Research Technician


Nov 2016 – Present KSA
Computer Algebra for Differential Equations: Automation of symbolic PDE analysis with Wolfram Mathematica.

Junior Researcher

Institute of Mathematics of National Academy of Sciences: Real Analysis Department

Aug 2014 – Jun 2019 Armenia
Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals.

Search Engine Developer

Teamable Software

Apr 2014 – Nov 2016 Armenia
Working extensively on data quality and all aspects of search engine in the product. Building intelligent, advanced and scalable search engine with Apache Solr.

Recent Publications

Various gradient compression schemes have been proposed to mitigate the communication cost in distributed training of large scale machine learning models. Sign-based methods, such as signSGD, have recently been gaining popularity because of their simple compression rule and connection to adaptive gradient methods, like ADAM. In this paper, we perform a general analysis of sign-based methods for non-convex optimization. Our analysis is built on intuitive bounds on success probabilities and does not rely on special noise distributions nor on the boundedness of the variance of stochastic gradients. Extending the theory to distributed setting within a parameter server framework, we assure variance reduction with respect to number of nodes, maintaining 1-bit compression in both directions and using small mini-batch sizes. We validate our theoretical findings experimentally.

We prove Fatou type theorem on almost everywhere convergence of convolution integrals in spaces Lp(1<p<∞) for general kernels, forming an approximate identity. For a wide class of kernels we show that obtained convergence regions are optimal in some sense. It is also established a weak boundedness of the corresponding maximal operator in Lp(1≤p<∞).

The paper considers differentiation properties of density bases formed of bounded open sets.We prove that two quasi-equivalent subbases of some density basis differentiate the same class of non-negative functions. Applications for bases formed of rectangles are discussed.