The echo index and multistability in input-driven recurrent neural networks – Lorenzo Livi
2020/2021 NEXUS ONLINE DATA ENLIGHTENING SERIES, (NODES) SEMINAR SERIES
Thursday, November 26, 2020
Online Webinar & Q&A
Livestream Link – https://www.youtube.com/watch?v=UZ8l-f1Vs9s
Q&A – Sli.do event code #F211
A recurrent neural network (RNN) possesses the echo state property (ESP) if, for a given input sequence, it “forgets“ any internal states of the driven (nonautonomous) system and asymptotically follows a unique, possibly complex trajectory. The lack of ESP is conventionally understood as a lack of reliable behaviour in RNNs. Here, we show that RNNs can reliably perform computations under a more general principle that accounts only for their local behaviour in phase space. To this end, we formulate a generalization of the ESP and introduce an echo index to characterize the number of simultaneously stable responses of a driven RNN. We show that it is possible for the echo index to change with inputs, highlighting a potential source of computational errors in RNNs due to characteristics of the inputs driving the dynamics.
Lorenzo Livi received a BSc. degree and MSc. degree from the Department of Computer Science, Sapienza University of Rome, Italy, in 2007 and 2010, respectively, and the Ph.D. degree from the Department of Information Engineering, Electronics, and Telecommunications at Sapienza University of Rome, in 2014. He has been with the ICT industry during his studies. From January 2014 until April 2016, he was a Post-Doctoral Fellow at Ryerson University, Toronto, Canada. From May 2016 until September 2016, he was a Post-Doctoral Fellow at the Politecnico di Milano, Italy, and Universita’ della Svizzera Italiana, Lugano, Switzerland.
Currently, he is an Assistant Professor jointly appointed with the Departments of Computer Science and Mathematics at the University of Manitoba, Canada. He is also a Lecturer (Assistant Professor) in Data Science at the Department of Computer Science, University of Exeter, United Kingdom. In November 2018, Dr. Livi was awarded the prestigious Tier 2 Canada Research Chair in Complex Data. He is an Associate Editor of the IEEE-TNNLS, Applied Soft Computing (Elsevier), and a regular reviewer for several international journals, including IEEE Transactions and Elsevier journals. His research interests include Machine Learning, Time Series Analysis, and Complex Dynamical Systems, with focused applications in Systems Biology and Computational Neuroscience.