Title: A Memristor-Based Optimization Framework for AI Applications,
Abstract: Memristors have recently received significant attention as ubiquitous
device-level components for building a novel generation of computing systems.
These devices have many promising features, such as non-volatility, low power
consumption, high density, and excellent scalability. The ability to control
and modify biasing voltages at the two terminals of memristors make them
promising candidates to perform matrix-vector multiplications and solve systems
of linear equations. In this article, we discuss how networks of memristors
arranged in crossbar arrays can be used for efficiently solving optimization
and machine learning problems. We introduce a new memristor-based optimization
framework that combines the computational merit of memristor crossbars with the
advantages of an operator splitting method, alternating direction method of
multipliers (ADMM). Here, ADMM helps in splitting a complex optimization
problem into subproblems that involve the solution of systems of linear
equations. The capability of this framework is shown by applying it to linear
programming, quadratic programming, and sparse optimization. In addition to
ADMM, implementation of a customized power iteration (PI) method for
eigenvalue/eigenvector computation using memristor crossbars is discussed. The
memristor-based PI method can further be applied to principal component
analysis (PCA). The use of memristor crossbars yields a significant speed-up in
computation, and thus, we believe, has the potential to advance optimization
and machine learning research in artificial intelligence (AI).