Colloquium Speaker:
Dr. Boyu Li, Ph.D.
New Mexico State University, New Mexico, United States
Title: Finite-dimensional dilation theory and application to simple cycle reservoirs
Abstract: Reservoir computation models form a subclass of recurrent neural networks with fixed non-trainable input and dynamic coupling weights. Reservoir models have been successfully applied to a variety of tasks and have been shown to be universal approximators of time-invariant fading memory dynamic filters across various settings. Simple cycle reservoirs (SCR) have been proposed as a severely restricted reservoir architecture, with equal-weight ring connectivity among reservoir units and input-to-reservoir weights of binary nature with the same absolute value. Such architectures are well-suited for hardware implementations without performance degradation in many practical tasks.
We study the expressive power of SCR and show that they can universal-approximate any unrestricted linear reservoir system and, hence, any time-invariant fading memory filter over uniformly bounded input streams. Surprisingly, the main technique in our study comes from finite-dimensional dilation techniques in operator theory. I will briefly introduce the background of reservoir computing and explain how dilation theory techniques are applied in this setting. This is a joint work with Robert Simon Fong and Peter Tino.
Day & Time: Wednesday, April 15, 2026, at 3:00pm
Location: Lambton Tower, Room 9-118
Counts toward seminar attendance for MSc and PhD students in Math & Stats.