Abstract

We present an all-optical neuron that utilizes a logistic sigmoid activation function, using a Wavelength-Division Multiplexing (WDM) input & weighting scheme. The activation function is realized by means of a deeply-saturated differentially-biased Semiconductor Optical Amplifier-Mach-Zehnder Interferometer (SOA-MZI) followed by a SOA-Cross-Gain-Modulation (XGM) gate. Its transfer function is both experimentally and theoretically analyzed, showing excellent agreement between theory and experiment and an almost perfect fitting with a logistic sigmoid function. The optical sigmoid transfer function is then exploited in the experimental demonstration of a photonic neuron, demonstrating successful thresholding over a 100psec-long pulse sequence with 4 different weighted-and-summed power levels.

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

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2018 (4)

X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” Science 361, 1004–1008 (2018).
[Crossref] [PubMed]

H. T. Peng, M. A. Nahmias, T. F. De Lima, A. N. Tait, B. J. Shastri, and P. R. Prucnal, “Neuromorphic Photonic Integrated Circuits,” IEEE J. Sel. Top. Quantum Electron. 24, 1–16 (2018).
[Crossref]

I. Chakraborty, G. Saha, A. Sengupta, and K. Roy, “Toward Fast Neural Computing using All-Photonic Phase Change Spiking Neurons,” Sci. Reports 8, 1–10 (2018).

M. Miscuglio, A. Mehrabian, Z. Hu, S. I. Azzam, J. George, A. V. Kildishev, M. Pelton, and V. J. Sorger, “All-optical nonlinear activation function for photonic neural networks [Invited],” Opt. Mater. Express 8, 3851 (2018).
[Crossref]

2017 (3)

A. N. Tait, T. F. De Lima, E. Zhou, A. X. Wu, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Neuromorphic photonic networks using silicon photonic weight banks,” Sci. Reports 7, 1–10 (2017).

N. P. Jouppi, A. Borchers, R. Boyle, P.-l. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, C. Young, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, N. Patil, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, D. Killebrew, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Patterson, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, G. Agrawal, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, R. Bajwa, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, S. Bates, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, D. H. Yoon, S. Bhatia, and N. Boden, “In-Datacenter Performance Analysis of a Tensor Processing Unit,” ACM SIGARCH Comput. Archit. News 45, 1–12 (2017).
[Crossref]

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]

2016 (2)

C. Mesaritakis, A. Kapsalis, A. Bogris, and D. Syvridis, “Artificial Neuron Based on Integrated Semiconductor Quantum Dot Mode-Locked Lasers,” Sci. Reports 6, 1–10 (2016).

M. A. Nahmias, A. N. Tait, L. Tolias, M. P. Chang, T. Ferreira De Lima, B. J. Shastri, and P. R. Prucnal, “An integrated analog O/E/O link for multi-channel laser neurons,” Appl. Phys. Lett. 108, 151106 (2016).
[Crossref]

2015 (4)

K. Xu, J. Ba, R. Kiros, K. Cho, A. Courville, R. Salakhutdinov, R. Zemel, and Y. Bengio, “Show, Attend and Tell: Neural Image Caption Generation with Visual Attention,” Sci. Total. Environ. 572, 169–176 (2015).

A. N. Tait, J. Chang, B. J. Shastri, M. A. Nahmias, and P. R. Prucnal, “Demonstration of WDM weighted addition for principal component analysis,” Opt. Express 23, 12758 (2015).
[Crossref] [PubMed]

J. M. Shalf and R. Leland, “Computing beyond Moore’s Law,” Computer 48, 14–23 (2015).
[Crossref]

F. Akopyan, J. Sawada, A. Cassidy, R. Alvarez-Icaza, J. Arthur, P. Merolla, N. Imam, Y. Nakamura, P. Datta, G. J. Nam, B. Taba, M. Beakes, B. Brezzo, J. B. Kuang, R. Manohar, W. P. Risk, B. Jackson, and D. S. Modha, “TrueNorth: Design and Tool Flow of a 65 mW 1 Million Neuron Programmable Neurosynaptic Chip,” IEEE Transactions on Comput. Des. Integr. Circuits Syst. 34, 1537–1557 (2015).
[Crossref]

2014 (1)

A. N. Tait, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Broadcast and Weight: An Integrated Network For Scalable Photonic Spike Processing,” J. Light. Technol. 32, 4029–4041 (2014).
[Crossref]

2013 (3)

S. B. Furber, D. R. Lester, L. A. Plana, J. D. Garside, E. Painkras, S. Temple, and A. D. Brown, “Overview of the SpiNNaker system architecture,” IEEE Transactions on Comput. 62, 2454–2467 (2013).
[Crossref]

