Stochastic Logic Realization of Matrix Operations

Stochastic computing (SC) is a re-emerging technique to process probability data encoded in digital bit-streams. Its main advantage is that arithmetic operations can be implemented by extremely small and low-power logic circuits. This makes SC suitable for signal-processing applications involving matrix operations whose VLSI implementation is very costly. Previous SC approaches only address basic matrix operations with relatively low accuracy needs. We explore the use of SC to implement a representative complex matrix operation, namely eigenvector computation. We apply it to a training task for visual face recognition, and show that our SC design has performance comparable to its conventional binary counterpart, while being able to trade computation time for accuracy.

[1]  José Luis Lázaro,et al.  Implementation in Fpgas of Jacobi Method to Solve the Eigenvalue and Eigenvector Problem , 2006, 2006 International Conference on Field Programmable Logic and Applications.

[2]  Madhusudana Shashanka,et al.  Linear Methods for Regression , 2009 .

[3]  Brian R. Gaines,et al.  Stochastic Computing Systems , 1969 .

[4]  D BrownBradley,et al.  Stochastic Neural Computation II , 2001 .

[5]  Howard C. Card,et al.  Stochastic Neural Computation I: Computational Elements , 2001, IEEE Trans. Computers.

[6]  Chi-Hsiang Yeh,et al.  Accumulative parallel counters , 1995, Conference Record of The Twenty-Ninth Asilomar Conference on Signals, Systems and Computers.

[7]  Barruquer Moner.  IX. References , 1971 .

[8]  Xin Li,et al.  An Architecture for Fault-Tolerant Computation with Stochastic Logic , 2011, IEEE Transactions on Computers.

[9]  John P. Hayes,et al.  Survey of Stochastic Computing , 2013, TECS.

[10]  P. Mars,et al.  High-speed matrix inversion by stochastic computer , 1976 .

[11]  Alex Pentland,et al.  Face recognition using eigenfaces , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[12]  G. M. D. Corso.  Estimating an Eigenvector by the Power Method with a Random Start , 1997 .

[13]  Georgi Kuzmanov,et al.  Reconfigurable sparse/dense matrix-vector multiplier , 2009, 2009 International Conference on Field-Programmable Technology.

[14]  Séamas McGettrick,et al.  Hardware Computation of the PageRank Eigenvector , 2010, 2010 International Conference on Reconfigurable Computing and FPGAs.

[15]  Amy Nicole Langville,et al.  A Reordering for the PageRank Problem , 2005, SIAM J. Sci. Comput..

[16]  Alan J. Laub,et al.  Matrix analysis - for scientists and engineers , 2004 .

[17]  David J. Kriegman,et al.  Acquiring linear subspaces for face recognition under variable lighting , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[18]  Vincent C. Gaudet,et al.  Iterative decoding using stochastic computation , 2003 .

[19]  John P. Hayes,et al.  Stochastic circuits for real-time image-processing applications , 2013, 2013 50th ACM/EDAC/IEEE Design Automation Conference (DAC).