Delay-Space Arithmetic and Architecture

Rhys Gretsch

doi:10.1109/MM.2025.3588787

Delay-Space Arithmetic and Architecture

2025-07-01

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DOI：10.1109/MM.2025.3588787

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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.

Keywords:

Delays

Arithmetic

Wires

Transforms

Training

Three-dimensional displays

Standards

Hardware

Data mining

Voltage measurement

Time measurement

Delay-Space Arithmetic and Architecture

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