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Deep learning with coherent VCSEL neural networks


Deep neural networks (DNNs) are reshaping the field of information processing. With the exponential growth of these DNNs challenging existing computing hardware, optical neural networks (ONNs) have recently emerged to process DNN tasks with high clock rates, parallelism and low-loss data transmission. However, existing challenges for ONNs are high energy consumption due to their low electro-optic conversion efficiency, low compute density due to large device footprints and channel crosstalk, and long latency due to the lack of inline nonlinearity. Here we experimentally demonstrate a spatial-temporal-multiplexed ONN system that simultaneously overcomes all these challenges. We exploit neuron encoding with volume-manufactured micrometre-scale vertical-cavity surface-emitting laser (VCSEL) arrays that exhibit efficient electro-optic conversion (<5 attojoules per symbol with a π-phase-shift voltage of Vπ = 4 mV) and compact footprint (<0.01 mm2 per device). Homodyne photoelectric multiplication allows matrix operations at the quantum-noise limit and detection-based optical nonlinearity with instantaneous response. With three-dimensional neural connectivity, our system can reach an energy efficiency of 7 femtojoules per operation (OP) with a compute density of 6 teraOP mm2 s−1, representing 100-fold and 20-fold improvements, respectively, over state-of-the-art digital processors. Near-term development could improve these metrics by two more orders of magnitude. Our optoelectronic processor opens new avenues to accelerate machine learning tasks from data centres to decentralized devices.

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Fig. 1: VCSEL-ONN architecture.
Fig. 2: Experimental scheme of VCSEL-ONN.
Fig. 3: Characterization of compute accuracy.
Fig. 4: Benchmarking of machine learning inference with VCSEL-ONN.
Fig. 5: Comparison of state-of-the-art neural network accelerators.

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Data availability

All the data that support the findings of this study are included in the main text and Supplementary Information. The data are available from the corresponding authors upon reasonable request.


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This work is supported by the Army Research Office under grant no. W911NF17-1-0527, NTT Research under project no. 6942193 and NTT Netcast award 6945207. I.C. acknowledges support from the National Defense Science and Engineering Graduate Fellowship Program and National Science Foundation (NSF) award DMR-1747426. L.B. is supported by the National Science Foundation EAGER programme (CNS-1946976) and the Natural Sciences and Engineering Research Council of Canada (PGSD3-517053-2018). L.A. acknowledges support from the NSF Graduate Research Fellowship (grant no. 1745302). S.R. acknowledges financial support from the Volkswagen Foundation via the project NeuroQNet 2. We thank S. Bandyopadhyay and C. Brabec of MIT and Y. Cui of TUM for comments on the manuscript. We also thank D.A.B. Miller of Stanford University, N. Harris and D. Bunandar of Lightmatter, and S. Lloyd of MIT for informative discussions.

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Authors and Affiliations



Z.C., R.H. and D.E. conceived the experiments. Z.C. performed the experiment, assisted by A.S., R.D. and I.C. A.S. conducted high-speed measurements on the VCSEL transmitters and developed the integrating electronics. R.D. created the software model for neural network training. I.C. performed electronic packaging on the VCSEL arrays. L.A. assisted with assembling an initial set-up for testing VCSEL samples. A.S. and L.B. assisted with discussions on the experimental data. T.H., N.H., J.A.L. and S.R. designed and fabricated the VCSEL arrays and characterized their performance. R.H. and D.E. provided critical insights regarding the experimental implementation and results analysis. Z.C. wrote the manuscript with contributions from all authors.

Corresponding authors

Correspondence to Zaijun Chen, Ryan Hamerly or Dirk Englund.

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Competing interests

Z.C., D.E. and R.H. have filed a patent related to VCSEL ONNs, under application no. 63/341,601. D.E. serves as scientific advisor to and holds equity in Lightmatter Inc. A.S. is a senior photonic architect at Lightmatter Inc. and holds equity. Other authors declare no competing interests.

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Nature Photonics thanks Xingyuan Xu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Figs. 1–12, Discussion and Tables 1–3.

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Chen, Z., Sludds, A., Davis, R. et al. Deep learning with coherent VCSEL neural networks. Nat. Photon. 17, 723–730 (2023).

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