Gated Recurrent Units Viewed Through the Lens of Continuous Time Dynamical Systems

• Published in: Frontiers in computational neuroscience Vol. 15; p. 678158
• Main Authors: Jordan, Ian D., Sokół, Piotr Aleksander, Park, Il Memming
• Format: Journal Article
• Language: English
• Published: Lausanne Frontiers Research Foundation 22.07.2021; Frontiers Media S.A
• Subjects: bifurcations; continuous time; Dynamical systems; Machine learning; Memory; Neural networks; Neuroscience; Neurosciences; Ordinary differential equations; Oscillations; recurrent neural network; System theory; Time series
• ISSN: 1662-5188; 1662-5188
• DOI: 10.3389/fncom.2021.678158

Gated recurrent units (GRUs) are specialized memory elements for building recurrent neural networks. Despite their incredible success on various tasks, including extracting dynamics underlying neural data, little is understood about the specific dynamics representable in a GRU network. As a result, it is both difficult to know a priori how successful a GRU network will perform on a given task, and also their capacity to mimic the underlying behavior of their biological counterparts. Using a continuous time analysis, we gain intuition on the inner workings of GRU networks. We restrict our presentation to low dimensions, allowing for a comprehensive visualization. We found a surprisingly rich repertoire of dynamical features that includes stable limit cycles (nonlinear oscillations), multi-stable dynamics with various topologies, and homoclinic bifurcations. At the same time we were unable to train GRU networks to produce continuous attractors, which are hypothesized to exist in biological neural networks. We contextualize the usefulness of different kinds of observed dynamics and support our claims experimentally.