Abstract

Artificial neural networks (ANNs) have been widely used for industrial applications and have played a more important role in fundamental research. Although most ANN hardware systems are electronic-based, their optical implementation is particularly attractive because of its intrinsic parallelism and low energy consumption. Here, we demonstrate a fully functioning all-optical neural network (AONN), in which linear operations are programmed by spatial light modulators and Fourier lenses, while nonlinear optical activation functions are realized in laser-cooled atoms with electromagnetically induced transparency. Because all errors from different optical neurons are independent, it is possible to scale up the size of such an AONN. Moreover, our hardware system is reconfigurable for different applications without the need to modify the physical structure. We confirm its capability and feasibility in machine-learning application by successfully classifying order and disorder phases of a statistical Ising model. The demonstrated AONN scheme can be used to construct various ANN architectures with intrinsic optical parallel computation.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]

2019 (3)

S. D. Sarma, D.-L. Deng, and L.-M. Duan, “Machine learning meets quantum physics,” Phys. Today 72(3), 48–54 (2019).
[Crossref]

J. Feldmann, N. Youngblood, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “All-optical spiking neurosynaptic networks with self-learning capabilities,” Nature 569, 208–214 (2019).
[Crossref]

Y. Wang, J. Li, S. Zhang, K. Su, Y. Zhou, K. Liao, S. Du, H. Yan, and S.-L. Zhu, “Efficient quantum memory for single-photon polarization qubits,” Nat. Photonics 13, 346–351 (2019).
[Crossref]

2018 (5)

2017 (9)

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljačić, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).
[Crossref]

J. Carrasquilla and R. G. Melko, “Machine learning phases of matter,” Nat. Phys. 13, 431–434 (2017).
[Crossref]

G. Carleo and M. Troyer, “Solving the quantum many-body problem with artificial neural networks,” Science 355, 602–606 (2017).
[Crossref]

J. Liu, Y. Qi, Z. Y. Meng, and L. Fu, “Self-learning Monte Carlo method,” Phys. Rev. B 95, 041101 (2017).
[Crossref]

L. Huang and L. Wang, “Accelerated Monte Carlo simulations with restricted Boltzmann machines,” Phys. Rev. B 95, 035105 (2017).
[Crossref]

D.-L. Deng, X. Li, and S. D. Sarma, “Machine learning topological states,” Phys. Rev. B 96, 195145 (2017).
[Crossref]

J. Liu, H. Shen, Y. Qi, Z. Y. Meng, and L. Fu, “Self-learning Monte Carlo method and cumulative update in fermion systems,” Phys. Rev. B 95, 241104 (2017).
[Crossref]

Y. Zhang and E.-A. Kim, “Quantum loop topography for machine learning,” Phys. Rev. Lett. 118, 216401 (2017).
[Crossref]

C. Wang and H. Zhai, “Machine learning of frustrated classical spin models. I. Principal component analysis,” Phys. Rev. B 96, 144432 (2017).
[Crossref]

2016 (1)

P. Raccuglia, K. C. Elbert, P. D. Adler, C. Falk, M. B. Wenny, A. Mollo, M. Zeller, S. A. Friedler, J. Schrier, and A. J. Norquist, “Machine-learning-assisted materials discovery using failed experiments,” Nature 533, 73–76 (2016).
[Crossref]

2015 (1)

M. I. Jordan and T. M. Mitchell, “Machine learning: trends, perspectives, and prospects,” Science 349, 255–260 (2015).
[Crossref]

2014 (1)

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Beguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4, 021034 (2014).
[Crossref]

2012 (5)

S. Zhang, J. F. Chen, C. Liu, S. Zhou, M. M. T. Loy, G. K. L. Wong, and S. Du, “A dark-line two-dimensional magneto-optical trap of 85Rb atoms with high optical depth,” Rev. Sci. Instrum. 83, 073102 (2012).
[Crossref]

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, and S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 287 (2012).
[Crossref]

D. Woods and T. J. Naughton, “Photonic neural networks,” Nat. Phys. 8, 257–259 (2012).
[Crossref]

L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutiérrez, L. Pesquera, C. R. Mirasso, and I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20, 3241–3249 (2012).
[Crossref]

F. Duport, B. Schneider, A. Smerieri, M. Haelterman, and S. Massar, “All-optical reservoir computing,” Opt. Express 20, 22783–22795(2012).
[Crossref]

2010 (2)

D. M. Farkas, K. M. Hudek, E. A. Salim, S. R. Segal, M. B. Squires, and D. Z. Anderson, “A compact, transportable, microchip-based system for high repetition rate production of Bose-Einstein condensates,” Appl. Phys. Lett. 96, 093102 (2010).
[Crossref]

