Computing with Stuart-Landau Recurrent Neural Networks: Interplay between Task Data and Neural Network Dynamics
The Stuart-Landau (SL) equation is a canonical model that describes the behavior of nonlinear oscillatory systems near a supercritical Hopf bifurcation, being a promising platform to study real-world dynamical systems as RNNs. The SL model captures in particular the interplay of amplitude and phase in the dynamics of nonlinear oscillators and has been successfully applied to describe dynamical features and synchronization behavior of physical systems, including semiconductor lasers and models of neural populations. Here, we investigate a trainable, fully connected RNN of SL oscillators (SL-RNN) for sequential information processing. Due to its inherent nonlinearity, the SL-RNN, capable of showing various undriven autonomous dynamics, reacts differently to the input structure of different tasks. We studied the performance for IMDb sentiment analysis, sequential MNIST digit recognition, and Mackey-Glass time series forecasting, and its dependence on various autonomous dynamical states. We find the best performance to occur for a variety of autonomous (undriven) dynamical regimes including slightly damped, near-critical dynamics for long-range linear memory tasks, to sustained limit-cycle oscillations for more periodic input structures. These results connect the temporal structure of computational tasks to dynamical properties of the physical substrate, being a first step towards identifying design guidelines for versatile and resource-efficient physical computing systems.
This Annual PhD student seminar will be broadcasted in the following zoom link: https://us06web.zoom.us/j/89466064429?pwd=po9p99eAEYVPaNI8xIIGoOIz0hOqaF.1
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