M. A. Nahmias, B. J. Shastri, A. N. Tait, and P. R. Prucnal, “A leaky integrate-and-fire laser neuron for ultrafast cognitive computing,” IEEE J. on Sel. Top. Quantum Electron. 19, 1–12 (2013).
[Crossref]

A. N. Tait, B. J. Shastri, M. P. Fok, M. A. Nahmias, and P. R. Prucnal, “The DREAM: An integrated photonic thresholder,” J. Light. Technol. 31, 1263–1272 (2013).
[Crossref]

2012 (1)

N. S. Rafidi, K. S. Kravtsov, Yue Tian, M. P. Fok, M. A. Nahmias, A. N. Tait, and P. R. Prucnal, “Power Transfer Function Tailoring in a Highly Ge-Doped Nonlinear Interferometer-Based All-Optical Thresholder Using Offset-Spectral Filtering,” IEEE Photonics J. 4, 528–534 (2012).
[Crossref]

2011 (2)

K. S. Kravtsov, M. P. Fok, P. R. Prucnal, and D. Rosenbluth, “Ultrafast All-Optical Implementation of a Leaky Integrate-and-Fire Neuron,” Opt. Express 19, 2133 (2011).
[Crossref] [PubMed]

M. Spyropoulou, N. Pleros, K. Vyrsokinos, D. Apostolopoulos, M. Bougioukos, D. Petrantonakis, A. Miliou, and H. Avramopoulos, “40 Gb/s NRZ wavelength conversion using a differentially-biased SOA-MZI: Theory and experiment,” J. Light. Technol. 29, 1489–1499 (2011).
[Crossref]

2009 (1)

2004 (1)

N. Pleros, C. Bintjas, G. T. Kanellos, K. Vlachos, H. Avramopoulos, and G. Guekos, “Recipe for intensity modulation reduction in SOA-based interferometric switches,” J. Light. Technol. 22, 2834–2841 (2004).
[Crossref]

1998 (1)

G. Morthier, J. Sun, T. Gyselings, and R. Baets, “A novel optical decision circuit based on a Mach-Zehnder or Michelson interferometer and gain-clamped semiconductor optical amplifiers,” IEEE Photonics Technol. Lett. 10, 1162–1164 (1998).
[Crossref]

1997 (1)

S. Hochreiter and J. Schmidhuber, “Long short-term memory,” Neural computation 9, 1735–1780 (1997).
[Crossref] [PubMed]

Agrawal, G.

N. P. Jouppi, A. Borchers, R. Boyle, P.-l. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, C. Young, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, N. Patil, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, D. Killebrew, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Patterson, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, G. Agrawal, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, R. Bajwa, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, S. Bates, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, D. H. Yoon, S. Bhatia, and N. Boden, “In-Datacenter Performance Analysis of a Tensor Processing Unit,” ACM SIGARCH Comput. Archit. News 45, 1–12 (2017).
[Crossref]

Akopyan, F.

F. Akopyan, J. Sawada, A. Cassidy, R. Alvarez-Icaza, J. Arthur, P. Merolla, N. Imam, Y. Nakamura, P. Datta, G. J. Nam, B. Taba, M. Beakes, B. Brezzo, J. B. Kuang, R. Manohar, W. P. Risk, B. Jackson, and D. S. Modha, “TrueNorth: Design and Tool Flow of a 65 mW 1 Million Neuron Programmable Neurosynaptic Chip,” IEEE Transactions on Comput. Des. Integr. Circuits Syst. 34, 1537–1557 (2015).
[Crossref]

Alexoudi, T.

G. Mourgias-alexandris, A. Tsakyridis, T. Alexoudi, K. Vyrsokinos, and N. Pleros, “Optical thresholding device with a sigmoidal transfer function,” in Proceedings Of Photonics in Switching and Computing, (2018).

Alvarez-Icaza, R.

F. Akopyan, J. Sawada, A. Cassidy, R. Alvarez-Icaza, J. Arthur, P. Merolla, N. Imam, Y. Nakamura, P. Datta, G. J. Nam, B. Taba, M. Beakes, B. Brezzo, J. B. Kuang, R. Manohar, W. P. Risk, B. Jackson, and D. S. Modha, “TrueNorth: Design and Tool Flow of a 65 mW 1 Million Neuron Programmable Neurosynaptic Chip,” IEEE Transactions on Comput. Des. Integr. Circuits Syst. 34, 1537–1557 (2015).
[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 Advanced Photonics 2018 (BGPP, IPR, NP, NOMA, Sensors, Networks, SPPCom, SOF), (Optical Society of America, 2018), p. SpW4G.3.
[Crossref]

Apostolopoulos, D.

