Trainable label regions in classification-oriented diffractive neural networks

The spatial configuration of label regions on the detection plane plays a critical role in classification-oriented diffractive neural networks (DNNs), yet it remains largely underexplored. In this work, we propose a label-trainable diffractive neural network (Lt-DNN), in which the positions and sizes of label regions are treated as learnable parameters and jointly optimized with the diffractive layers. The training is formulated as a joint optimization problem, and a latent-variable-based method enables stochastic exploration through reparameterization and annealing. To further improve global search capability, a particle swarm optimization (PSO)-based decoupled framework is developed to separate label optimization from network training. Numerical results demonstrate improved classification accuracy, signal-to-noise ratio (SNR), and robustness compared to fixed-label configurations, with consistent performance across datasets. Notably, these gains are achieved without additional optical components or increased inference complexity. More importantly, these results reveal that label region configuration constitutes a critical and previously underutilized degree of freedom in diffractive neural networks. By explicitly incorporating and optimizing this component, the proposed framework provides new insight into the role of label regions as a decision layer and suggests a promising direction for improving optical neural computing systems without increasing system complexity.