A Generalized Block-Matrix Circuit for Closed-Loop Analog In-Memory Computing

Matrix-based computing is ubiquitous in an increasing number of present-day machine learning applications such as neural networks, regression, and 5G communications. Conventional systems based on von-Neumann architecture are limited by the energy and latency bottleneck induced by the physical separation of the processing and memory units. In-memory computing (IMC) is a novel paradigm where computation is performed directly within the memory, thus eliminating the need for constant data transfer. IMC has shown exceptional throughput and energy efficiency when coupled with crosspoint arrays of resistive memory devices in open-loop matrix-vector-multiplication and closed-loop inverse-matrix-vector multiplication (IMVM) accelerators. However, each application results in a different circuit topology, thus complicating the development of reconfigurable, general-purpose IMC systems. In this article, we present a generalized closed-loop IMVM circuit capable of performing any linear matrix operation by proper memory remapping. We derive closed-form equations for the ideal input-output transfer functions, static error, and dynamic behavior, introducing a novel continuous-time analytical model allowing for orders-of-magnitude simulation speedup with respect to SPICE-based solvers. The proposed circuit represents an ideal candidate for general-purpose accelerators of machine learning.