Abstract

Optical implementation of content addressable associative memory based on the Hopfield model for neural networks and on the addition of nonlinear iterative feedback to a vector–matrix multiplier is described. Numerical and experimental results presented show that the approach is capable of introducing accuracy and robustness to optical processing while maintaining the traditional advantages of optics, namely, parallelism and massive interconnection capability. Moreover a potentially useful link between neural processing and optics that can be of interest in pattern recognition and machine vision is established.

© 1985 Optical Society of America

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References

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  1. J. J. Hopfield, “Neural Networks and Physical Systems with Emergent Collective Computational Abilities,” Proc. Natl. Acad. Sci. USA 79, 2554 (1982).
    [CrossRef] [PubMed]
  2. R. J. McEliece, E. C. Posner, S. Venkatesh, California Institute of Technology, Electrical Engineering Department; private communication.
  3. G. E. Hinton, J. A. Anderson, Parallel Models of Associative Memory (LEA Publishers, Hillsdale, N.J., 1981).
  4. T. Kohonen, Content Addressable Memories (Springer, New York, 1980).
    [CrossRef]
  5. D. Psaltis, N. Farhat, “A New Approach to Optical Information Processing Based On the Hopfield Model,” in Technical Digest, ICO-13 Conference, Sapporo (1984), p. 24.
  6. D. Psaltis, N. Farhat, “Optical Information Processing Based on an Associative-Memory Model of Neural Nets with Thresholding and Feedback,” Opt. Lett. 10, 98 (1985).
    [CrossRef] [PubMed]
  7. W. Ross, D. Psaltis, R. Anderson, “Two-Dimensional Magneto-Optic Spatial Light Modulator For Signal Processing,” Opt. Eng. 22, 485 (1983).
    [CrossRef]
  8. J. W. Goodman, A. R. Dias, L. M. Woody, “Fully Parallel, High-Speed Incoherent Optical Method for Performing Discrete Fourier Transforms,” Opt. Lett. 2, 1 (1978).
    [CrossRef] [PubMed]
  9. Z. Porada, “Thin Film Light Amplifier with Optical Feedback,” Thin Solid Films 109, 213 (1983).
    [CrossRef]
  10. H. M. Gibbs et al., “Optical Bistable Devices: The Basic Components of All-Optical Circuits,” Proc. Soc. Photo-Opt. Instrum. Eng. 269, 75 (1981).

1985

1983

W. Ross, D. Psaltis, R. Anderson, “Two-Dimensional Magneto-Optic Spatial Light Modulator For Signal Processing,” Opt. Eng. 22, 485 (1983).
[CrossRef]

Z. Porada, “Thin Film Light Amplifier with Optical Feedback,” Thin Solid Films 109, 213 (1983).
[CrossRef]

1982

J. J. Hopfield, “Neural Networks and Physical Systems with Emergent Collective Computational Abilities,” Proc. Natl. Acad. Sci. USA 79, 2554 (1982).
[CrossRef] [PubMed]

1981

H. M. Gibbs et al., “Optical Bistable Devices: The Basic Components of All-Optical Circuits,” Proc. Soc. Photo-Opt. Instrum. Eng. 269, 75 (1981).

1978

Anderson, J. A.

G. E. Hinton, J. A. Anderson, Parallel Models of Associative Memory (LEA Publishers, Hillsdale, N.J., 1981).

Anderson, R.

W. Ross, D. Psaltis, R. Anderson, “Two-Dimensional Magneto-Optic Spatial Light Modulator For Signal Processing,” Opt. Eng. 22, 485 (1983).
[CrossRef]

Dias, A. R.

Farhat, N.

D. Psaltis, N. Farhat, “Optical Information Processing Based on an Associative-Memory Model of Neural Nets with Thresholding and Feedback,” Opt. Lett. 10, 98 (1985).
[CrossRef] [PubMed]

D. Psaltis, N. Farhat, “A New Approach to Optical Information Processing Based On the Hopfield Model,” in Technical Digest, ICO-13 Conference, Sapporo (1984), p. 24.