B. Wu, J. F. Hulbert, E. J. Lunt, K. Hurd, A. R. Hawkins, and H. Schmidt, “Slow light on a chip via atomic quantum state control,” Nat. Photonics 4, 776–779 (2010).
[Crossref]

2007 (1)

2005 (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[Crossref]

2004 (1)

S. Du, M. B. Squires, Y. Imai, L. Czaia, R. A. Saravanan, V. Bright, J. Reichel, T. W. Hansch, and D. Z. Anderson, “Atom-chip Bose-Einstein condensation in a portable vacuum cell,” Phys. Rev. A 70, 053606 (2004).
[Crossref]

1997 (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
[Crossref]

1996 (1)

S. Jutamulia and F. Yu, “Overview of hybrid optical neural networks,” Opt. Laser Technol. 28, 59–72 (1996).
[Crossref]

1994 (2)

1990 (1)

K. Lu and B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
[Crossref]

1989 (1)

H. J. Caulfield, J. Kinser, and S. K. Rogers, “Optical neural networks,” Proc. IEEE 77, 1573–1583 (1989).
[Crossref]

1987 (2)

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, “Trapping of neutral sodium atoms with radiation pressure,” Phys. Rev. Lett. 59, 2631 (1987).
[Crossref]

Y. Abu-Mostafa and D. Psaltis, “Optical neural computers,” Sci. Am. 256, 88–95 (1987).
[Crossref]

1986 (1)

D. Z. Anderson, “Optical resonators and neural networks,” AIP Conf. Proc. 151, 12 (1986).
[Crossref]

Abu-Mostafa, Y.

Y. Abu-Mostafa and D. Psaltis, “Optical neural computers,” Sci. Am. 256, 88–95 (1987).
[Crossref]

Adler, P. D.

P. Raccuglia, K. C. Elbert, P. D. Adler, C. Falk, M. B. Wenny, A. Mollo, M. Zeller, S. A. Friedler, J. Schrier, and A. J. Norquist, “Machine-learning-assisted materials discovery using failed experiments,” Nature 533, 73–76 (2016).
[Crossref]

Amin, R.

J. George, R. Amin, A. Mehrabian, J. Khurgin, T. El-Ghazawi, P. R. Prucnal, and V. J. Sorger, “Electrooptic nonlinear activation functions for vector matrix multiplications in optical neural networks,” in Signal Processing in Photonic Communications (Optical Society of America, 2018), paper SpW4G-3.

Anderson, D. Z.

D. M. Farkas, K. M. Hudek, E. A. Salim, S. R. Segal, M. B. Squires, and D. Z. Anderson, “A compact, transportable, microchip-based system for high repetition rate production of Bose-Einstein condensates,” Appl. Phys. Lett. 96, 093102 (2010).
[Crossref]

S. Du, M. B. Squires, Y. Imai, L. Czaia, R. A. Saravanan, V. Bright, J. Reichel, T. W. Hansch, and D. Z. Anderson, “Atom-chip Bose-Einstein condensation in a portable vacuum cell,” Phys. Rev. A 70, 053606 (2004).
[Crossref]

G. Zhou and D. Z. Anderson, “Acoustic signal recognition with a photorefractive time-delay neural network,” Opt. Lett. 19, 655–657 (1994).
[Crossref]

D. Z. Anderson, “Optical resonators and neural networks,” AIP Conf. Proc. 151, 12 (1986).
[Crossref]

Appeltant, L.

Azzam, S. I.

Baehr-Jones, T.

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljačić, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).
[Crossref]

Barredo, D.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Beguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4, 021034 (2014).
[Crossref]

Beguin, L.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Beguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4, 021034 (2014).
[Crossref]

Bhaskaran, H.

J. Feldmann, N. Youngblood, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “All-optical spiking neurosynaptic networks with self-learning capabilities,” Nature 569, 208–214 (2019).
[Crossref]

Bright, V.

S. Du, M. B. Squires, Y. Imai, L. Czaia, R. A. Saravanan, V. Bright, J. Reichel, T. W. Hansch, and D. Z. Anderson, “Atom-chip Bose-Einstein condensation in a portable vacuum cell,” Phys. Rev. A 70, 053606 (2004).
[Crossref]

Browaeys, A.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Beguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4, 021034 (2014).
[Crossref]

Brunner, D.

Bueno, J.

Butler, K. T.

K. T. Butler, D. W. Davies, H. Cartwright, O. Isayev, and A. Walsh, “Machine learning for molecular and materials science,” Nature 559, 547–555 (2018).
[Crossref]

Cable, A.

