In this paper we consider Multiple-Input-Multiple-Output (MIMO) detection using deep neural networks. We introduce two different deep architectures: a standard fully connected multi-layer network, and a Detection Network (DetNet) which is specifically designed for the task. The structure of DetNet is obtained by unfolding the iterations of a projected gradient descent algorithm into a network. We compare the accuracy and runtime complexity of the purposed approaches and achieve state-of-the-art performance while maintaining low computational requirements. Furthermore, we manage to train a single network to detect over an entire distribution of channels. Finally, we consider detection with soft outputs and show that the networks can easily be modified to produce soft decisions.

In this paper, we consider the use of deep neural networks in the context of Multiple-Input-Multiple-Output (MIMO) detection. We give a brief introduction to deep learning and propose a modern neural network architecture suitable for this detection task. First, we consider the case in which the MIMO channel is constant, and we learn a detector for a specific system. Next, we consider the harder case in which the parameters are known yet changing and a single detector must be learned for all multiple varying channels. We demonstrate the performance of our deep MIMO detector using numerical simulations in comparison to competing methods including approximate message passing and semidefinite relaxation. The results show that deep networks can achieve state of the art accuracy with significantly lower complexity while providing robustness against ill conditioned channels and mis-specified noise variance.

Koller, D., A. Poljakoff‐Mayber, A. Berg, and T. Diskin. (Hebrew U., Jerusalem, Israel.) Germination‐regulating mechanisms in Citrullus colocynthis. Amer. Jour. Bot. 50(6): 597–603. Illus. 1963.—Intact seeds from mature, dry fruits of Citrullus colocynthis, collected in the southern Negev desert, did not germinate under a wide variety of experimental conditions. This inhibition was imposed by the testa, since germination was made possible by mechanically forcing open the testa, or by its complete removal. However, various pretreatments, including some which modified or even pierced the testa, failed to effect germination. No inhibitors were found in the testa and the manner in which it inhibits germination is yet unknown. How this inhibition is overcome in nature is also unknown. Germination of decoated seeds was inhibited by continuous light in combination with temperatures below 25 C. Removal of the inner seed membrane removed this inhibition, but, growth of the naked embryos at all temperatures was greatly reduced by continuous light, which also strongly influenced early development. An intact inner seed membrane had no effect on germination in darkness, but inhibited it in light at temperatures below 25 C. Inhibitory effects of the inner seed membrane could be duplicated by enclosing the naked embryos in moist filter paper and are thus probably the result of an interference with exchange of respiratory gases between the embryo and the atmosphere. Very low light intensities sufficed to inhibit decoated seeds, but at least 12‐hr daily illumination was required to produce significant inhibition. The blue region of the visible spectrum, transmitted by green and blue cellophane filters, was the most inhibitory. The site of light perception was located in the radicular portions of the embryo.

We consider distance functions between conditional distributions functions. We focus on the Wasserstein metric and its Gaussian case known as the Frechet Inception Distance (FID). We develop conditional versions of these metrics, and analyze their relations. Then, we numerically compare the metrics in the context of performance evaluation of conditional generative models. Our results show that the metrics are similar in classical models which are less susceptible to conditional collapse. But the conditional distances are more informative in modern unsupervised, semisupervised and unpaired models where learning the relations between the inputs and outputs is the main challenge.

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