M. Spyropoulou, N. Pleros, K. Vyrsokinos, D. Apostolopoulos, M. Bougioukos, D. Petrantonakis, A. Miliou, and H. Avramopoulos, “40 Gb/s NRZ wavelength conversion using a differentially-biased SOA-MZI: Theory and experiment,” J. Light. Technol. 29, 1489–1499 (2011).
[Crossref]

Arthur, J.

F. Akopyan, J. Sawada, A. Cassidy, R. Alvarez-Icaza, J. Arthur, P. Merolla, N. Imam, Y. Nakamura, P. Datta, G. J. Nam, B. Taba, M. Beakes, B. Brezzo, J. B. Kuang, R. Manohar, W. P. Risk, B. Jackson, and D. S. Modha, “TrueNorth: Design and Tool Flow of a 65 mW 1 Million Neuron Programmable Neurosynaptic Chip,” IEEE Transactions on Comput. Des. Integr. Circuits Syst. 34, 1537–1557 (2015).
[Crossref]

Avramopoulos, H.

M. Spyropoulou, N. Pleros, K. Vyrsokinos, D. Apostolopoulos, M. Bougioukos, D. Petrantonakis, A. Miliou, and H. Avramopoulos, “40 Gb/s NRZ wavelength conversion using a differentially-biased SOA-MZI: Theory and experiment,” J. Light. Technol. 29, 1489–1499 (2011).
[Crossref]

N. Pleros, C. Bintjas, G. T. Kanellos, K. Vlachos, H. Avramopoulos, and G. Guekos, “Recipe for intensity modulation reduction in SOA-based interferometric switches,” J. Light. Technol. 22, 2834–2841 (2004).
[Crossref]

Azzam, S. I.

Ba, J.

K. Xu, J. Ba, R. Kiros, K. Cho, A. Courville, R. Salakhutdinov, R. Zemel, and Y. Bengio, “Show, Attend and Tell: Neural Image Caption Generation with Visual Attention,” Sci. Total. Environ. 572, 169–176 (2015).

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]

Baets, R.

G. Morthier, J. Sun, T. Gyselings, and R. Baets, “A novel optical decision circuit based on a Mach-Zehnder or Michelson interferometer and gain-clamped semiconductor optical amplifiers,” IEEE Photonics Technol. Lett. 10, 1162–1164 (1998).
[Crossref]

Bajwa, R.

N. P. Jouppi, A. Borchers, R. Boyle, P.-l. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, C. Young, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, N. Patil, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, D. Killebrew, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Patterson, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, G. Agrawal, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, R. Bajwa, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, S. Bates, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, D. H. Yoon, S. Bhatia, and N. Boden, “In-Datacenter Performance Analysis of a Tensor Processing Unit,” ACM SIGARCH Comput. Archit. News 45, 1–12 (2017).
[Crossref]

Bates, S.

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Clark, C.

N. P. Jouppi, A. Borchers, R. Boyle, P.-l. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, C. Young, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, N. Patil, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, D. Killebrew, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Patterson, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, G. Agrawal, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, R. Bajwa, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, S. Bates, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, D. H. Yoon, S. Bhatia, and N. Boden, “In-Datacenter Performance Analysis of a Tensor Processing Unit,” ACM SIGARCH Comput. Archit. News 45, 1–12 (2017).
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Daley, M.

N. P. Jouppi, A. Borchers, R. Boyle, P.-l. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, C. Young, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, N. Patil, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, D. Killebrew, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Patterson, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, G. Agrawal, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, R. Bajwa, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, S. Bates, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, D. H. Yoon, S. Bhatia, and N. Boden, “In-Datacenter Performance Analysis of a Tensor Processing Unit,” ACM SIGARCH Comput. Archit. News 45, 1–12 (2017).
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Dean, J.

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Law, J.

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Leary, C.

N. P. Jouppi, A. Borchers, R. Boyle, P.-l. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, C. Young, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, N. Patil, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, D. Killebrew, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Patterson, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, G. Agrawal, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, R. Bajwa, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, S. Bates, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, D. H. Yoon, S. Bhatia, and N. Boden, “In-Datacenter Performance Analysis of a Tensor Processing Unit,” ACM SIGARCH Comput. Archit. News 45, 1–12 (2017).
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Liu, Z.

