Abstract

An incoherent optical neuron is proposed that subtracts inhibitory inputs from excitatory inputs optically by utilizing two separate device responses. Functionally it accommodates positive and negative weights, excitatory and inhibitory inputs, and nonnegative neuron outputs, and it can be used in a variety of neural network models. An extension is given to include bipolar neuron outputs in the case of fully connected networks.

© 1988 Optical Society of America

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References

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  1. A. F. Gmitro, G. R. Gindi, in Proceedings of the First International IEEE Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1987), p. III-599.
  2. R. D. Te Kolste, C. C. Guest, in Proceedings of the First International IEEE Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1987), p. III-625.
  3. M. Wang, A. Freeman, Neural Function (Little, Brown, Boston, 1987).
  4. S. A. Ellias, S. Grossberg, Biol. Cybern. 20, 69 (1975).
    [CrossRef]
  5. S.-I. Amari, IEEE Trans. Comput. C-21, 1197 (1972).
    [CrossRef]
  6. J. J. Hopfield, Proc. Natl. Acad. Sci. USA 79, 2554 (1982).
    [CrossRef] [PubMed]
  7. B. K. Jenkins, C. H. Wang, J. Opt. Soc. Am. A 4(13), P127 (1987).

1987 (1)

B. K. Jenkins, C. H. Wang, J. Opt. Soc. Am. A 4(13), P127 (1987).

1982 (1)

J. J. Hopfield, Proc. Natl. Acad. Sci. USA 79, 2554 (1982).
[CrossRef] [PubMed]

1975 (1)

S. A. Ellias, S. Grossberg, Biol. Cybern. 20, 69 (1975).
[CrossRef]

1972 (1)

S.-I. Amari, IEEE Trans. Comput. C-21, 1197 (1972).
[CrossRef]

Amari, S.-I.

S.-I. Amari, IEEE Trans. Comput. C-21, 1197 (1972).
[CrossRef]

Ellias, S. A.

S. A. Ellias, S. Grossberg, Biol. Cybern. 20, 69 (1975).
[CrossRef]

Freeman, A.

M. Wang, A. Freeman, Neural Function (Little, Brown, Boston, 1987).

Gindi, G. R.

A. F. Gmitro, G. R. Gindi, in Proceedings of the First International IEEE Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1987), p. III-599.

Gmitro, A. F.

A. F. Gmitro, G. R. Gindi, in Proceedings of the First International IEEE Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1987), p. III-599.

Grossberg, S.

S. A. Ellias, S. Grossberg, Biol. Cybern. 20, 69 (1975).
[CrossRef]

Guest, C. C.

R. D. Te Kolste, C. C. Guest, in Proceedings of the First International IEEE Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1987), p. III-625.

Hopfield, J. J.

J. J. Hopfield, Proc. Natl. Acad. Sci. USA 79, 2554 (1982).
[CrossRef] [PubMed]

Jenkins, B. K.

B. K. Jenkins, C. H. Wang, J. Opt. Soc. Am. A 4(13), P127 (1987).

Te Kolste, R. D.

R. D. Te Kolste, C. C. Guest, in Proceedings of the First International IEEE Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1987), p. III-625.

Wang, C. H.

B. K. Jenkins, C. H. Wang, J. Opt. Soc. Am. A 4(13), P127 (1987).

Wang, M.

M. Wang, A. Freeman, Neural Function (Little, Brown, Boston, 1987).

Biol. Cybern. (1)

S. A. Ellias, S. Grossberg, Biol. Cybern. 20, 69 (1975).
[CrossRef]

IEEE Trans. Comput. (1)

S.-I. Amari, IEEE Trans. Comput. C-21, 1197 (1972).
[CrossRef]

J. Opt. Soc. Am. A (1)

B. K. Jenkins, C. H. Wang, J. Opt. Soc. Am. A 4(13), P127 (1987).

Proc. Natl. Acad. Sci. USA (1)

J. J. Hopfield, Proc. Natl. Acad. Sci. USA 79, 2554 (1982).
[CrossRef] [PubMed]

Other (3)

A. F. Gmitro, G. R. Gindi, in Proceedings of the First International IEEE Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1987), p. III-599.

R. D. Te Kolste, C. C. Guest, in Proceedings of the First International IEEE Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1987), p. III-625.

M. Wang, A. Freeman, Neural Function (Little, Brown, Boston, 1987).

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Figures (4)

Fig. 1
Fig. 1

The ION. (a) The inhibitory element; (b) the unnormalized inhibitory element; (c) the nonlinear element; (d) the structure.

Fig. 2
Fig. 2

Characteristic response of a Hughes twisted-nematic liquid-crystal light valve, a possible device for the homogeneous ION model.

Fig. 3
Fig. 3

Simulation of imperfect I elements in the one-dimensional on-center-off-surround competitive network. (S1 is the input attenuation factor for the I element; mse is the normalized mean-squared error deviation from linearity of the I element response.) (a) The network input. (b)–(f) The network outputs for (b) the linear I element; (c) a = 0.46, b = 2.1, S1 = 1.0, mse = 19%; (d) a = 0.25, b = 1.2, S1 = 2.5, mse = 4%; (e) a = 0.33, b = 1.5, S1 = 1.5, mse = 14%; (f) a = 0.16, b = 0.9, S1 = 5.0, mse = 7%.

Fig. 4
Fig. 4

Single layer feedback net using a single spatial light modulator, SLM, to implement both I and N elements. B. S., beam splitter; ND, neutral-density filter.

Equations (7)

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I out ( I ) = I ^ inh = 1 - I inh ,
I out ( N ) = ψ [ I in ( N ) - α ] = ψ ( I ^ inh + I exc + I bias - α ) ,
I out ( N ) = ψ ( I exc - I inh ) ,
N in ( max ) = Δ I s ( N ) I r = extinction ratio of element N .
N out max = I s ( N ) a 1 N in ( max ) Δ I s ( N ) a 1 N in ( max ) ,
V ^ i = ψ ( j = 1 N W i j V j ) ,
1 2 ( 1 + V ^ i ) = ψ [ j = 1 N ( 1 - W i j ) 2 ( 1 - V j ) 2 + j = 1 N ( 1 + W i j ) 2 ( 1 + V j ) 2 ] ,

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