Hyperdimensional Computing Provides a Programming Paradigm for Oscillatory Systems

The increasing difficulty in continued development of digital electronic logic has led to a renewed interest in alternative approaches. Oscillatory computing is one such approach that leverages alternative physical systems and computation strategies, but it lacks high-level paradigms for system design and programming. We address this gap by describing a model based on hyperdimensional computing that serves as an "instruction set" to integrate oscillatory networks into algorithms for real-valued computing. The expressiveness and compositionality of these instructions allow oscillatory systems to implement both common tasks and novel functions, providing a clear computational role for many emerging hardware devices. We detail the computational primitives of this system, prove how they can be executed via oscillatory systems, quantify the performance of these operations, and apply them to execute multiple tasks including compression, factorization, and classification.