McCulloch, W. & Pitts, W. A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biophys. 5 , 115–133 (1943)..

McCulloch, W. & Pitts, W. The statistical organization of nervous activity . Biometrics 4 , 91–99 (1948)..

Hebb, D. O. The Organization of Behavior (Wiley, 1949).

McCarthy, J. et al. A proposal for the Dartmouth summer research project on artificial intelligence: August 31, 1955. AI Mag. 27 , 12–14 (2006)..

Rosenblatt, F. The perceptron: a probabilistic model for information storage and organization in the brain. Psychol. Rev. 65 , 386–408 (1958)..

Rumelhart, D. E. et al. Learning representations by back-propagating errors. Nature 323 , 533–536 (1986)..

Le Cun, Y. et al. Handwritten digit recognition with a back-propagation network. In Proc. 2nd International Conference on Neural Information Processing Systems 396–404 (MIT Press, 1989).

Krizhevsky, A. et al. ImageNet classification with deep convolutional neural networks. In Proc. 25th International Conference on Neural Information Processing Systems 1097–1105 (Curran Associates Inc, 2012).

Liu, P. R. et al. Application of artificial intelligence in medicine: an overview. Curr. Med. Sci. 41 , 1105–1115 (2021)..

Zhao, S., Blaabjerg, F. & Wang, H. An overview of artificial intelligence applications for power electronics. IEEE Trans. Power Electron. 36 , 4633–4658 (2021)..

Lawal, A. I. & Kwon, S. Application of artificial intelligence to rock mechanics: an overview. J. Rock. Mech. Geotech. Eng. 13 , 248–266 (2021)..

Assunção, G. et al. An overview of emotion in artificial intelligence. IEEE Trans. Artif. Intell. 3 , 867–886 (2022)..

Hochhegger, B. et al. Artificial intelligence for cardiothoracic imaging: overview of current and emerging applications. Semin. Roentgenol. 58 , 184–195 (2023)..

Misra, J. & Saha, I. Artificial neural networks in hardware: a survey of two decades of progress. Neurocomputing 74 , 239–255 (2010)..

Poon, C. S. & Zhou, K. Neuromorphic silicon neurons and large-scale neural networks: challenges and opportunities. Front. Neurosci. 5 , 108 (2011)..

Silver, D. et al. Mastering the game of Go with deep neural networks and tree search. Nature 529 , 484–489 (2016)..

Esser, S. K. et al. Convolutional networks for fast, energy-efficient neuromorphic computing. Proc. Natl Acad. Sci. USA 113 , 11441–11446 (2016)..

Shafiee, A. et al. ISAAC: a convolutional neural network accelerator with insitu analog arithmetic in crossbars. In Proc. 2016 ACM/IEEE 43rd Annual International Symposium on Computer Architecture (ISCA) 14–26 (IEEE, 2016).

Graves, A. et al. Hybrid computing using a neural network with dynamic external memory. Nature 538 , 471–476 (2016)..

Chen, Y. H. et al. Eyeriss: an energy-efficient reconfigurable accelerator for deep convolutional neural networks. IEEE J. Solid-State Circuits 52 , 127–138 (2017)..

Liu, Y. Q. et al. Effective scaling of blockchain beyond consensus innovations and Moore's law: challenges and opportunities. IEEE Syst. J. 16 , 1424–1435 (2022)..

Lugt, A. V. Signal detection by complex spatial filtering. IEEE Trans. Inf. Theory 10 , 139–145 (1964)..

Goodman, J. W., Dias, A. R. & Woody, L. M. Fully parallel, high-speed incoherent optical method for performing discrete Fourier transforms. Opt. Lett. 2 , 1–3 (1978)..

Farhat, N. H. et al. Optical implementation of the Hopfield model. Appl. Opt. 24 , 1469–1475 (1985)..

Fisher, A. D. et al. Optical implementations of associative networks with versatile adaptive learning capabilities. Appl. Opt. 26 , 5039–5054 (1987)..

Caulfield, H. J., Kinser, J. & Rogers, S. K. Optical neural networks. Proc. IEEE 77 , 1573–1583 (1989)..

