Energy-Optimal Control of Generalized Laguerre Neural Network

Generalized Laguerre neural network (GLNN) is a specialized artificial neural network that employs generalized Laguerre polynomials (GLPs) as activation functions for hidden neurons, offering distinct advantages in function approximation tasks. Statistically, the larger number of activated GLPs, the more hidden neurons utilizing these GLPs will be engaged, thereby enhancing approximation accuracy. However, this comes with a tradeoff: Each arithmetic operation inherent to GLP computations consumes energy, leading to higher energy consumption. Consequently, optimizing the activation patterns of GLPs to strike an optimal tradeoff between approximation accuracy and energy efficiency emerges as a compelling research issue. To address this issue, this paper establishes an energy-constrained approximation accuracy optimization framework. