D. L. Fleischer, G. Naitzat and L. Prokupets, "An RSA processor for near real-time operation," 2009 IEEE International Conference on Microwaves, Communications, Antennas and Electronics Systems, Tel Aviv, 2009, pp. 1-4.
Naitzat, Gregory & Adler, Robert J., 2017. "A central limit theorem for the Euler integral of a Gaussian random field" Stochastic Processes and their Applications, Elsevier, vol. 127(6), pages 2036-2067.
Liwen Zhang, Gregory Naitzat, Lek-Heng Lim; "Tropical Geometry of Deep Neural Networks" Proceedings of the 35th International Conference on Machine Learning, PMLR 80:5824-5832, 2018.
G Naitzat, N Lokare, J Silva, I Kaynar-Kabul, M-Boost: Profiling and Refining Deep Neural Networks with Topological Data Analysis. Workshop on Interactive Data Exploration and Analytics, KDD 2018, London, UK.
Seminar talk at Technion, Probability and applied topology seminar, Haifa, Israel
Poster at DARPA, YAI meeting, poster presentation, Arlington, VA, US
Seminar talk at The University of Chicago, Computational and Applied Mathematics RTG Student Seminars, Chicago, IL, US
Conference proceedings talk at the 35th International Conference on Machine Learning, Stockholm, Sweden
Seminar talk at MIT, Cambridge, MA, US
Seminar talk at ICIAM 2019 Minisymposium on Deep Learning, Valencia, Spain
Seminar talk at SIAM Applied Algebraic Geometry minisymposium, Bern, Switzerland
Topology of Deep Neural Networks. A key insight of topological data analysis is that “data has shape”. We study how modern deep neural networks transform shape of data sets, with the goal of shedding light on their breathtaking yet somewhat mysterious effectiveness. Most existing approaches tend to focus on what a network does to a single object, e.g. an image of a cat; but we are interested in what it does to all objects in the same class, e.g. the set of all cats. As in topological data analysis, we employ persistent homology — a computational topology tool with proven stability, robust algorithms, and high-quality software — to track changes in the topology of a data set as it passes through the layers of neural network. 
Tropical algebra and tropical geometry of deep neural network.
In this study, presented at ICML2018 conference in Stockholm, we’ve establish connections between feedforward neural networks with ReLU activation and tropical geometry. We’ve shown that the family of such neural networks is equivalent to the family of tropical rational maps. This novel connection between two previously distinct areas of research allowed us to use machinery of tropical algebraic geometry for the study of neural networks.
D. L. Fleischer, G. Naitzat and L. Prokupets, "An RSA processor for near real-time operation," 2009 IEEE International Conference on Microwaves, Communications, Antennas and Electronics Systems, Tel Aviv, 2009, pp. 1-4.
Naitzat, Gregory & Adler, Robert J., 2017. "A central limit theorem for the Euler integral of a Gaussian random field" Stochastic Processes and their Applications, Elsevier, vol. 127(6), pages 2036-2067.
Liwen Zhang, Gregory Naitzat, Lek-Heng Lim; "Tropical Geometry of Deep Neural Networks" Proceedings of the 35th International Conference on Machine Learning, PMLR 80:5824-5832, 2018.
G Naitzat, N Lokare, J Silva, I Kaynar-Kabul, M-Boost: Profiling and Refining Deep Neural Networks with Topological Data Analysis. Workshop on Interactive Data Exploration and Analytics, KDD 2018, London, UK.
Seminar talk at Technion, Probability and applied topology seminar, Haifa, Israel
Poster at DARPA, YAI meeting, poster presentation, Arlington, VA, US
Seminar talk at The University of Chicago, Computational and Applied Mathematics RTG Student Seminars, Chicago, IL, US
Conference proceedings talk at the 35th International Conference on Machine Learning, Stockholm, Sweden
Seminar talk at MIT, Cambridge, MA, US
Seminar talk at ICIAM 2019 Minisymposium on Deep Learning, Valencia, Spain
Seminar talk at SIAM Applied Algebraic Geometry minisymposium, Bern, Switzerland