Psaltis, D. et al. Holography in artificial neural networks. Nature 343 , 325–330 (1990)..

Reck, M. et al. Experimental realization of any discrete unitary operator. Phys. Rev. Lett. 73 , 58–61 (1994)..

Clements, W. R. et al. Optimal design for universal multiport interferometers. Optica 3 , 1460–1465 (2016)..

Tait, A. N. et al. Microring weight banks. IEEE J. Sel. Top. Quantum Electron. 22 , 312–325 (2016)..

Liu, J. et al. Research progress in optical neural networks: theory, applications and developments. PhotoniX 2 , 5 (2021)..

Zhou, H. L. et al. Photonic matrix multiplication lights up photonic accelerator and beyond. Light Sci. Appl. 11 , 30 (2022)..

Huang, C. R. et al. Prospects and applications of photonic neural networks. Adv. Phys. X 7 , 1981155 (2022)..

Sheng, H. Y. Review of integrated diffractive deep neural networks. Highlights Sci. Eng. Technol. 24 , 264–278 (2022)..

Bai, Y. P. et al. Photonic multiplexing techniques for neuromorphic computing. Nanophotonics 12 , 795–817 (2023)..

Chen, Y. S. 4f-type optical system for matrix multiplication. Opt. Eng. 32 , 77–79 (1993)..

Chang, J. L. et al. Hybrid optical-electronic convolutional neural networks with optimized diffractive optics for image classification. Sci. Rep. 8 , 12324 (2018)..

Yan, T. et al. Fourier-space diffractive deep neural network. Phys. Rev. Lett. 123 , 023901 (2019)..

Zuo, Y. et al. All-optical neural network with nonlinear activation functions. Optica 6 , 1132–1137 (2019)..

Miscuglio, M. et al. Massively parallel amplitude-only Fourier neural network. Optica 7 , 1812–1819 (2020)..

Momeni, A. et al. Backpropagation-free training of deep physical neural networks. Science 382 , 1297–1303 (2023)..

Lin, X. et al. All-optical machine learning using diffractive deep neural networks. Science 361 , 1004–1008 (2018)..

Luo, Y. et al. Design of task-specific optical systems using broadband diffractive neural networks. Light Sci. Appl. 8 , 112 (2019)..

Qian, C. et al. Performing optical logic operations by a diffractive neural network. Light Sci. Appl. 9 , 59 (2020)..

Zhou, T. K. et al. In situ optical backpropagation training of diffractive optical neural networks. Photonics Res. 8 , 940–953 (2020)..

Wu, Z. C. et al. Neuromorphic metasurface. Photonics Res. 8 , 46–50 (2020)..

Zhou, T. K. et al. Large-scale neuromorphic optoelectronic computing with a reconfigurable diffractive processing unit. Nat. Photonics 15 , 367–373 (2021)..

Fang, T. et al. Classification accuracy improvement of the optical diffractive deep neural network by employing a knowledge distillation and stochastic gradient descent β-Lasso joint training framework. Opt. Express 29 , 44264–44274 (2021)..

Wang, P. P. et al. Orbital angular momentum mode logical operation using op tical diffractive neural network. Photonics Res. 9 , 2116–2124 (2021)..

Li, Y. J. et al. Real-time multi-task diffractive deep neural networks via hardware-software co-design. Sci. Rep. 11 , 11013 (2021)..

Sun, Y. C. et al. Modeling and simulation of all-optical diffractive neural network based on nonlinear optical materials. Opt. Lett. 47 , 126–129 (2022)..

Shi, W. X. et al. LOEN: Lensless opto-electronic neural network empowered machine vision. Light Sci. Appl. 11 , 121 (2022)..

Liu, C. et al. A programmable diffractive deep neural network based on a digital-coding metasurface array. Nat. Electron. 5 , 113–122 (2022)..

Li, J. X. et al. Polarization multiplexed diffractive computing: all-optical implementation of a group of linear transformations through a polarization-encoded diffractive network. Light Sci. Appl. 11 , 153 (2022)..

Rahman, M. S. S. et al. Universal linear intensity transformations using spatially incoherent diffractive processors. Light Sci. Appl. 12 , 195 (2023)..

