Hausdorff Difference-Based Adam Optimizer for Image Classification

To address the limitations of fixed-order update mechanisms in convolutional neural network parameter training, an adaptive parameter training method based on the Hausdorff difference is proposed in this paper. By deriving a Hausdorff difference formula that is suitable for discrete training processes and embedding it into the adaptive moment estimation framework, a generalized Hausdorff difference-based Adam algorithm (HAdam) is constructed. This algorithm introduces an order parameter to achieve joint dynamic control of the momentum intensity and the effective learning rate. Through theoretical analysis and numerical simulations, the influence of the order parameter and its value range on algorithm stability, parameter evolution trajectories, and convergence speed is investigated, and two adaptive order adjustment strategies based on iteration cycles and gradient feedback are designed. The experimental results on the Fashion-MNIST and CIFAR-10 benchmark datasets show that, compared with the standard Adam algorithm, the HAdam algorithm exhibits clear advantages in both convergence efficiency and recognition accuracy.