Neuromorphic Computing: A Theoretical Framework for Time, Space, and Energy Scaling (2507.17886v1)

Abstract: Neuromorphic computing (NMC) is increasingly viewed as a low-power alternative to conventional von Neumann architectures such as central processing units (CPUs) and graphics processing units (GPUs), however the computational value proposition has been difficult to define precisely. Here, we explain how NMC should be seen as general-purpose and programmable even though it differs considerably from a conventional stored-program architecture. We show that the time and space scaling of NMC is equivalent to that of a theoretically infinite processor conventional system, however the energy scaling is significantly different. Specifically, the energy of conventional systems scales with absolute algorithm work, whereas the energy of neuromorphic systems scales with the derivative of algorithm state. The unique characteristics of NMC architectures make it well suited for different classes of algorithms than conventional multi-core systems like GPUs that have been optimized for dense numerical applications such as linear algebra. In contrast, the unique characteristics of NMC make it ideally suited for scalable and sparse algorithms whose activity is proportional to an objective function, such as iterative optimization and large-scale sampling (e.g., Monte Carlo).