Li, J. X. et al. Rapid sensing of hidden objects and defects using a single-pixel diffractive terahertz sensor. Nat. Commun. 14 , 6791 (2023)..

Li, J. X. et al. Massively parallel universal linear transformations using a wavelength-multiplexed diffractive optical network. Adv. Photonics 5 , 016003 (2023)..

Zheng, Z. Y. et al. Dual adaptive training of photonic neural networks. Nat. Mach. Intell. 5 , 1119–1129 (2023)..

Duan, Z. Y., Chen, H. & Lin, X. Optical multi-task learning using multi-wavelength diffractive deep neural networks. Nanophotonics 12 , 893–903 (2023)..

Zhang, H. et al. An optical neural chip for implementing complex-valued neural network. Nat. Commun. 12 , 457 (2021)..

Cui, T. J., Liu, S. & Zhang, L. Information metamaterials and metasurfaces. J. Mater. Chem. C. 5 , 3644–3668 (2017)..

Duport, F. et al. Al l-optical reservoir computing. Opt. Express 20 , 22783–22795 (2012)..

Paquot, Y. et al. Optoelectronic reservoir computing. Sci. Rep. 2 , 287 (2012)..

Bueno, J. et al. Reinforcement learning in a large-scale photonic recurrentneural network. Optica 5 , 756–760 (2018)..

Cheng, T. Y. et al. Optical neural networks based on optical fiber-communication system. Neurocomputing 364 , 239–244 (2019)..

Huang, Y. Y. et al. Programmable matrix operation with reconfigurable time-wavelength plane manipulation and dispersed time delay. Opt. Express 27 , 20456–20467 (2019)..

Zang, Y. B. et al. Electro-optical neural networks based on time-stretch method. IEEE J. Sel. Top. Quantum Electron. 26 , 7701410 (2020)..

Xu, X. Y. et al. 11 TOPS photonic convolutional accelerator for optical neural networks. Nature 589 , 44–51 (2021)..

Xiang, S. Y. et al. Computing primitive of fully VCSEL-based all-optical spiking neural network for supervised learning and pattern classification. IEEE Trans. Neural Netw. Learn. Syst. 32 , 2494–2505 (2021)..

Zhang, L. H. et al. Optical machine learning using time-lens deep neural networks. Photonics 8 , 78 (2021)..

Stelzer, F. et al. Deep neural networks using a single neuron: folded-in-time architecture using feedback-modulated delay loops. Nat. Commun. 12 , 5164 (2021)..

Gu, B. L. et al. Enhanced prediction performance of a time-delay reservoir computing system based on a VCSEL by dual-training method. Opt. Express 30 , 30779–30790 (2022)..

Xiang, S. Y. et al. Hardware-algorithm collaborative computing with photonic spiking neuron chip based on an integrated Fabry–Perot laser with a saturable absorber. Optica 10 , 162–171 (2023)..

Xiang, S. Y. et al. Photonic integrated neuro-synaptic core for convolutional spiking neural network. Opto Electron. Adv. 6 , 230140 (2023)..

Shi, Y. C. et al. Phot onic integrated spiking neuron chip based on a self-pulsating DFB laser with a saturable absorber. Photonics Res. 11 , 1382–1389 (2023)..

Guo, X. X. et al. Photonic implementation of the input and reservoir layers for a reservoir computing system based on a single VCSEL with two Mach-Zehnder modulators. Opt. Express 32 , 17452–17463 (2024)..

Nahmias, M. A. et al. A leaky integrate-and-fire laser neuron for ultrafast cognitive computing. IEEE J. Sel. Top. Quantum Electron. 19 , 1800212 (2013)..

Chakraborty, I. et al. Toward fast neural computing using all-photonic phase change spiking neurons. Sci. Rep. 8 , 12980 (2018)..

Peng, H. T. et al. Temporal information processing with an integrated laser neuron. IEEE J. Sel. Top. Quantum Electron. 26 , 5100209 (2020)..

Xiang, J. L. et al. All-optical silicon microring spiking neuron. Photonics Res. 10 , 939–946 (2022)..

Jha, A. et al. Photonic spiking neural networks and graphene-on-silicon spiking neurons. J. Lightwave Technol. 40 , 2901–2914 (2022)..

