About me
Note: Since May 2020, I’m no longer maintaining this website.
In the winter quarter (2019-2020) I’ve completed my PhD at the University of Chicago, in the department of Statistics. In my research I have applied non-standard tools from abstract algebra and topology to the study of neural networks. My research was conducted under the supervision of Prof. Lek-Heng Lim. Currently my interests have shifted from academic research towards industry applications.
Past conferences (partial list)
- I gave a talk at ICIAM 2019 Minisymposium on Deep Learning that took place in Valencia, organized by Tingran Gao and Haizhao Yang.
- I’ve oraganized 2019 SIAM minisymposium on application of tropical geometry for machine learning (with focus on deep neural networks) (SIAM AG19), Bern, Switzerland.
- Last December I have participated in a course on finite elements modeling using FEniCS in Paris organized by Prof. L.R. Scott.
- I gave a talk at applied algebra day at MIT on tropical geometry of deep neural networks.
- I’ve participated in Oberwolfach Seminar: Mathematics of Deep Learning, that took place in Oct 14-20 2018, in Oberwolfach, Germany.
- During the summer of 2018 I’ve spent wonderful time working as a PhD machine learning intern in Blink startup (Haifa, Israel) working with TensorFlow and Caffe.
Past research projects
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.
- Topological data analysis to boost performance of neural networks. Topological data analysis (TDA) is a relatively new area of research which has rapidly developed in the past decade. TDA uses ideas from topology for data analysis. In the past I’ve considered TDA in a setting where point cloud data is contaminated by noise and proved a theoretical convergence results for the Euler Integral, which is one of the tools in TDA (Justin Curry Et al.). In this project I use another tool from TDA, a mapper algorithm, (G Singh Et al., 2007) for profiling of neural networks and boosting their performance. The proposed algorithm provides topological summary for the input data shape, this summary is used to measure local performance of neural network in the input, which in turn guides an ensemble scheme that improves neural network performance.
Past research interests and professional experience
- In the past I worked in logic design and hardware engineering:
- I did a research project at the Technion where we designed a near real time logic circuit for RSA encryption.
- For the period between 2006-2015 I worked as a board designer, FPGA engineer and FPGA development team leader.
Honors & Awards
- 2018 Invited to participate in Oberwolfach Seminar: Mathematics of Deep Learning. The Institute will cover the expenses for accommodation and meals. and reimburse travel expenses.
- 2018 ICML conference, I have been selected for a travel award covering travel and acommodation expenses.
- 2017 SAS institute prize for patent initiative 2017.
- 2015-2017: McCormick Fellowship.
- 2004-2008: Technion President Excellence Award. Received 2 times.
- 2004-2008: “Psagot”(Hebrew) excellence program.
Publications and workshops
An RSA processor for near real-time operation
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.
A central limit theorem for the Euler integral of a Gaussian random field
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.
Tropical Geometry of Deep Neural Networks
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.
M-Boost: Profiling and Refining Deep Neural Networks with Topological Data Analysis
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.
Talks and posters
A central limit theorem for the Euler integral of a Gaussian random field
Seminar talk at Technion, Probability and applied topology seminar, Haifa, Israel
Application of tropical geometry for the study of feedforward neural networks
Poster at DARPA, YAI meeting, poster presentation, Arlington, VA, US
Application of tropical geometry for the study of feedforward neural networks
Seminar talk at The University of Chicago, Computational and Applied Mathematics RTG Student Seminars, Chicago, IL, US
Tropical Geometry of Deep Neural Networks
Conference proceedings talk at the 35th International Conference on Machine Learning, Stockholm, Sweden
MIT Seminar on Applied Algebra and Geometry
Seminar talk at MIT, Cambridge, MA, US
Tropical geometry in machine learning
Seminar talk at ICIAM 2019 Minisymposium on Deep Learning, Valencia, Spain
Tropical geometry in machine learning
Seminar talk at SIAM Applied Algebraic Geometry minisymposium, Bern, Switzerland
Teaching
Past service and leadership (partial)
- 2019 - One of the organizers of “RTG Summer Lectures” at The University of Chicago
- 2018 - Leading team of PhD and master students to helps the law school at the university of Chicago analyze gender dynamics and gender achievement disparities at the school. The report can be found here.
- 2017 - Leading a team of PhD and master students to help reserchers in biology department analyze spatial patterns of migrating cells in zebrafish embryos (analysis of cell movement within embryo).
- Peer review for “Artificial Intelligence Review”
- Peer review for “Linear Algebra and its Applications”
- Peer review for “Journal of Symbolic Computation”
- Peer review for “The Annals of Probability” (unofficial)