A spiking photonic neural network of 40.000 neurons, trained with rank-order coding for leveraging sparsity

TL;DR

The paper tackles the challenge of scalable, energy-efficient neuromorphic computing by building a 40,000-neuron photonic spiking neural network driven by a slow–fast Ikeda-map–based excitability. It combines latency encoding and rank-order sparsity with a hardware-friendly SPSA-trained readout to perform MNIST digit recognition, achieving up to 83.5% accuracy with only 22% of neurons active and maintaining meaningful performance at very high sparsity. The approach leverages off-the-shelf LCOS-SLM and CMOS camera components, enabling large-scale, low-latency photonic processing, and demonstrates a novel integration of photonic nonlinearity, excitability, and sparse computation. This work provides a practical pathway toward large-scale, energy-efficient photonic neuromorphic systems and lays groundwork for future hardware-accelerated spiking networks.

Abstract

Spiking neural networks are neuromorphic systems that emulate certain aspects of biological neurons, offering potential advantages in energy efficiency and speed by for example leveraging sparsity. While CMOS-based electronic SNN hardware has shown promise, scalability and parallelism challenges remain. Photonics provides a promising platform for SNNs due to the speed of excitable photonic devices standing in as neurons and the parallelism and low-latency of optical signal conduction. Here, we present a photonic SNN comprising 40,000 neurons using off-the-shelf components, including a spatial light modulator and a CMOS camera, enabling scalable and cost-effective implementations for photonic SNN proof of concept studies. The system is governed by a modified Ikeda map, were adding additional inhibitory feedback forcing introduces excitability akin to biological dynamics. Using latency encoding and sparsity, the network achieves 83.5% accuracy on MNIST using 22% of neurons, and 77.5% with 8.5% neuron utilization. Training is performed via liquid state machine concepts combined with the hardware-compatible SPSA algorithm, marking its first use in photonic neural networks. This demonstration integrates photonic nonlinearity, excitability, and sparse computation, paving the way for efficient large-scale photonic neuromorphic systems.

Figures (6)

• Figure 1: (a) Schematic of the optical setup. The spatial light modulator (SLM) is illuminated by a single-mode fiber coupled superluminescent diode (SLED) that collimated by $\textrm{L}_1$, polarization filters by a polarizing beam splitter (PBS). Lens $\textrm{L}_{2}$ and microscope objective $\textrm{MO}_1$ image the SLED's colimated beam, illuminating $\sim40000$ SLM pixels. $\textrm{L}_{3}$ and $\textrm{MO}_{2}$ image the SLM on to a camera (CAM), and a diffractive optical element introduced optical coupling between the pixels. (b) Excitable dynamics via the high-pass filtered Ikeda map. We apply below excitation strength stimulus via input $u(5:55)=0.5$ (red shaded area) and above excitation strength stimulus $u(150:155)=1$ (green shaded area). The neuron's state variable $s(t)$ exhibits an excitable dynamical response only for the second input. Slow dynamics $y(t)$ create strong negative forcing only in the second case. (c) Concept of excitability with slow, negative-feedback forcing an Ikeda map. At rest, the system resides close to stable fixed-point A. If an external perturbation pushes the state past the unstable fixed-point B, the system is attracted to the upper stable fixed-point C, trajectory illustrated by green arrow. There, the slow-feedback term builds up until it projects the system back to stable fixed point A, trajectory illustrated by red arrow. Parameters were $\gamma=0.3$, $\beta=0.45$, $\delta=0.1$, $\Theta=-0.1\pi$, $\eta=0.995$.
• Figure 2: Response to a short perturbation, with $u(500:end)=1$. (a) Excitability of $x(t+1)$ in Eq. (\ref{['eq:SlowIkeda']}) as a function of injection strength $\gamma$. An excitable response is attained for $\gamma>0.25$. (b) Experimental data agrees exceptionally well to the numerical model. (c) Maximum amplitude of a response versus $\gamma$ displays the almost ideal all-or-nothing response of the slow-negative feedback forced Ikeda map.
• Figure 3: Spike rate and refractory period. (a) Continuous stimulation with $u(500:\textrm{end})=1$ results in a continuous spike train as soon as the excitation threshold is crossed. (b) The spike rate as a function of injection strength $\gamma$ exhibits classical type 1 excitability characteristics. (c) Numerical simulation. After an initial excitation with $u(500:505)=1$ we subject the neuron to a second spike at time $u(506+\tau : 510+\tau)=1$ at $\gamma=0.3$. For $\tau<12$ the neuron cannot be re-excited, demonstrating the refractory period this modified Ikeda map. All data are from the experiment.
• Figure 4: between applying an above threshold perturbation and a neuron's response. (a) Typical spike latency of a biological neuron, data from recio2014. (b) Our experimental results of spike latency $\delta$ exhibits very similar behavior.
• Figure 5: (a) Spatio-temporal spike pattern responses of our photonic SNN's to MNIST examples of digits 2, 8 and 1. Histogram of spike latencies $\Delta$ for (b) $\Delta^{\textrm{l}}=1$ and (c) for $\Delta^{\textrm{l}}=23$. This corresponds to only allowing the earliest or neurons to spike, respectively, resulting in corresponding sparsities of 98.98% and 18.5%.