Performance limits of reservoir computers at the edge of chaos

Reservoir computers use dynamic systems to perform calculations, often leveraging the increased complexity of systems near chaos. In his paper, Thomas Carroll shows that changes in signal dimensionality and frequency near the edge of chaos would degrade performance in some reservoir computers. On the contrary, he discovered that some computers actually reach peak performance away from the edge, breaking with long-standing assumptions.

“Theories of computation state that a computer should function best when it is about to make a transition from an ordered state to a disordered state,” says Carroll. “This transition is often called the ‘edge of chaos.’ At this point, the computer has the maximum complexity, so it should have the highest computational complexity. I found that when a computer is built from a dynamical system, there are other dynamical effects that offset this increased complexity.”

Carroll examined two designs of reservoir computers based on third-order polynomials. One was based on ordinary differential equations while the other used a polynomial map. The parameters of each computer were randomized to explore a wide range of possible designs.

Two performance limiting factors were identified. One came from increasingly poor frequency matching between the reservoir and the problem being solved. Another came from the dimensional shift in the output signal.

“Think of the standard two-dimensional map of the earth – it is an attempt to represent a three-dimensional object in two dimensions, so parts of the map are distorted,” says Carroll. “When the signals in a reservoir computer change dimension, the added distortion decreases the accuracy of the computer.”

Carroll hopes that this work will encourage others to explore a wider range of reservoir computer designs.

Source: “Do reservoir computers work best at the edge of chaos?,” by Thomas Carroll, Chaos (2020). The article can be accessed at https://doi.org/10.1063/5.0038163 .