Ribeiro, A. et al. Demonstration of a 4 × 4-port universal linear circuit. Optica 3 , 1348–1357 (2016)..

Shen, Y. C. et al. Deep learning with coherent nanophotonic circuits. Nat. Photonics 11 , 441–446 (2017)..

Hughes, T. W. et al. Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5 , 864–871 (2018)..

Harris, N. C. et al. Linear programmable nanophotonic processors. Optica 5 , 1623–1631 (2018)..

Ong, J. R. et al. Photonic convolutional neural networks using integrated diffractive optics. IEEE J. Sel. Top. Quantum Electron. 26 , 7702108 (2020)..

Shokraneh, F., Geoffroy-Gagnon, S. & Liboiron-Ladouceur, O. The diamond mesh, a phase-error-and loss-tolerant field-programmable MZI-based optical processor for optical neural networks. Opt. Express 28 , 23495–23508 (2020)..

Bogaerts, W. et al. Programmable photonic circuits. Nature 586 , 207–216 (2020)..

Bandyopadhyay, S., Hamerly, R. & Englund, D. Hardware error correction for programmable photonics. Optica 8 , 1247–1255 (2021)..

Zhu, H. H. et al. Space-efficient optical computing with an integrated chip diffractive neural network. Nat. Commun. 13 , 1044 (2022)..

Wang, X. Y. et al.Chip-based high-dimensional optical neural network. Nano-Micro Lett. 14 , 221 (2022)..

Pai, S. et al. Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380 , 398–404 (2023)..

Tait, A. N. et al. Neuromorphic photonic networks using silicon photonic weight banks. Sci. Rep. 7 , 7430 (2017)..

Tait, A. N. et al. Feedback control for microring weight banks. Opt. Express 26 , 26422–26443 (2018)..

Tait, A. N. et al. Silicon photonic modulator neuron. Phys. Rev. Appl. 11 , 064043 (2019)..

Feldmann, J. et al. All-optical spiking neurosynaptic networks with self-learning capabilities. Nature 569 , 208–214 (2019)..

Ohno, S. et al. Si microring resonator crossbar arrays for deep learning accelerator. Jpn. J. Appl. Phys. 59 , SGGE04 (2020)..

Feldmann, J. et al. Parallel convolutional processing using an integrated photonic tensor core. Nature 589 , 52–58 (2021)..

Huang, C. R. et al. A silicon photonic–electronic neural network for fibre nonlinearity compensation. Nat. Electron. 4 , 837–844 (2021)..

Ohno, S. et al. Si microring resonator crossbar array for on-chip inference and training of the optical neural network. ACS Photonics 9 , 2614–2622 (2022)..

Xu, S. F. et al. High-order tensor flow processing using integrated photonic circuits. Nat. Commun. 13 , 7970 (2022)..

Zhang, W. P. et al. Silicon microring synapses enable photonic deep learning beyond 9-bit precision. Optica 9 , 579–584 (2022)..

Bai, B. W. et al. Microcomb-based integrated photonic processing unit. Nat. Commun. 14 , 66 (2023)..

Yin, R. Y. et al. Integrated WDM-compatible optical mode division multiplexing neural network accelerator. Optica 10 , 1709–1718 (2023)..

Cheng, J. W. et al. Human emotion recognition with a microcomb-enabled integrated optical neural network. Nanophotonics 12 , 3883–3894 (2023)..

Yu, N. F. et al. Light propagation with phase discontinuities: generalized laws of reflection and refraction. Science 334 , 333–337 (2011)..

Zarei, S., Marzban, M. R. & Khavasi, A. Integrated photonic neural network based on silicon metalines. Opt. Express 28 , 36668–36684 (2020)..

Fu, T. Z. et al. On-chip photonic diffractive optical neural network based on a spatial domain electromagnetic propagation model. Opt. Express 29 , 31924–31940 (2021)..

Goi, E. et al. Nanoprinted high-neuron-density optical linear perceptrons performing near-infrared inference on a CMOS chip. Light Sci. Appl. 10 , 40 (2021)..