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, “Trapping of neutral sodium atoms with radiation pressure,” Phys. Rev. Lett. 59, 2631 (1987).
[Crossref]

Carleo, G.

G. Carleo and M. Troyer, “Solving the quantum many-body problem with artificial neural networks,” Science 355, 602–606 (2017).
[Crossref]

G. Carleo, C. Ignacio, C. Kyle, D. Laurent, S. Maria, T. Naftali, V.-M. Leslie, and Z. Lenka, “Machine learning and the physical sciences,” arXiv:1903.10563 (2019).

Carrasquilla, J.

J. Carrasquilla and R. G. Melko, “Machine learning phases of matter,” Nat. Phys. 13, 431–434 (2017).
[Crossref]

Cartwright, H.

K. T. Butler, D. W. Davies, H. Cartwright, O. Isayev, and A. Walsh, “Machine learning for molecular and materials science,” Nature 559, 547–555 (2018).
[Crossref]

Caulfield, H. J.

H. J. Caulfield, J. Kinser, and S. K. Rogers, “Optical neural networks,” Proc. IEEE 77, 1573–1583 (1989).
[Crossref]

Chen, J. F.

S. Zhang, J. F. Chen, C. Liu, S. Zhou, M. M. T. Loy, G. K. L. Wong, and S. Du, “A dark-line two-dimensional magneto-optical trap of 85Rb atoms with high optical depth,” Rev. Sci. Instrum. 83, 073102 (2012).
[Crossref]

Chen, P.

Y. Zuo, B. Li, Y. Zhao, Y. Jiang, Y.-C. Chen, P. Chen, G.-B. Jo, J. Liu, and S. Du, “All optical neural network with nonlinear activation functions,” arXiv: 1904.10819 (2019).

Chen, Y.-C.

Y. Zuo, B. Li, Y. Zhao, Y. Jiang, Y.-C. Chen, P. Chen, G.-B. Jo, J. Liu, and S. Du, “All optical neural network with nonlinear activation functions,” arXiv: 1904.10819 (2019).

Chu, S.

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, “Trapping of neutral sodium atoms with radiation pressure,” Phys. Rev. Lett. 59, 2631 (1987).
[Crossref]

Czaia, L.

S. Du, M. B. Squires, Y. Imai, L. Czaia, R. A. Saravanan, V. Bright, J. Reichel, T. W. Hansch, and D. Z. Anderson, “Atom-chip Bose-Einstein condensation in a portable vacuum cell,” Phys. Rev. A 70, 053606 (2004).
[Crossref]

Dambre, J.

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, and S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 287 (2012).
[Crossref]

Davies, D. W.

K. T. Butler, D. W. Davies, H. Cartwright, O. Isayev, and A. Walsh, “Machine learning for molecular and materials science,” Nature 559, 547–555 (2018).
[Crossref]

Deng, D.-L.

S. D. Sarma, D.-L. Deng, and L.-M. Duan, “Machine learning meets quantum physics,” Phys. Today 72(3), 48–54 (2019).
[Crossref]

D.-L. Deng, X. Li, and S. D. Sarma, “Machine learning topological states,” Phys. Rev. B 96, 195145 (2017).
[Crossref]

Di, L. R.

Dong, B.-Z.

Du, S.

Y. Wang, J. Li, S. Zhang, K. Su, Y. Zhou, K. Liao, S. Du, H. Yan, and S.-L. Zhu, “Efficient quantum memory for single-photon polarization qubits,” Nat. Photonics 13, 346–351 (2019).
[Crossref]

S. Zhang, J. F. Chen, C. Liu, S. Zhou, M. M. T. Loy, G. K. L. Wong, and S. Du, “A dark-line two-dimensional magneto-optical trap of 85Rb atoms with high optical depth,” Rev. Sci. Instrum. 83, 073102 (2012).
[Crossref]

S. Du, M. B. Squires, Y. Imai, L. Czaia, R. A. Saravanan, V. Bright, J. Reichel, T. W. Hansch, and D. Z. Anderson, “Atom-chip Bose-Einstein condensation in a portable vacuum cell,” Phys. Rev. A 70, 053606 (2004).
[Crossref]

Y. Zuo, B. Li, Y. Zhao, Y. Jiang, Y.-C. Chen, P. Chen, G.-B. Jo, J. Liu, and S. Du, “All optical neural network with nonlinear activation functions,” arXiv: 1904.10819 (2019).

Duan, L.-M.

S. D. Sarma, D.-L. Deng, and L.-M. Duan, “Machine learning meets quantum physics,” Phys. Today 72(3), 48–54 (2019).
[Crossref]

Duport, F.

