
**LOCATION CHANGE**CS Colloquium: Ioannis Panageas (SUTD)  Depthwidth tradeoffs for ReLU networks via Sharkovsky's theorem
Thu, Mar 12, 2020 @ 04:00 PM  05:00 PM
Thomas Lord Department of Computer Science
Conferences, Lectures, & Seminars
Speaker: Ioannis Panageas, Singapore University of Technology and Design
Talk Title: Depthwidth tradeoffs for ReLU networks via Sharkovsky's theorem
Series: CS Colloquium
Abstract: Understanding the representational power of Deep Neural Networks (DNNs) and how their structural properties (e.g., depth, width, type of activation unit) affect the functions they can compute, has been an important yet challenging question in deep learning and approximation theory. In a seminal paper, Telgarsky highlighted the benefits of depth by presenting a family of functions (based on simple triangular waves) for which DNNs achieve zero classification error, whereas shallow networks with fewer than exponentially many nodes incur constant error. Even though Telgarsky's work reveals the limitations of shallow neural networks, it does not inform us on why these functions are difficult to represent and in fact he states it as a tantalizing open question to characterize those functions that cannot be wellapproximated by smaller depths. In this talk, we will point to a new connection between DNNs expressivity and Sharkovsky's Theorem from dynamical systems, that enables us to characterize the depthwidth tradeoffs of ReLU networks for representing functions based on the presence of generalized notion of fixed points, called periodic points (a fixed point is a point of period 1). Motivated by our observation that the triangle waves used in Telgarsky's work contain points of period 3  a period that is special in that it implies chaotic behavior based on the celebrated result by LiYorke  we will give general lower bounds for the width needed to represent periodic functions as a function of the depth. Technically, the crux of our approach is based on an eigenvalue analysis of the dynamical system associated with such functions.
This lecture satisfies requirements for CSCI 591: Research Colloquium
Biography: Ioannis Panageas is an Assistant Professor at Information Systems Department of SUTD since September 2018. Prior to that he was a MIT postdoctoral fellow working with Constantinos Daskalakis. He received his PhD in Algorithms, Combinatorics and Optimization from Georgia Institute of Technology in 2016, a Diploma in EECS from National Technical University of Athens (summa cum laude) and a M.Sc. in Mathematics from Georgia Institute of Technology. His work lies on the intersection of optimization, probability, learning theory, dynamical systems and algorithms. He is the recipient of the 2019 NRF fellowship for AI (analogue of NSF CAREER award).
URL Website: https://panageas.github.io/
Host: Shaddin Dughmi
Location: Ronald Tutor Hall of Engineering (RTH)  115
Audiences: Everyone Is Invited
Contact: Assistant to CS chair