Gibbs, H. M.

H. M. Gibbs et al., “Optical Bistable Devices: The Basic Components of All-Optical Circuits,” Proc. Soc. Photo-Opt. Instrum. Eng. 269, 75 (1981).

Goodman, J. W.

Hinton, G. E.

G. E. Hinton, J. A. Anderson, Parallel Models of Associative Memory (LEA Publishers, Hillsdale, N.J., 1981).

Hopfield, J. J.

J. J. Hopfield, “Neural Networks and Physical Systems with Emergent Collective Computational Abilities,” Proc. Natl. Acad. Sci. USA 79, 2554 (1982).
[CrossRef] [PubMed]

Kohonen, T.

T. Kohonen, Content Addressable Memories (Springer, New York, 1980).
[CrossRef]

McEliece, R. J.

R. J. McEliece, E. C. Posner, S. Venkatesh, California Institute of Technology, Electrical Engineering Department; private communication.

Porada, Z.

Z. Porada, “Thin Film Light Amplifier with Optical Feedback,” Thin Solid Films 109, 213 (1983).
[CrossRef]

Posner, E. C.

R. J. McEliece, E. C. Posner, S. Venkatesh, California Institute of Technology, Electrical Engineering Department; private communication.

Psaltis, D.

D. Psaltis, N. Farhat, “Optical Information Processing Based on an Associative-Memory Model of Neural Nets with Thresholding and Feedback,” Opt. Lett. 10, 98 (1985).
[CrossRef] [PubMed]

W. Ross, D. Psaltis, R. Anderson, “Two-Dimensional Magneto-Optic Spatial Light Modulator For Signal Processing,” Opt. Eng. 22, 485 (1983).
[CrossRef]

D. Psaltis, N. Farhat, “A New Approach to Optical Information Processing Based On the Hopfield Model,” in Technical Digest, ICO-13 Conference, Sapporo (1984), p. 24.

Ross, W.

W. Ross, D. Psaltis, R. Anderson, “Two-Dimensional Magneto-Optic Spatial Light Modulator For Signal Processing,” Opt. Eng. 22, 485 (1983).
[CrossRef]

Venkatesh, S.

R. J. McEliece, E. C. Posner, S. Venkatesh, California Institute of Technology, Electrical Engineering Department; private communication.

Woody, L. M.

Opt. Eng.

W. Ross, D. Psaltis, R. Anderson, “Two-Dimensional Magneto-Optic Spatial Light Modulator For Signal Processing,” Opt. Eng. 22, 485 (1983).
[CrossRef]

Opt. Lett.

Proc. Natl. Acad. Sci. USA

J. J. Hopfield, “Neural Networks and Physical Systems with Emergent Collective Computational Abilities,” Proc. Natl. Acad. Sci. USA 79, 2554 (1982).
[CrossRef] [PubMed]

Proc. Soc. Photo-Opt. Instrum. Eng.

H. M. Gibbs et al., “Optical Bistable Devices: The Basic Components of All-Optical Circuits,” Proc. Soc. Photo-Opt. Instrum. Eng. 269, 75 (1981).

Thin Solid Films

Z. Porada, “Thin Film Light Amplifier with Optical Feedback,” Thin Solid Films 109, 213 (1983).
[CrossRef]

Other

R. J. McEliece, E. C. Posner, S. Venkatesh, California Institute of Technology, Electrical Engineering Department; private communication.

G. E. Hinton, J. A. Anderson, Parallel Models of Associative Memory (LEA Publishers, Hillsdale, N.J., 1981).

T. Kohonen, Content Addressable Memories (Springer, New York, 1980).
[CrossRef]

D. Psaltis, N. Farhat, “A New Approach to Optical Information Processing Based On the Hopfield Model,” in Technical Digest, ICO-13 Conference, Sapporo (1984), p. 24.

