Pixel Club: How Structure can Improve the Theory and Practice in Neural Networks?

Raja Giryes (Tel-Aviv University)
Tuesday, 3.1.2017, 10:30
Room 337 Taub Bld.

The past five years have seen a dramatic increase in the performance of recognition systems due to the introduction of deep architectures for feature learning and classification. However, the mathematical reasons for this success remain elusive. In this talk we will briefly survey some existing theory of deep learning. In particular, we will focus on data structure based theory and discuss two recent developments.

The first work studies the generalization error of deep neural network. We will show how the generalization error of deep networks can be bounded via their classification margin. We will also discuss the implications of our results for the regularization of the networks. For example, the popular weight decay regularization guarantees the margin preservation, but it leads to a loose bound to the classification margin. We show that a better regularization strategy can be obtained by directly controlling the properties of the network’s Jacobian matrix.

The second work focuses on solving minimization problems with neural networks. Relying on recent recovery techniques developed for settings in which the desired signal belongs to some low-dimensional set, we show that using a coarse estimate of this set leads to faster convergence of certain iterative algorithms with an error related to the accuracy of the set approximation. Our theory ties to recent advances in sparse recovery, compressed sensing and deep learning. In particular, it provides an explanation for the successful approximation of the ISTA (iterative shrinkage and thresholding algorithm) solution by neural networks with layers representing iterations.

The is a joint work with Guillermo Sapiro, Miguel Rodrigues, Jure Sokolic, Alex Bronstein and Yonina Eldar.

Raja Giryes is an assistant professor in the school of electrical engineering at Tel Aviv University. He received the B.Sc (2007), M.Sc. (supervision by Prof. M. Elad and Prof. Y. C. Eldar, 2009), and PhD (supervision by Prof. M. Elad 2014) degrees from the Department of Computer Science, The Technion - Israel Institute of Technology, Haifa. Raja was a postdoc at the computer science department at the Technion (Nov. 2013 till July 2014) and at the lab of Prof. G. Sapiro at Duke University, Durham, USA (July 2014 and Aug. 2015). His research interests lie at the intersection between signal and image processing and machine learning, and in particular, in deep learning, inverse problems, sparse representations, and signal and image modeling. Raja received the Maof prize for excellent young faculty (2016-2019), VATAT scholarship for excellent postdoctoral fellows (2014-2015), Intel Research and Excellence Award (2005, 2013), the Excellence in Signal Processing Award (ESPA) from Texas Instruments (2008) and was part of the Azrieli Fellows program (2010-2013). He has co-organized workshops and tutorials on deep learning in leading conference such as ICML 2016, ICCV 2015, CVPR 2016, EUSIPCO 2016 and ACCV 2016.

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