantees are developed for ReLU networks trained with the novel SGD leveraging classic compression bounds. These guarantees highlight a key difference (at least in the worst case) between reliably learning a ReLU network as well as a leaky ReLU network in terms of sample complexity. Numerical tests using both synthetic data and real images validate the effectiveness of the algorithm and the practical merits of the theory.
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