The brains of all bilaterally symmetric animals on Earth are divided into left and right hemispheres. The anatomy and functionality of the hemispheres have a large degree of overlap, but there are asymmetries, and they specialise in possesses different attributes. Other authors have used computational models to mimic hemispheric asymmetries with a focus on reproducing human data on semantic and visual processing tasks. We took a different approach and aimed to understand how dual hemispheres in a bilateral architecture interact to perform well in a given task. We propose a bilateral artificial neural network that imitates lateralisation observed in nature: that the left hemisphere specialises in local features and the right in global features. We used different training objectives to achieve the desired specialisation and tested it on an image classification task with two different CNN backbones: ResNet and VGG. Our analysis found that the hemispheres represent complementary features that are exploited by a network head that implements a type of weighted attention. The bilateral architecture outperformed a range of baselines of similar representational capacity that do not exploit differential specialisation, with the exception of a conventional ensemble of unilateral networks trained on dual training objectives for local and global features. The results demonstrate the efficacy of bilateralism, contribute to the discussion of bilateralism in biological brains, and the principle may serve as an inductive bias for new AI systems.