Asymptotically Stable Quaternion-valued Hopfield-structured Neural Network with Periodic Projection-based Supervised Learning Rules

Researchers propose a quaternion-valued supervised learning Hopfield neural network (QSHNN) that leverages quaternions' geometric advantages for representing rotations and postures. The model introduces periodic projection-based learning rules to maintain quaternionic consistency while achieving high accuracy and fast convergence, with potential applications in robotics and control systems.

• →QSHNN extends classic Hopfield neural networks to the quaternionic domain with proven asymptotic stability and unique fixed points.
• →Periodic projection strategy preserves quaternionic structure during training while maintaining convergence properties.
• →The model demonstrates high accuracy, fast convergence, and reliability across randomly generated target sets in experiments.
• →Evolution trajectories exhibit well-bounded curvature, making it suitable for robotic control systems and path planning applications.
• →The framework provides a general methodology for designing neural networks under hypercomplex algebraic structures.