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)

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. TopologyChange2

  • 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.

Polytopes

  • 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.

Topological Data summary

Past research interests and professional experience

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

Talks and posters

Teaching

Past service and leadership (partial)

Past collaborations