Energy-Efficient Time-Domain Vector-by-Matrix Multiplier for Neurocomputing and Beyond

Abstract

We propose an extremely energy-efficient mixed-signal ${N} \times {N}$ vector-by-matrix multiplication (VMM) in a time domain. Multi-bit inputs/outputs are represented with time-encoded digital signals, while multi-bit matrix weights are realized with adjustable current sources, e.g., transistors biased in subthreshold regime. The major advantage of the proposed approach over other types of mixed-signal implementations is very compact peripheral circuits, which would be essential for achieving high energy efficiency and speed at the system level. As a case study, we have designed a multilayer perceptron, based on two layers of 10 $ \times $ 10 four-quadrant multipliers, in 55-nm process with embedded NOR flash memory technology, which allows for compact implementation of adjustable current sources. Our analysis, based on memory cell measurements, shows that >6 bit operation can be ensured for larger ( ${N} >$ 50) VMMs. Post-layout estimates for 55-nm 6-bit VMM, which take into account the impact of PVT variations, noise, and overhead of I/O circuitry for converting between conventional digital and time domain representations, show ~7 fJ/Op for ${N} >$ 500. The energy efficiency can be further improved to POp/J regime for more optimal and aggressive designs.