N. P. Jouppi, A. Borchers, R. Boyle, P.-l. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, C. Young, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, N. Patil, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, D. Killebrew, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Patterson, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, G. Agrawal, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, R. Bajwa, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, S. Bates, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, D. H. Yoon, S. Bhatia, and N. Boden, “In-Datacenter Performance Analysis of a Tensor Processing Unit,” ACM SIGARCH Comput. Archit. News 45, 1–12 (2017).
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Lucke, K.

N. P. Jouppi, A. Borchers, R. Boyle, P.-l. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, C. Young, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, N. Patil, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, D. Killebrew, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Patterson, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, G. Agrawal, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, R. Bajwa, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, S. Bates, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, D. H. Yoon, S. Bhatia, and N. Boden, “In-Datacenter Performance Analysis of a Tensor Processing Unit,” ACM SIGARCH Comput. Archit. News 45, 1–12 (2017).
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Lundin, A.

N. P. Jouppi, A. Borchers, R. Boyle, P.-l. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, C. Young, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, N. Patil, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, D. Killebrew, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Patterson, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, G. Agrawal, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, R. Bajwa, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, S. Bates, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, D. H. Yoon, S. Bhatia, and N. Boden, “In-Datacenter Performance Analysis of a Tensor Processing Unit,” ACM SIGARCH Comput. Archit. News 45, 1–12 (2017).
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Luo, Y.

X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” Science 361, 1004–1008 (2018).
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MacKean, G.

N. P. Jouppi, A. Borchers, R. Boyle, P.-l. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, C. Young, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, N. Patil, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, D. Killebrew, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Patterson, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, G. Agrawal, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, R. Bajwa, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, S. Bates, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, D. H. Yoon, S. Bhatia, and N. Boden, “In-Datacenter Performance Analysis of a Tensor Processing Unit,” ACM SIGARCH Comput. Archit. News 45, 1–12 (2017).
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Maggiore, A.

N. P. Jouppi, A. Borchers, R. Boyle, P.-l. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, C. Young, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, N. Patil, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, D. Killebrew, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Patterson, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, G. Agrawal, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, R. Bajwa, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, S. Bates, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, D. H. Yoon, S. Bhatia, and N. Boden, “In-Datacenter Performance Analysis of a Tensor Processing Unit,” ACM SIGARCH Comput. Archit. News 45, 1–12 (2017).
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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).
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Zhou, E.

A. N. Tait, T. F. De Lima, E. Zhou, A. X. Wu, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Neuromorphic photonic networks using silicon photonic weight banks,” Sci. Reports 7, 1–10 (2017).

ACM SIGARCH Comput. Archit. News (1)

N. P. Jouppi, A. Borchers, R. Boyle, P.-l. Cantin, C. Chao, C. Clark, J. Coriell, M. Daley, M. Dau, J. Dean, B. Gelb, C. Young, T. V. Ghaemmaghami, R. Gottipati, W. Gulland, R. Hagmann, C. R. Ho, D. Hogberg, J. Hu, R. Hundt, D. Hurt, J. Ibarz, N. Patil, A. Jaffey, A. Jaworski, A. Kaplan, H. Khaitan, D. Killebrew, A. Koch, N. Kumar, S. Lacy, J. Laudon, J. Law, D. Patterson, D. Le, C. Leary, Z. Liu, K. Lucke, A. Lundin, G. MacKean, A. Maggiore, M. Mahony, K. Miller, R. Nagarajan, G. Agrawal, R. Narayanaswami, R. Ni, K. Nix, T. Norrie, M. Omernick, N. Penukonda, A. Phelps, J. Ross, M. Ross, A. Salek, R. Bajwa, E. Samadiani, C. Severn, G. Sizikov, M. Snelham, J. Souter, D. Steinberg, A. Swing, M. Tan, G. Thorson, B. Tian, S. Bates, H. Toma, E. Tuttle, V. Vasudevan, R. Walter, W. Wang, E. Wilcox, D. H. Yoon, S. Bhatia, and N. Boden, “In-Datacenter Performance Analysis of a Tensor Processing Unit,” ACM SIGARCH Comput. Archit. News 45, 1–12 (2017).
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Appl. Phys. Lett. (1)

M. A. Nahmias, A. N. Tait, L. Tolias, M. P. Chang, T. Ferreira De Lima, B. J. Shastri, and P. R. Prucnal, “An integrated analog O/E/O link for multi-channel laser neurons,” Appl. Phys. Lett. 108, 151106 (2016).
[Crossref]

Computer (1)

J. M. Shalf and R. Leland, “Computing beyond Moore’s Law,” Computer 48, 14–23 (2015).
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IEEE J. on Sel. Top. Quantum Electron. (1)

