Computing with Dynamical Systems

The effort to develop larger-scale computing systems introduces a set of related challenges: Large machines are more difficult to synchronize. The sheer quantity of hardware introduces more opportunities for errors. New... [ view full abstract ]

The effort to develop larger-scale computing systems introduces a set of related challenges: Large machines are more difficult to synchronize. The sheer quantity of hardware introduces more opportunities for errors. New approaches to hardware, such as low-energy or neuromorphic devices are not directly programmable by traditional methods.

These three challenges may be addressed, at least for a subset of interesting problems, by a dynamical systems approach. The initial state of system represents the problem, and the final state of the system represents the solution. By carefully controlling the attractive basin of the system, we can move it between these two points while tolerating errors, which appear as perturbations.

Here we describe both conventional and neural computers as dynamical systems, and show how to construct algorithms with resilience to noise, using traditional numerical problems as a special case. This suggests a reduction from numerical problems to spiking neural hardware such as IBM's TrueNorth.