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Figures (8)

Fig. 1
Fig. 1

(a) Insertion and (b) readout of memories.

Fig. 2
Fig. 2

Numerical example of recovery from partial input; N = 20, M = 4. (a) Stored vectors, (b) memory or (synaptic) matrix, (c) results of initializing with a partial version of b i ( 4 ) .

Fig. 3
Fig. 3

Concept for optical implementation of a content addressable memory based on the Hopfield model, (a) Matrix–vector multiplier incorporating nonlinear electronic feedback, (b) Scheme for realizing a binary bipolar memory mask transmittance in incoherent light.

Fig. 4
Fig. 4

Stored words, their Hamming distances, and their clipped T ij memory matrix.

Fig. 5
Fig. 5

Two halves of T ij memory mask.

Fig. 6
Fig. 6

Arrangement for optical implementation of the Hopfield model: (a) optoelectronic circuit diagram, (b) pictorial view.

Fig. 7
Fig. 7

Views of (a) input LED array and (b) memory submask/PD array assemblies.

Fig. 8
Fig. 8

Word composer and display box.

Tables (1)

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Table I Optical CAM Performance

Equations (56)

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T i j = m = 1 M v i ( m ) v j ( m ) , i , j = 1 , 2 , 3 N , T i i = 0 ,
v ̂ i ( m o ) = j N T i j v j ( m o ) = j i N m M v i ( m ) v j ( m ) v j ( m o )
= ( N 1 ) v i ( m o ) + m m 0 α m , m o v i ( m ) ,
α m , m o = j N v j ( m o ) v j ( m ) .
v i ( m o ) = sgn [ v ̂ i ( m o ) ] = { + 1 if v ̂ i ( m o ) > 0 1 otherwise .
3 ̅ , 2 ( 3 ̅ )
3 ̅ ( 3 ̅ )
3 ( 2 ̅ )
1 , 3 ̅ ( 1 )
3 ( 2 ̅ )
2 , 3 ( 2 ̅ )
2 ̅ ( 2 ̅ )
2 ̅ ( 2 ̅ )
1 ( 2 ̅ )
3 ( 2 ̅ )
2 ̅ ( 2 ̅ )
2 ̅ ( 2 ̅ )
3 ( 1 ̅ )
2 ̅ ( 2 ̅ )
2 ̅ ( OSC )
1 , 2 ( 1 ̅ )
2 ̅ ( 2 ̅ )
3 ̅ ( OSC )
3 ( 1 ̅ )
2 ̅ ( 2 ̅ )
3 ̅ ( OSC )
1 ̅ ( 1 ̅ )
2 ̅ ( 2 ̅ )
3 ̅ ( OSC )
1 ̅ ( 1 ̅ )
2 ̅ ( 2 ̅ )
3 ̅ ( 3 ̅ )
1 ̅ ( 1 ̅ )
2 ̅ ( 2 ̅ )
3 ̅ ( 3 ̅ )
1 ̅ ( 1 ̅ )
2 ̅ ( 2 ̅ )
3 ̅ ( 3 ̅ )
1 ̅ ( 1 ̅ )
2 ̅ ( 2 ̅ )
3 ̅ ( 3 ̅ )
1 ̅ ( 1 ̅ )
2 ̅ ( 2 ̅ )
3 ̅ ( 3 ̅ )
1 ̅ ( 1 ̅ )
2 ̅ ( 2 ̅ )
3 ̅ ( 3 ̅ )
1 ̅ ( 1 ̅ )
2 ̅ ( 2 ̅ )
3 ̅ ( 3 ̅ )
1 ̅ ( 1 ̅ )
2 ̅ ( 2 ̅ )
3 ̅ ( 3 ̅ )
1 ̅ ( 1 ̅ )
2 ̅ ( 2 ̅ )
3 ̅ ( 3 ̅ )

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