Optimization Algorithms Based on Double-Integral Coevolutionary Neurodynamics in Deep Learning

Deep neural networks are increasingly exposed to attack threats, and at the same time, the need for privacy protection is growing. As a result, the challenge of developing neural networks that are both robust and capable of strong generalization while maintaining privacy becomes pressing. Training neural networks under privacy constraints is one way to minimize privacy leakage, and one way to do this is to add noise to the data or model. However, noise may cause gradient directions to deviate from the optimal trajectory during training, leading to unstable parameter updates, slow convergence, and reduced model generalization capability. To overcome these challenges, we propose an optimization algorithm based on double-integral coevolutionary neurodynamics (DICND), designed to accelerate convergence and improve generalization in noisy conditions. Theoretical analysis proves the global convergence of the DICND algorithm and demonstrates its ability to converge to near-global minima efficiently under noisy conditions. Numerical simulations and image classification experiments further confirm the DICND algorithm's significant advantages in enhancing generalization performance.