Abstract
In‐memory computing with cross‐point resistive memory arrays has gained enormous attention to accelerate the matrix‐vector multiplication in the computation of data‐centric applications. By combining a cross‐point array and feedback amplifiers, it is possible to compute matrix eigenvectors in one step without algorithmic iterations. Herein, time complexity of the eigenvector computation is investigated, based on the feedback analysis of the cross‐point circuit. The results show that the computing time of the circuit is determined by the mismatch degree of the eigenvalues implemented in the circuit, which controls the rising speed of output voltages. For a dataset of random matrices, the time for computing the dominant eigenvector in the circuit is constant for various matrix sizes; namely, the time complexity is O(1). The O(1) time complexity is also supported by simulations of PageRank of real‐world datasets. This work paves the way for fast, energy‐efficient accelerators for eigenvector computation in a wide range of practical applications.
Highlights
In-memory computing with cross-point resistive memory arrays has gained enormous attention to accelerate the matrix-vector multiplication in the computation of data-centric applications
We find that which is an elementary operation in several algebraic problems, the computational time is governed by the highest eigenvalue of for instance, the training and inference of neural networks,[2,3] an associated matrix, which, in turn, is controlled by the signal and image processing,[4,5] and the iterative solution of mismatch degree between the practical and the nominal conduclinear systems[6] or differential equations.[7]
The tations, the cross-point matrix-vector multiplication (MVM) is executed for several iteration O(1) time complexity is further supported by circuit simulations cycles according to the algorithmic workflow, which might raise of the calculation of dominant eigenvectors of random matrices an issue in terms of processing time and energy efficiency of the and of PageRank evaluation for the Harvard 500 database and its computation
Summary
Where the insignificant terms have been omitted, due to the fact that L0 is usually much larger than 1. The scattering of the computing time over the N range is due to the variation of λh with N (Figure S6, Supporting Information), which, in turn, is due to the specific structure of the transition matrices These results support the O(1) time complexity of the eigenvector circuit for practical application of PageRank. As the mismatch degree δ is generally considered to be small to maintain the eigenvector accuracy, it may suffer from the conductance variation, i.e., the feedback conductance values of the TIAs being slightly different In this case, the associated matrix of Equation (10) becomes. All the results of computing time and solution error show a tight distribution around the ones of the uniform case (Figure S9, Supporting Information), confirming the robustness of the circuit against feedback conductance variations in a practical implementation
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