Memristors have recently received significant attention as 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 memristor terminals make them promising candidates to efficiently 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 merits of memristor crossbars with the advantages of an operator splitting method, the 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 strength 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 method for eigenvalue/eigenvector computation using memristor crossbars is discussed. The memristor-based power iteration method can further be applied to principal component analysis. The use of memristor crossbars yields a significant speed-up in computation, and thus, we believe, hasmore »
Ultra-fast robust compressive sensing based on memristor crossbars
In this paper, we propose a new approach for robust compressive sensing (CS) using memristor crossbars that are constructed by recently invented memristor devices. The exciting features of a memristor crossbar, such as high density, low power and great scalability, make it a promising candidate to perform large-scale matrix operations. To apply memristor crossbars to solve a robust CS problem, the alternating directions method of multipliers (ADMM) is employed to split the original problem into subproblems that involve the solution of systems of linear equations. A system of linear equations can then be solved using memristor crossbars with astonishing O(1) time complexity. We also study the impact of hardware variations on the memristor crossbar based CS solver from both theoretical and practical points of view. The resulting overall complexity is given by O(n), which achieves O(n2.5) speed-up compared to the state-of-the-art software approach. Numerical results are provided to illustrate the effectiveness of the proposed CS solver.
- Award ID(s):
- Publication Date:
- NSF-PAR ID:
- Journal Name:
- 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
- Page Range or eLocation-ID:
- 1133 to 1137
- Sponsoring Org:
- National Science Foundation
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The increasing complexity of deep learning systems has pushed conventional computing technologies to their limits. While the memristor is one of the prevailing technologies for deep learning acceleration, it is only suited for classical learning layers where only two operands, namely weights and inputs, are processed simultaneously. Meanwhile, to improve the computational efficiency of deep learning for emerging applications, a variety of non-traditional layers requiring concurrent processing of many operands are becoming popular. For example, hypernetworks improve their predictive robustness by simultaneously processing weights and inputs against the application context. Two-electrode memristor grids cannot directly map emerging layers’ higher-order multiplicative neural interactions. Addressing this unmet need, we present crossbar processing using dual-gated memtransistors based on two-dimensional semiconductor MoS 2 . Unlike the memristor, the resistance states of memtransistors can be persistently programmed and can be actively controlled by multiple gate electrodes. Thus, the discussed memtransistor crossbar enables several advanced inference architectures beyond a conventional passive crossbar. For example, we show that sneak paths can be effectively suppressed in memtransistor crossbars, whereas they limit size scalability in a passive memristor crossbar. Similarly, exploiting gate terminals to suppress crossbar weights dynamically reduces biasing power by ∼20% in memtransistor crossbars for a fullymore »
Analyzing the Impact of Memristor Variability on Crossbar Implementation of Regression Algorithms With Smart Weight Update Pulsing TechniquesThis paper presents an extensive study of linear and logistic regression algorithms implemented with 1T1R memristor crossbars arrays. Using a sophisticated simulation platform that wraps circuit-level simulations of 1T1R crossbars and physics-based models of RRAM (memristors), we elucidate the impact of device variability on algorithm accuracy, convergence rate and precision. Moreover, a smart pulsing strategy is proposed for practical implementation of synaptic weight updates that can accelerate training in real crossbar architectures. Stochastic multi-variable linear regression shows robustness to memristor variability in terms of prediction accuracy but reveals impact on convergence rate and precision. Similarly, the stochastic logistic regression crossbar implementation reveals immunity to memristor variability as determined by negligible effects on image classification accuracy but indicates an impact on training performance manifested as reduced convergence rate and degraded precision.
Algorithm-hardware co-optimization of the memristor-based framework for solving SOCP and homogeneous QCQP problemsA memristor crossbar, which is constructed with memristor devices, has the unique ability to change and memorize the state of each of its memristor elements. It also has other highly desirable features such as high density, low power operation and excellent scalability. Hence the memristor crossbar technology can potentially be utilized for developing low-complexity and high-scalability solution frameworks for solving a large class of convex optimization problems, which involve extensive matrix operations and have critical applications in multiple disciplines. This paper, as the first attempt towards this direction, proposes a novel memristor crossbar-based framework for solving two important convex optimization problems, i.e., second-order cone programming (SOCP) and homogeneous quadratically constrained quadratic programming (QCQP) problems. In this paper, the alternating direction method of multipliers (ADMM) is adopted. It splits the SOCP and homogeneous QCQP problems into sub-problems that involve the solution of linear systems, which could be effectively solved using the memristor crossbar in O(1) time complexity. The proposed algorithm is an iterative procedure that iterates a constant number of times. Therefore, algorithms to solve SOCP and homogeneous QCQP problems have pseudo-O(N) complexity, which is a significant reduction compared to the state-of-the-art software solvers (O(N3.5)-O(N4)).
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