# Information Theory of Deep Learning

- Speaker:
- Naftali Tishby - COLLOQUIUM LECTURE
- Date:
- Tuesday, 21.11.2017, 14:30
- Place:
- Room 337 Taub Bld.
- Affiliation:
- Hebrew University
- Host:
- Yuval Filmus

I will present a novel comprehensive theory of large scale learning with Deep Neural Networks, based on the correspondence between Deep Learning and the Information Bottlneck framework. The theory is based on the following components: (1) rethinking Learning theory. I will prove a new generalization bound, the input-compression bound, which shows that compression of the input variable is far more important for generalization than the dimension of the hypothesis class, an ill defined notion for deep learning. (2) I will than prove that for large scale Deep Neural Networks the mutual information on the input and the output variables, for the last hidden layer, provide a complete characterization of the sample complexity and accuracy of the network. This put the information Bottlneck bound as the optimal trade-off between sample complexity and accuracy with ANY learning algorithm. (3) I will then show how stochastic gradient descent, as used in Deep Learning, actually achieves this optimal bound. In that sense, Deep Learning is a method for solving the Information Bottlneck problem for large scale supervised learning problems. The theory gives concrete predictions for the structure of the layers of Deep Neural Networks, and design principles for such Networks, which turns out to depend solely on the joint distribution of the input and output and the sample size. Based partly on joint works with Ravid Shwartz-Ziv and Noga Zaslavsky. Short Bio: ========== Dr. Naftali Tishby is a professor of Computer Science, and the incumbent of the Ruth and Stan Flinkman Chair for Brain Research at the Edmond and Lily Safra Center for Brain Science (ELSC) at the Hebrew University of Jerusalem. He is one of the leaders of machine learning research and computational neuroscience in Israel and his numerous ex-students serve at key academic and industrial research positions all over the world. Prof. Tishby was the founding chair of the new computer-engineering program, and a director of the Leibnitz research center in computer science, at the Hebrew university. Tishby received his PhD in theoretical physics from the Hebrew university in 1985 and was a research staff member at MIT and Bell Labs from 1985 and 1991. Prof. Tishby was also a visiting professor at Princeton NECI, University of Pennsylvania, UCSB, and IBM research. His current research is at the interface between computer science, statistical physics, and computational neuroscience. He pioneered various applications of statistical physics and information theory in computational learning theory. More recently, he has been working on the foundations of biological information processing and the connections between dynamics and information. He has introduced with his colleagues new theoretical frameworks for optimal adaptation and efficient information representation in biology, such as the Information Bottleneck method and the Minimum Information principle for neural coding.