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 (e.g. Digital humanities).

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. 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). Next, I will propose a different type of refinement that involves not only translation and rescaling but also mirroring. I will rigorously show that the limit function of the new refinement process is Holder continuous, and has Holder continuity of the highest-order well-defined derivatives.

In the second part of my talk, I will highlight the significance of learning from data obtained through data-driven applications, emphasizing a cohesive line of research present in various Digital Humanities applications, by understanding the data geometry. I will exemplify the efficacy of machine learning in acquiring multispectral images and developing image-processing tools for the segmentation and comparison of the handwriting found in ancient documents pertaining to c.a. 600 BCE. The results of this study provide empirical evidence regarding the literacy rates at that time. This will illustrate the data dialog, between the humanities and the hard sciences, that enriches the knowledge and our understanding of historical events using digital tools.