Analog Acceleration of the Power Method using Memristor Crossbars

Abstract

Determining the dominant eigenvector of matrices and graphs is one of the most fundamental tasks in many machine learning problems, including spectral clustering, Hyperlink Induced Topic Search (HITS), Markov Chains, PageRank and eigenvector centralities. Among the several algorithms used, the Power Method is one of the simplest iterative approaches. It relies on multiple vector-matrix multiplications (VMMs) and a normalization step to prevent divergent behaviours. Recently, efficiency of the memristor crossbars in solving VMMs have been demonstrated using fundamental laws of the circuit theory. In this work, we propose a circuit to accelerate the Power iteration algorithm including current-mode termination for the memristor crossbars and a normalization circuit. The normalization step together with the feedback loop of the complete circuit ensure stability and convergence of the dominant eigenvector. The system allows the observation of the evolution of the outputs. We implement a transistor level peripheral circuitry around the memristor crossbar and take non-idealities such as wire parasitics, source driver resistance and finite memristor precision into account. We compute the eigenvector centrality to demonstrate the performance of the proposed system. We compare our results to the ones coming from the conventional digital computers and observe significant energy savings while maintaining a competitive accuracy.