Abstract:  

The central question of my talk is what can the mathematics of dynamical systems theory and complex systems theory tell us about machine learning and future quantum computing? The primary tool I will use to study this exchange in the reservoir computer (RC). RCs provide a useful paradigm for studying both dynamical systems and recurrent neural networks. They are random recurrent dynamical networks driven by an input time series, in which only the output layer is trained — typically via linear regression and regularization. This makes them lightweight and general-purpose, yet remarkably powerful for modelling nonlinear dynamical systems. I will explain why this is the case, showing that the internal state of the RC captures the same features as a time-delay embedding — that is, it faithfully (and generically) reconstructs the underlying high-dimensional dynamics from a scalar observable time series. Using what we call Reservoir Time Series Analysis I will show that this internal state encodes enough information to rival state-of-the-art tools in nonlinear time-series analysis, including recurrence quantification methods. Next, I will introduce new work constructing a reservoir substrate from the ordinal encoding of a time series, demonstrating that even this simple representation suffices for reservoir-based information processing — opening the door to new applications of reservoir computing. Finally, I will briefly outline some future directions in the application of this toolkit for quantum computation.

Biography:

Michael Small is Professor of Applied Mathematics in the School of Physics, Mathematics and Computing at The University of Western Australia (UWA) and Director of the UWA Data Institute. He trained in pure mathematics at UWA before completing a PhD in nonlinear dynamical systems and time series analysis, and held positions at Heriot-Watt University in Edinburgh and then at the Hong Kong Polytechnic University from 2001 to 2011, before returning to UWA as an ARC Future Fellow. From 2016 to 2025 he held the CSIRO–UWA Chair in Complex Systems. His research develops data-driven methods at the interface of dynamical systems theory, complex networks and machine learning, with particular emphasis on reservoir computing, the inference of dynamics from data, and the synchronisation of chaotic and learning systems; he has also contributed to quantum algorithms on networks. He has published more than 300 papers and four books, including Applied Nonlinear Time Series Analysis and Propagation Dynamics on Complex Networks. He is Editor-in-Chief of Chaos: An Interdisciplinary Journal of Nonlinear Science and Main Editor of Physica A, a Fellow of the Australian Mathematical Society, and recipient of the 2022 Afraimovich Award for his contributions to nonlinear dynamics. He is currently a Chief Investigator and node-lead of both the $A35M Australian Research Council Centre of Excellence for Post Quantum Computation (MathQuEST) and the Australian Research Council Training Centre in Electrifying Australia for a Net-zero Future.