Wang, Z. et al. Integrated photonic metasystem for image classifications at telecommunication wavelength. Nat. Commun. 13 , 2131 (2022)..

Yan, T. et al. All-optical graph representation learning using integrated diffractive photonic computing units. Sci. Adv. 8 , eabn7630 (2022)..

Luo, X. H. et al. Metasurface-enabled on-chip multiplexed diffractive neural networks in the visible. Light Sci. Appl. 11 , 158 (2022)..

Zarei, S. & Khavasi, A. Realization of optical logic gates using on-chip diffractive optical neural networks. Sci. Rep. 12 , 15747 (2022)..

Huang, Y. Y. et al. Sophisticated deep learning with on-chip optical diffractive tensor processing. Photonics Res. 11 , 1125–1138 (2023)..

Fu, T. Z. et al. Photonic machine learning with on-chip diffractive optics. Nat. Commun. 14 , 70 (2023)..

Poordashtban, O., Marzabn, M. R. & Khavasi, A. Integrated photonic convolutional neural network based on silicon metalines. IEEE Access 11 , 61728–61737 (2023)..

Fu, T. Z. et al. Integrated diffractive optical neural network with space-time interleaving. Chin. Opt. Lett. 21 , 091301 (2023)..

Liu, W. C. et al. C-DONN: compact diffractive optical neural network with deep learning regression. Opt. Express 31 , 22127–22143 (2023)..

Fu, T. Z. et al. Miniature on-chip diffractive optical neural network design. In Proc. Conference on Lasers and Electro-Optics (CLEO) 1–2 (IEEE, 2023).

Sun, R. et al. Multimode diffractive optical neural network. Adv. Photonics Nexus 3 , 026007 (2024)..

Zhang, J. J. et al. Ultrashort and efficient adiabatic waveguide taper based on thin flat focusing lenses. Opt. Express 25 , 19894–19903 (2017)..

Wang, Z. et al. On-chip wavefront shaping with dielectric metasurface. Nat. Commun. 10 , 3547 (2019)..

Vandoorne, K. et al. Experimental demonstration of reservoir computing on a silicon photonics chip. Nat. Commun. 5 , 3541 (2014)..

Perez, D. et al. Silicon photonics rectangular universal interferometer. Laser Photonics Rev. 11 , 1700219 (2017)..

Khoram, E. et al. Nanophotonic media for artificial neural inference. Photonics Res. 7 , 823–827 (2019)..

Hughes, T. W. et al. Wave physics as an analog recurrent neural network. Sci. Adv. 5 , eaay6946 (2019)..

Zhang, T. et al. Efficient training and design of photonic neural network through neuroevolution. Opt. Express 27 , 37150–37163 (2019)..

Moughames, J. et al. Three-dimensional waveguide interconnects for scalable integration of photon ic neural networks. Optica 7 , 640–646 (2020)..

Qu, Y. R. et al. Inverse design of an integrated-nanophotonics optical neural network. Sci. Bull. 65 , 1177–1183 (2020)..

Zhao, X. M. et al. On-chip reconfigurable optical neural networks. at URL: https://www.researchsquare.com/article/rs-155560/v1 https://www.researchsquare.com/article/rs-155560/v1 (2021).

Wu, C. M. et al. Programmable phase-change metasurfaces on waveguides for multimode photonic convolutional neural network. Nat. Commun. 12 , 96 (2021)..

Sunada, S. & Uchida, A. Photonic neural field on a silicon chip: large-scale, high-speed neuro-inspired computing and sensing. Optica 8 , 1388–1396 (2021)..

Cheng, J. W. et al. Photonic emulator for inverse design. ACS Photonics 10 , 2173–2181 (2023)..

Ashtiani, F., Geers, A. J. & Aflatouni, F. An on-chip photonic deep neural network for image classification. Nature 606 , 501–506 (2022)..

Liao, K. et al. Matrix eigenvalue solver based on reconfigurable photonic neural network. Nanophotonics 11 , 4089–4099 (2022)..

Ling, Q. et al. On-chip optical matrix-vector multiplier based on mode division multiplexing. Chip 2 , 100061 (2023)..

Wu, T. W. et al. Lithography-free reconfigurable integrated photonic processor. Nat. Photonics 17 , 710–716 (2023)..

