Delay-Space Arithmetic and Architecture

What operations can you perform efficiently when you use the “time of arrival” of a signal’s edge to represent a number? Past work has shown how linear representations can be effectively used to optimize problems expressed in max-plus algebras, but efficient general-purpose arithmetic operations have remained elusive. We present negative-logarithmic delay-space arithmetic as a completely new approach to temporal coding. Under this approach, general-purpose arithmetic is transformed to a “soft” version of the standard temporal operations in such a way that preserves all of the algebraic identities. We further show that these soft operations can be approximated by composing the original “sharp” temporal operators, resulting in simple, energy-efficient implementations. We demonstrate the effectiveness of this novel arithmetic with a near-sensor architecture for energy-efficient convolutions. Cycle-over-cycle operation is supported through temporal recurrence, dramatically limiting the need for expensive domain conversions or noise-prone temporal memories.