Diffractive Arithmetic Processing by Conditional Optical Generative Models

Arithmetic competence is a unique feature of biological intelligence that combines abilities including perception, computation, and result-presentation, yet emerging artificial intelligence still lacks these capabilities. This paper demonstrates diffractive visual processors that can perform arithmetic operations based on all-optical and hybrid optoelectronic computing. Taking handwritten digit images as input, the diffractive networks functioned as conditional optical generative models that output adaptive arithmetic results within a single, compact design for all four basic arithmetic operations. Such optical processors were designed via knowledge distillation, where (1) a generative adversarial network (GAN) was trained as the teacher model to generate the arithmetic results based on input digits and (2) a diffractive processor was trained as the student model to replicate the transformation of the digital generator in the previous step. Compared to an arithmetic processor that generated computing output with fixed writing style, the adaptive processor achieved 60.5% operational accuracy in addition, significantly exceeding the 42.7% accuracy of the fixed-style approach. The addition of a nonlinear encoding mechanism to the network further boosted this accuracy to 89.7%. This study represents the first analysis for the numerical competence of free-space optical processors via their combined capabilities of visual sensation, analog computing, and optical image generation.