The Importance of Inquiry Across Disciplines: Top Deep Math Conference Features Halıcıoğlu Data Science Professors and Faculty Members

by Trista Sobeck

On Nov 5, 2020, a virtual Deep Math conference took place featuring several HDSI faculty members. The Conference on the “Mathematical Theory of Deep Neural Networks” has a mission—especially this year—to bring together researchers from several fields. Much like HDSI’s interdisciplinary ethos, this conference focused on what deep learning means through different perspectives.

However, Assistant Professor Mikio Aoi with joint appointments at UC San Diego’s Halıcıoğlu Data Science Institute and Biological Sciences & Neurobiology would like to flip that idea on its head.

Aoi has been with the conference planning board since its inception—three years ago–and in fact, is one of the core co-organizers. He explains deep learning as a type of Rorschach test.

“[P]eople see in deep learning the signatures of their own perspectives. Our view is that if people from different backgrounds could be brought together to think about the problems of understanding deep learning through different lenses, then perhaps the cross-pollination of ideas could accelerate our understanding,” says Aoi.

This conference also allows for the freedom of those interested in expanding their specific fields of research. According to Mikhail (Misha) Belkin, Professor at the Halıcıoğlu Data Science Institute and one of eight speakers invited to the conference, deep learning has been one of the most recent developments in perhaps all of science.

“We do not yet have a strong mathematical theory for deep learning. Indeed, the practice has shown significant gaps in our mathematical understanding of learning phenomena.”  He says a fundamental mathematical theory is key for conceptual understanding and improving existing methods and building new algorithms.

To put it plainly, we need to look at things differently – at all times if we are going to create new ideas.

According to Gal Mishne, Assistant Professor at Halıcıoğlu Data Science Institute and one of the co-organizers of the conference this year, there is still much unknown about why deep learning is so successful. “The Deep Math conference brings together researchers from Mathematics, Physics, Machine Learning, Signal Processing, Neuroscience and more who otherwise might not necessarily interact, to discuss and explore different perspectives underlying the theory of deep learning,” she says. Furthermore, the conference format encourages debate among the invited speakers beyond their individual presentations.

What makes this conference so unique? Many things. But, according to Aoi, to his knowledge, this is the only one focused on the discussion and promotion of theories of deep learning across disciplines. “There have been many ad hoc events, many of which were either attached to larger conferences or were focused on specific disciplinary perspectives.”

Belkin concurs and says that deep learning has changed everything in the last 10 years and feels fortunate to be able to participate in developments “[T]his is an exciting time, certainly the most exciting time of my career, perhaps even in the whole history of the whole subject of machine learning,” he says.

In what first was developed as a casual conversation about deep learning while he was a postdoc at Princeton, Aoi recounts that he was part of a journal club for theories of deep learning.

“There were few papers at the time, and we had many questions we couldn’t answer. We realized that many of the people we would like to hear from were at the Institute for Advanced Study (IAS) just down the road.

This independent postdoctoral research center for theoretical research and intellectual inquiry has served as the academic home of internationally preeminent scholars, including Albert Einstein and J. Robert Oppenheimer. “This gave us the idea of a mini-conference of local speakers, but as local interest grew, we realized that there was enough demand for a larger event with multiple speakers.”

And here we are today where some of the top researchers on mathematical theory of deep learning and related topics gather. “It is a great opportunity to communicate recent progress to an audience like that and learn about new developments in the area,” says Belkin.

Mishne, the first faculty member hired at HDSI says she has a goal to help define and develop the new field of data science. Organizing such conferences bringing together researchers from multiple disciplines is just one step. She wants to answer the ongoing question, ‘what is the core knowledge and skills that a data scientist needs?’

“I hope my students learn that being a data scientist requires [skills] beyond just good analytical and coding skills,” says Mishne. “It requires curiosity–a drive to understand and explain information hidden in data, as well as communication – being able to present and explain your findings in an effective manner to different audiences.”

The next annual Deep Math Conference is scheduled for November 2021.

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