Analog physical neural networks, which hold promise for improved energy efficiency and speed compared to digital electronic neural networks, are nevertheless typically operated in a relatively high-power regime so that the signal-to-noise ratio (SNR) is large (>10). What happens if an analog system is instead operated in an ultra-low-power regime, in which the behavior of the system becomes highly stochastic and the noise is no longer a small perturbation on the signal? In this paper, we study this question in the setting of optical neural networks operated in the limit where some layers use only a single photon to cause a neuron activation. Neuron activations in this limit are dominated by quantum noise from the fundamentally probabilistic nature of single-photon detection of weak optical signals. We show that it is possible to train stochastic optical neural networks to perform deterministic image-classification tasks with high accuracy in spite of the extremely high noise (SNR ~ 1) by using a training procedure that directly models the stochastic behavior of photodetection. We experimentally demonstrated MNIST classification with a test accuracy of 98% using an optical neural network with a hidden layer operating in the single-photon regime; the optical energy used to perform the classification corresponds to 0.008 photons per multiply-accumulate (MAC) operation, which is equivalent to 0.003 attojoules of optical energy per MAC. Our experiment used >40x fewer photons per inference than previous state-of-the-art low-optical-energy demonstrations, to achieve the same accuracy of >90%. Our work shows that some extremely stochastic analog systems, including those operating in the limit where quantum noise dominates, can nevertheless be used as layers in neural networks that deterministically perform classification tasks with high accuracy if they are appropriately trained.

翻译：模拟物理神经网络有望比数字电子神经网络实现更高的能效和速度，但通常需在高功率模式下运行以保证信噪比(SNR)足够大(>10)。若将模拟系统切换至超低功率模式运行，其行为将呈现高度随机性，此时噪声不再是信号的微小扰动，系统将发生怎样的变化？本文以光学神经网络为研究对象，探索在部分层级仅需单个光子即可触发神经元激活的极限情形。在此极限下，神经元激活过程主要受量子噪声支配，这源于弱光信号单光子探测固有的概率特性。我们证明，通过采用直接建模光电探测随机行为的训练方法，即便在极高噪声条件(SNR ~ 1)下，仍可训练随机光学神经网络高精度完成确定性图像分类任务。我们基于带单光子工作隐藏层的光学神经网络进行的MNIST分类实验实现了98%的测试准确率；执行分类所需的光学能量折合每次乘积累加(MAC)操作仅需0.008个光子，相当于每次MAC消耗0.003阿焦耳光学能量。与先前达到同等>90%准确率的最优低光学能量方案相比，本实验每次推理所需光子数减少了40倍以上。这项工作表明，经过适当训练后，包括量子噪声主导的极端随机模拟系统在内的一些高度随机系统，仍可作为神经网络层级用于高精度确定性分类任务。