M. A. Nahmias, B. J. Shastri, A. N. Tait, and P. R. Prucnal, “A leaky integrate-and-fire laser neuron for ultrafast cognitive computing,” IEEE J. on Sel. Top. Quantum Electron. 19, 1–12 (2013).
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IEEE J. Sel. Top. Quantum Electron. (1)

H. T. Peng, M. A. Nahmias, T. F. De Lima, A. N. Tait, B. J. Shastri, and P. R. Prucnal, “Neuromorphic Photonic Integrated Circuits,” IEEE J. Sel. Top. Quantum Electron. 24, 1–16 (2018).
[Crossref]

IEEE Photonics J. (1)

N. S. Rafidi, K. S. Kravtsov, Yue Tian, M. P. Fok, M. A. Nahmias, A. N. Tait, and P. R. Prucnal, “Power Transfer Function Tailoring in a Highly Ge-Doped Nonlinear Interferometer-Based All-Optical Thresholder Using Offset-Spectral Filtering,” IEEE Photonics J. 4, 528–534 (2012).
[Crossref]

IEEE Photonics Technol. Lett. (1)

G. Morthier, J. Sun, T. Gyselings, and R. Baets, “A novel optical decision circuit based on a Mach-Zehnder or Michelson interferometer and gain-clamped semiconductor optical amplifiers,” IEEE Photonics Technol. Lett. 10, 1162–1164 (1998).
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A. N. Tait, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Broadcast and Weight: An Integrated Network For Scalable Photonic Spike Processing,” J. Light. Technol. 32, 4029–4041 (2014).
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N. Pleros, C. Bintjas, G. T. Kanellos, K. Vlachos, H. Avramopoulos, and G. Guekos, “Recipe for intensity modulation reduction in SOA-based interferometric switches,” J. Light. Technol. 22, 2834–2841 (2004).
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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 Advanced Photonics 2018 (BGPP, IPR, NP, NOMA, Sensors, Networks, SPPCom, SOF), (Optical Society of America, 2018), p. SpW4G.3.
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Figures (5)

Fig. 1
Fig. 1 (a) Artificial neuron, (b) Optical WDM neuron.
Fig. 2
Fig. 2 (a) Photonic thresholder layout, (b)–(f) Principle of operation for the photonic thresholder, (g) Experimental setup for the measurement of transfer function.
Fig. 3
Fig. 3 (a) Multi-level signal for the activation function evaluation, (b)–(d) Time traces at activation’s function output for 8, 3 and −2dBm average input optical power, Plot for the experimental transfer function and its y-error, the sigmoid fitting and the theoretical transfer function in: (e) logarithmic and (f) linear scale, Plot for the theoretical curve by varying the: (g) control attenuation factor af and (h) biasing attenuation factor b. y-axis scale: 3.5mV/div, x-axis scale: 1ns/div.
Fig. 4
Fig. 4 Experimental setup for the optical sigmoid neuron.
Fig. 5
Fig. 5 (a) Time trace (200psec/div) of the multi-level signal at the input of activation unit, where the dashed lines denote the different power levels. The corresponding eye diagram is also presented below (50psec/div). (b), (d), (f) and (h): Time traces at the output of the SOA-MZI, (c), (e), (g), and (i): Time traces (200psec/div) and eye diagrams (50psec/div) at the output of the optical neuron. y-axis scale: (4mV/div).

Equations (7)

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f ( x ) = A 2 + A 1 A 2 ( 1 + e ( ( x x 0 ) / d ) )
P G ( t ) = P noise + 1 4 P λ 0 [ G 1 ( t ) + G 2 ( t ) 2 G 1 ( t ) G 2 ( t ) cos ( Δ ϕ ( t ) ) ]
P F ( t ) = P noise + 1 4 P λ 0 [ G 1 ( t ) + G 2 ( t ) + 2 G 1 ( t ) G 2 ( t ) cos ( Δ ϕ ( t ) ) ]
Δ ϕ ( t ) = α 2 ln [ G 1 ( t ) / G 2 ( t ) ]
G 1 ( t ) = [ 1 ( 1 1 G CW ( 1 ) exp ( 1 t ( 1 b ) P in ( t ) d t / U sat ) ] 1
G 2 ( t ) = [ 1 ( 1 1 G CW ( 2 ) exp ( t ( 1 a f ) ( 1 b ) P in ( t ) d t / U sat ) ] 1
P Activation Unit ( t ) = P noise + P λ 2 [ 1 ( 1 1 G CW ( SOA ) ) exp ( t P G ( t ) d t / U sat ) ] 1