Dong, B. W. et al. Higher-dimensional processing using a photonic tensor core with continuous-time data. Nat. Photonics 17 , 1080–1088 (2023)..

Meng, X. Y. et al. Compact optical convolution processing unit based on multimode interference. Nat. Commun. 14 , 3000 (2023)..

Giamougiannis, G. et al. Neuromorphic silicon photonics with 50 GHz tiled matrix multiplication for deep-learning applications. Adv. Photonics 5 , 016004 (2023)..

Zheng, D. Z. et al. Experimental demonstration of coherent pho tonic neural computing based on a Fabry-Perot laser with a saturable absorber. Photonics Res. 11 , 65–71 (2023)..

Rivenson, Y. et al. Phase recovery and holographic image reconstruction using deep learning in neural networks. Light Sci. Appl. 7 , 17141 (2018)..

Shi, L. et al. Towards real-time photorealistic 3D holography with deep neural networks. Nature 591 , 234–239 (2021)..

Zheng, H. Y. et al. Multichannel meta-imagers for accelerating machine vision. Nat. Nanotechnol. 19 , 471–478 (2024)..

Zhong, C. Y. et al. Graphene/silicon heterojunction for reconfigurable phase-relevant activation function in coherent optical neural networks. Nat. Commun. 14 , 6939 (2023)..

Shi, Y. et al. Nonlinear germanium-silicon photodiode for activation and monitoring in photonic neuromorphic networks. Nat. Commun. 13 , 6048 (2022)..

Cheng, Z. G. et al. On-chip photonic synapse. Sci. Adv. 3 , e1700160 (2017)..

Wright, C. D., Bhaskaran, H. & Pernice, W. H. P. Integrated phase-change photonic devices and systems. MRS Bull. 44 , 721–727 (2019)..

Nisar, M. S. et al. On-chip integrated photonic devices based on phase change materials. Photonics 8 , 205 (2021)..

Delaney, M. et al. Nonvolatile programmable silicon photonics using an ultralow-loss Sb 2 Se 3 phase change material. Sci. Adv. 7 , eabg3500 (2021)..

HUAWEI. Ascend 910 atURL: https://www.actfornet.com/products/intelligent-computing/atlas/huawei-ai/ai-chips/Ascend_910/features https://www.actfornet.com/products/intelligent-computing/atlas/huawei-ai/ai-chips/Ascend_910/features (2024).

NVIDIA. T4 tensor core datasheet at URL: https://www.nvidia.com/en-us/data-center/tesla-t4/ https://www.nvidia.com/en-us/data-center/tesla-t4/ (2024).

Xu, Z. H. et al. Large-scale photonic chiplet Taichi empowers 160-TOPS/W artificial general intelligence. Science 384 , 202–209 (2024)..

Ferdous, W. et al. New advancements, challenges and opportunities of multi-storey modular buildings—a state-of-the-art review. Eng. Struct. 183 , 883–893 (2019)..

Cheng, J. W., Zhou, H. L. & Dong, J. J. Photonic matrix computing: from fundamentals to applications. Nanomaterials 11 , 1683 (2021)..

Chen, Y. T. et al. All-analog photoelectronic chip for high-speed vision tasks. Nature 623 , 48–57 (2023)..

Sludds, A. et al. Delocalized photonic deep learning on the internet's edge. Science 378 , 270–276 (2022)..

Lightmatter. Envise and Passage at URL: https://lightmatter.co https://lightmatter.co (2023).

Lightelligence. Pace at URL: https://www.lightelligence.ai/index.php https://www.lightelligence.ai/index.php (2023).

Jouppi, N. P. et al. In-datacenter performance analysis of a tensor processing unit. In Proc. ACM/IEEE 44th Annual International Symposium on Computer Architecture (ISCA) 1–12 (IEEE, 2017).

Harris, S. E. Electromagnetically induced transparency. Phys. Today 50 , 36–42 (1997)..

Fleischhaue, M., Imamoglu, A. & Marangos, J. P. Electromagnetically induced transparency: optics in coherent media. Rev. Mod. Phys. 77 , 633–673 (2006)..