Convergence of backward-error-propagation learning in photorefractive crystals

Area of Science:

• Optics and Photonics
• Artificial Intelligence
• Materials Science

Background:

• Photorefractive-based optical neural networks (ONNs) offer unique advantages for adaptive optical interconnections.
• Understanding the convergence properties of learning algorithms is crucial for their practical implementation.
• Existing research often lacks analytical determination of convergence regions for specific ONN architectures.

Purpose of the Study:

• To analytically determine the region of convergence for the backward-error-propagation learning algorithm in two classes of photorefractive ONNs.
• To identify the relationship between neural learning parameters and key system design parameters.
• To establish sufficient conditions for guaranteed convergence in these optical neural networks.

Main Methods:

• Analytical derivation of weight updates for electric-field amplitude and intensity encoding architectures.
• Computation of conditions sufficient for network convergence based on derived weight updates.
• Empirical verification of results using simulations of the XOR problem.

Main Results:

• The backward-error-propagation algorithm exhibits a well-defined convergence region in photorefractive ONNs.
• Neural learning parameters (learning-rate, weight-decay) are directly linked to system gain and exposure energy.
• Sufficiently high system gain and low exposure energy per weight update guarantee convergence, barring spurious local minima.

Conclusions:

• Convergence in photorefractive ONNs using backward-error-propagation is analytically predictable and achievable.
• System gain and exposure energy are critical design parameters for controlling learning dynamics and ensuring convergence.
• The study provides a theoretical framework and practical guidelines for designing and operating stable optical neural networks.