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, and S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 287 (2012).
[Crossref]

F. Duport, B. Schneider, A. Smerieri, M. Haelterman, and S. Massar, “All-optical reservoir computing,” Opt. Express 20, 22783–22795(2012).
[Crossref]

Elbert, K. C.

P. Raccuglia, K. C. Elbert, P. D. Adler, C. Falk, M. B. Wenny, A. Mollo, M. Zeller, S. A. Friedler, J. Schrier, and A. J. Norquist, “Machine-learning-assisted materials discovery using failed experiments,” Nature 533, 73–76 (2016).
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See the supplemental material and Refs. [33–39] for (S1) the technical information of SLM; (S2) the Gerchberg–Saxton algorithm and feedback iteration process; (S3) the principle of linear optical power summation; (S4) the two matrices used for testing the linear operation; (S5) the operation of 2D MOT; (S6) the two-layer AONN implementation; (S7) the training of two-layer AONN; and (S8) Ising model related data processing.

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Supplementary Material (1)

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» Supplement 1       All optical neural network with nonlinear activation functions: supplementary material

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Figures (4)

Fig. 1.
Fig. 1. General AONN. (a) A typical two-layer neural network; (b) schematic of experimental realization of an optical neuron including linear and nonlinear operations. The linear operation zi=bi+jWijvj is achieved by combining a programmable SLM and a Fourier lens. φ is the nonlinear activation function.
Fig. 2.
Fig. 2. Linear optical operation and characterization. (a) Optical setup. FM, flip mirror; M, mirror; L1–L4, optical lens; SMF, single-mode fiber; C1–C2, camera. The coupling laser beam emitted from an SMF is collimated by lens L1 (f=10cm) and illuminates the surface of SLM1 (Leto, Holoeye), where it is selectively reflected to eight separate light spots on the surface of SLM2 (Pluto-2, Holoeye) by a 4f imaging system with lenses L2 (f=30cm) and L3 (f=25cm). An FM is inserted in the optical path to optionally reflect the beam to camera C1, which is located at the equivalent position of SLM2. SLM2 performs linear operation to transform the eight inputs to the four output beams, which are recorded by camera C2. (b) Histogram of 2000 random input vectors with elements equally distributing from 0 to 1; (c) error distribution of the input vectors. The standard deviation (STD) is 0.012. (d) Error distribution of the output vectors for the Hankel matrix operation. The STD is 0.014. (e) Fidelity distribution of the output vectors for the Hankel matrix operation.
Fig. 3.
Fig. 3. Realization of EIT nonlinear optical activation functions. (a) EIT experimental configuration with cold Rb85 atoms in the MOT; (b) three-level Λ-type EIT energy level diagram, where the Rb85 atomic states are |1=|5S1/2,F=2, |2=|5P1/2,F=3, and |3=|5S1/2,F=3. Both the circularly polarized (σ+) coupling (ωc) laser and probe (ωp) laser are on resonance with the transitions |2|3 and |1|3, respectively. (c) The EIT transmission spectrum of the probe beam. The solid (dashed) line is obtained without (with) the coupling beam. (d) and (e) are the nonlinear transmission functions for four on-resonance probe beams placed at different positions of the MOT. The coupling input and probe output are scaled for fitting the neural network input-output range [32].
Fig. 4.
Fig. 4. Fully functioning two-layer AONN. (a) Experimental configuration of the two-layer AONN. The input layer is the pattern encoded on SLM1, whose area is divided into multiple subareas. The first layer consists of a linear operation done by SLM1 and EIT nonlinear optical activation functions at MOT. The second layer contains SLM2, which converts four beams into two output beams at camera C3. The collimated coupling laser beam passing lens L1 (f=10cm) is incident on the SLM1, which generates four beams at the focal plane of L3 (f=75cm). A FM and camera C1 are used to monitor this linear operation. The four beams are imaged on the MOT through a 4f system consisting of L4 (f=75cm) and L5 (f=5cm). A collimated probe laser beam propagates along the opposite direction of the coupling beam, which is imaged on camera C2 through L5 and L6 (f=45cm). With further magnification by L7 (f=7.5cm) and L8 (f=45cm), four beams are incident on SLM2 and generate two beams and then are focused on camera C3. (b) and (c) are the mean probability of the order (blue) and disorder (red) phases as functions of temperature for 100 and 4000 configurations, respectively. The comparison is made between the results from the AONN (circle) and the computer NN (square).

Equations (2)

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Ip,out=Ip,ineOD4γ12γ13Ωc2+4γ12γ13=φ(Ωc2),
H(σ)=Jijσiσj,