Implicit Gradient Neural Networks with a Positive-Definite Mass Matrix for Online Linear Equations Solving
This work addresses the challenge of robustly solving linear equations in real-time for applications requiring stable neural network dynamics, though it appears incremental as it builds on existing implicit neural models.
The authors tackled the problem of solving online linear equations by designing a novel implicit neural model that introduces a positive-definite mass matrix, achieving globally exponential convergence to the unique theoretical solution and global stability even in no-solution and multi-solution scenarios, with simulative results verifying the theoretical analysis.
Motivated by the advantages achieved by implicit analogue net for solving online linear equations, a novel implicit neural model is designed based on conventional explicit gradient neural networks in this letter by introducing a positive-definite mass matrix. In addition to taking the advantages of the implicit neural dynamics, the proposed implicit gradient neural networks can still achieve globally exponential convergence to the unique theoretical solution of linear equations and also global stability even under no-solution and multi-solution situations. Simulative results verify theoretical convergence analysis on the proposed neural dynamics.