A high performance fully tunable laser-based neural network
Anas Skalli1*, Mirko Goldmann2, Xavier Porte3, Nasibeh Haghighi4, Stephan Reitzenstein4, James A. Lott4
and Daniel Brunner1
1.
2.

Institut FEMTO-ST, Université Bourgogne Franche-Comté, CNRS UMR6174, 15B Avenue des Montboucons Besançon, FranceInstituto de Física Interdisciplinar y Sistemas Complejos, IFISC (UIB-CSIC), Campus UIB, E-07122 Palma de Mallorca, Spain
3. Institute of Photonics, Department of Physics, University of Strathclyde, 99 George str., Glasgow G1 1RD, UK4. Institut für Festkörperphysik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany*anas.skalli@femto-st.fr

Summary. We experimentally demonstrate a high-performance, stable, autonomous, fully tunable,and scalable neural network of 350+ discrete nodes based on a semiconductor laser. Using
exclusively off the shelf components, our optical neural network achieves high performance and ahigh classification bandwidth of 15KHz for the MNIST dataset with potential scalability towards
the MHz range.

Artificial Neural Networks (ANNs) have become a ubiquitous technology; indeed, their flexibility
allows them to excel in a wide range of tasks, ranging from medical diagnosis to language models. Unlike
classical algorithms, these networks process information in parallel. Photonics, in particular, shows great
promise as a platform for implementing ANNs in terms of scalability, speed, energy efficiency and parallel
information processing [1]. In [2], we physically implemented the first fully autonomous PNN (photonicneural network), using spatially multiplexed modes of an injection locked large area vertical cavity surface
emitting laser (LA-VCSEL). All components of our PNN, including learning are fully realized in hardware
using off-the-shelf, commercially available, low energy consumption components, while still achieving>98% accuracy in 6-bit header recognition tasks and promising initial results for the MNIST hand written
digit recognition dataset, where we achieve 90% accuracy on average. Crucially, our system performs
classification at a high bandwidth of 15 kHz, which is not limited by the LA-VCSEL (GHz bandwidth) andcould potentially increase towards the MHz range.
The PNN presented here was first implemented in [2,3]. Whereas previously it followed the reservoir
computing (RC) concept, where input and internal weights are fixed and only the output weights are trained,
we now present an improved version of the setup where all connections in the PNN can be trained yielding
therefore a highly tunable network. The experimental scheme is shown in Fig. 1. Input images u displayedon a digital micromirror device (DMDa) are passed through a phase mask displayed on a spatial light
modulator (SLM) which encodes the input weights Win. The phase modulated input is injected onto theLA-VCSEL through a multimode fiber (MMF) which passively implements a random linear mixing Wrand.
The VCSEL then transforms the injected information non-linearly yielding the perturbed mode profile x.
The final part of the PNN is its output layer. The VCSEL’s surface is imaged onto DMDb, whose pixels
can flip between two positions, for one of which it reflects light onto the photodetector (DET), giving us
Boolean output weights Wout. 350+ nodes are implemented fully in parallel; the output of the PNN y is theoptical power detected at DET. Wout and Win are trained via iterative optimization based on evolutionary
search algorithms or gradient descent using gradient estimation methods from reinforcement learning.
Higher output weight resolutions can be achieved with higher imaging magnifications onto DMDb.
Additionally negative output weights can be achieved via recording the output of the PNN twice andimplementing an electronic subtraction.
Fig. 2.(a) shows preliminary classification performance for the MNIST task using Boolean weights(BOOL), and trinary weights (3val -1,0, +1) reaching an average performance of 90% for trinary weights
which have a significant positive impact on performance. In addition, we conducted a long-term stability
analysis in Fig. 2.(b), over a period of 10 hours, showing little to no degradation in performance or drift.
Moreover, the average cross correlation between different outputs over the 10 hours was 98%. We alsostudied the impact of different learning strategies and physical parameters of our PNN (injection power andwavelength, bias current, etc…) on its performance for classification tasks as well as how they impactedother dynamical properties such as consistency and dimensionality, showing a promising consistency of99%.
Input laser

DMDaSLMMMF𝐮𝑾in𝑾rand

LA-VCSEL𝒙Input

Reservoir

DMDb

DET𝑾outyOutput

Figure 1. Working principle of our experimental photonic neural networka)b)

Figure 2. (a) One-vs-all test accuracy for the hand written MNIST dataset using Boolean (BOOL) andtrinary (-1,0, +1) output weights. (b) Long term stability measurement showing minimal drift inperformance over 10 hours showcasing the stability of our PNN.
In conclusion, we have demonstrated a fully parallel PNN consisting of 350+ neurons realized
entirely in hardware. Our PNN shows long term stability and excellent performance in header recognition
tasks as well as XOR and digital to analog conversion, and additionally, promising performance in theMNIST dataset while achieving classification at a bandwidth of 15kHz. Our approach is highly relevant,fully parallel and scalable both in terms network size and depth as we have a clear avenue for using VCSELs
in a deep PNN configuration. Lastly the inference bandwidth is also highly scalable due to a fast VCSEL
response time without any significant increase in power consumption.

References[1] Skalli, Anas, Joshua Robertson, Dafydd Owen-Newns, Matej Hejda, Xavier Porte, Stephan Reitzenstein,
Antonio Hurtado, and D. Brunner. "Photonic neuromorphic computing using vertical cavity semiconductor
lasers." Optical Materials Express 12 (6), 2395-2414.
[2] Porte, X., Skalli, A., Haghighi, N. Reitzenstein, S, Lott, J, Brunner D. A complete, parallel, and autonomous
photonic neural network in a semiconductor multimode laser. J. Phys. Photonics 3, 024017 (2021).
[3] Skalli, A, Porte, X., Haghighi, N. Reitzenstein, S, Lott, J, Brunner D. "Computational metrics and parameters of
an injection-locked large area semiconductor laser for neural network computing." Optical Materials Express 12 (7),2793-2804 (2022).