An Initial Investigation on the Generation of Logic Gate Networks using Cartesian Genetic Programming

Logic Gate Networks (LGNs) are an appealing family of artificial intelligence models that efficiently perform inference, by replacing floating-point multiply–accumulate operations with Boolean ones. Despite their performance and efficiency, training still represents a problem: the selection and wiring of logic gates are discrete design choices, making the direct use of gradient-based optimization difficult, at least in its native form. This paper provides an initial investigation on whether Cartesian Genetic Programming (CGP) can be turned into a practical, gradient-free framework for evolving layered LGNs for image classification. To this purpose, we extend a CGP implementation with data handling functions specific for the modified National Institute of Standards and Technology (MNIST) dataset, redundant multi-bit output decoding, custom loss functions, batch-based evaluation, layered connectivity constraints, and adaptive mutation control. Experiments on binarized MNIST show that these design choices substantially improve the search process. In the final configuration, the proposed method reaches more than 80% test accuracy with a fully discrete evolutionary pipeline executed on a single processor core (CPU), providing a concrete indication that non-trivial logical classifiers can be obtained without back-propagation, Graphics Processing Units (GPUs), or continuous relaxations.