Large scalable electro-optical spiking neural network
Ria Talukder1, Anas Skalli1, Daniel Brunner1
1

FEMTO-ST/Optics Dept., UMR CNRS 6174, Univ. Bourgogne Franche-Comte, 15B Avenue des Mountboucons, 25030, Besancon Cedex FranceSummary. Photonic neural networks are currently a highly sought after area of research.
Comprehensive studies and experiments have laid a strong foundation for future high-performancecomplex computing. In artificial neural networks, neurons are simple, nonlinear maps. On thecontrary, information transmission and computation in biological neurons occur through spikes,
where spike time and/or rate presumably play a significant role. We developed the first large-scale
spiking photonic neural network that comprises of more than 30,000 excitable neurons, which serves
as an excellent proof of concept experiment for novel bio-inspired learning concepts.

Photonic hardware integration of neural networks can benefit from the inherent properties ofparallelism, high-speed data processing and potentially low energy consumption. Considering this, we
designed a photonic reservoir computer (RC) [1] based on photonic recurrent spiking neural networks(SNN) [2], i.e. a photonic liquid state machine (see Fig 1 (a)). Fig 1(a) shows that, the optical field ∣ 𝐸𝑖0 ∣2
is homogenized by a beam homogenizer and after getting transmitted through the polarizing beam splitter(PBS) and a half waveplate, a microscope objective 𝑀𝑂1 focuses it to illuminate the spatial light modulator(SLM) . Our neural network’s state is encoded in the pixels of the SLM, which makes the SLM function
as the substrate of our neurons. The half waveplate positioned after 𝑀𝑂1 is oriented in a way that enables
the SLM to operate in the amplitude modulation mode. After being reflected from the SLM, the opticalfield is transmitted through the polarizing beam splitter (PBS) where it acquires nonlinearity and is
subsequently modulated as follows:
𝐸𝑖 = 𝐸𝑖0 𝑐𝑜𝑠 (2𝜋𝑥𝑖𝑆𝐿𝑀 + 𝛷)
𝜅 𝑆𝐿𝑀

(1)

where, 𝑥𝑖𝑆𝐿𝑀 is the gray scale value of the SLM pixel i, 𝛷 is gray scale offset and a device constant and𝜅 𝑆𝐿𝑀 is the conversion factor between the polarization angle and the gray scale values of the SLM pixels.
A diffractive optical element (DOE) is introduced in between the PBS and the camera. The spacing between
the diffractive orders corresponds to the spacing between the SLM pixels. The beam reflected from thePBS, passes through the DOE, establishing recurrent coupling between the photonic neurons. Finally, thecamera positioned at the focal plane of the microscope objective 𝑀𝑂2 , record the neuron response. Thesignal (i.e. optical intensity) recorded by the camera can be represented as :𝑁2

𝐷𝑂𝐸
𝐼𝑖𝐶𝐴𝑀 = 𝛽(|∑ 𝑊𝑖,𝑗𝐸𝑗 | )

(2)

𝑗=1

where, 𝑊 𝐷𝑂𝐸 is the DOE created coupling matrix. Therefore, the recurrent loop is closed when the camera
images the SLM pixels (i.e. neurons), since the SLM is driven by the recorded images as electronicfeedback. So, the Ikeda map which can be used to define the state of our recurrent neural network (RNN)
can be represented as:𝑥( 𝑡 + 1) = − 𝛿 ∗ 𝑦(𝑡) + 𝑠𝑖𝑛2 (𝜋 (𝛼 ∗ 𝑥(𝑡) + 𝛾 ∗ 𝑢(𝑡 + 1)) + 𝜃)

(3)

where, 𝑥( 𝑡 + 1) is the SLM state sent to the SLM via MATLAB, 𝛽 is the feedback strength, 𝛾 is the signal
strength of the input signal sequence 𝑢(𝑡 + 1) (this contains elements normalized between 0 and 1. We go
beyond and create excitability of our electro-optical neurons by including a high-pass filter (given by Eq.
(4)) in the electronic feedback loop and experimentally demonstrate the neuron’s all-or-nothing spiking
response to input stimuli.

𝑦(𝑡 + 1) = 0.995 ∗ 𝑦(𝑡) + 𝑥(𝑡 + 1).

(4)

When at rest, the system resides in its lower stable fixed point, labelled A in Fig. 1(b). External input thenpushes the system across unstable fixed point B, resulting in an excursion to the upper stable fixed point C.
There, slow forcing governed by the high-pass dynamics of Eq. (4) projects it back to the lower stable fixedpoint A. This enabled us to demonstrate experimentally all-or-nothing spiking response (see Fig. 1(c)) to
the input stimuli. Fig. 1(d) shows the average network response amplitude with increasing injection strength(Gamma). Fig. 1(e) shows the spatio-temporal response of our network when two MNIST digits are given
as input to our system.
(a)(b)

CBA(d)(c)•(e)Fig. 1 Spiking photonic neural network. (a) Schematic diagram of the experimental setup.
(b) Non-linearity curve of the SLM. (c) Shows a characteristic response of one of our 36.000
photonic neurons. (d) Average network response amplitude. (e) Spatio-temporal network
response with two MNIST digits as input. This shows that the neurons respond differently
depending on the average value of the 784 pixels of each digit.

To conclude, our electro-optical system uses more than 30,000 excitable neurons [3-4], which is the first
proof-of-concept system that allows to implement learning in large scale photonic SNNs. Currently, we aretraining our system on the MNIST datasets for handwritten digit recognition and explore different learning
concepts.

References[1] J. Bueno, S. Maktoobi, L. Froehly, I. Fischer, M. Jacquot, L. Larger, and D. Brunner, “Reinforcement Learning
in a large scale photonic Recurrent Neural Network,” Optica, 5(6), 756-760 (2018).
[2] V. A. Pammi, K. Alfaro-Bittner, M. G. Clerc and S. Barbay, "Photonic Computing With Single and Coupled
Spiking Micropillar Lasers," IEEE Journal of Selected Topics in Quantum Electronics, 26(1), 1-7 (2020).
[3] M. Rafayelyan, J. Dong, Y. Tan, F. Krzakala, and S. Gigan, “Large-Scale Optical Reservoir Computing for
Spatiotemporal Chaotic Systems Prediction”, Phys. Rev. X 10, 041037 (2020).
[4] S. Maktoobi et al., "Diffractive Coupling For Photonic Networks: How Big Can We Go?," IEEE Journal of
Selected Topics in Quantum Electronics, 26(1), 1-8 (2020).