用参数偏移法实现光学神经网络的精确梯度计算
Gradients of unitary optical neural networks using parameter-shift rule
- 通过参数偏移法在干涉仪阵列中直接计算梯度
- 利用光干涉的傅里叶特性实现硬件测量中的解析梯度
- 适合研究光计算硬件训练策略的研究者
本文探讨了参数偏移法（PSR）在酉光学神经网络（UONNs）中计算梯度的应用。尽管反向传播在传统神经网络训练中至关重要，但其在光学神经网络中的实现因光学系统的物理限制而面临挑战。我们证明，通过在参数偏移值处评估函数，PSR可有效用于由马赫-曾德干涉仪阵列构成的UONNs的训练。该方法利用这些系统中光学干涉的固有傅里叶级数特性，直接从硬件测量中计算出精确的解析梯度。这一方法为传统离线训练提供了可行替代方案，并避免了有限差分近似和全光学反向传播实现的局限性。本文给出了应用PSR优化光学神经网络相位参数的理论框架与实用方法，有望推动光学计算系统高效硬件训练策略的发展。
原文摘要 · Abstract (English)
This paper explores the application of the parameter-shift rule (PSR) for computing gradients in unitary optical neural networks (UONNs). While backpropagation has been fundamental to training conventional neural networks, its implementation in optical neural networks faces significant challenges due to the physical constraints of optical systems. We demonstrate how PSR, which calculates gradients by evaluating functions at shifted parameter values, can be effectively adapted for training UONNs constructed from Mach-Zehnder interferometer meshes. The method leverages the inherent Fourier series nature of optical interference in these systems to compute exact analytical gradients directly from hardware measurements. This approach offers a promising alternative to traditional in silico training methods and circumvents the limitations of both finite difference approximations and all-optical backpropagation implementations. We present the theoretical framework and practical methodology for applying PSR to optimize phase parameters in optical neural networks, potentially advancing the development of efficient hardware-based training strategies for optical computing systems.
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