קולקוויום מחלקתי 31.1.24

Dr. Shira Faigenbaum-Golovin

Duke University

Will lecture on

The Power of Machine Learning: Theoretical and Practical Aspects

Machine learning and deep learning have become indispensable tools in today's technological landscape, playing a pivotal role in revolutionizing various industries. The significance of these fields lies in their ability to compute similarities, learn patterns, and make decisions. In this talk, I will explore two key facets of these technologies. The first involves an analysis of the theoretical aspects of the success of deep neural networks. The second aspect will delve into the power of learning within data-driven applications.

In the desire to quantify the success of neural networks in deep learning and other applications, there is a great interest in understanding which functions can efficiently be learned by the outputs of neural networks. By now, there exists a variety of results that show that a wide range of functions can be learned with sometimes surprising accuracy by these outputs. In this talk, we add to the latter class of rough functions by showing that it also includes multiscale functions. Multiscale functions, which are the solutions of refinement equations, are the building stones in many constructions; including subdivision schemes used in computer graphics, wavelets, as well as several fractals (some can represent parts in natural images). We prove that all multiscale functions can be implemented, up to arbitrarily high precision, by ReLu-based Neural Networks.

In the second part of my talk, I will highlight the potential that lies in learning from data which is acquired in data-driven applications. I will showcase the power of machine learning to acquire multispectral images of ancient inscriptions ca. 600 BCE, while improving the legibility of the text. Followed by developing image processing tools for segmentation and comparison of the handwriting found on these documents. 

Short bio

Dr. Shira Faigenbaum-Golovin is an Assistant Research Professor at Duke University, working with Prof. Ingrid Daubechies. In 2021 Shira obtained her Ph.D. in Applied Mathematics from Tel Aviv University. While pursuing her Ph.D. Shira contributed to the development of the Image Signal Processor at Intel for approximately eight years. Shira’s research interests are in the areas of data science, numerical analysis, and machine learning.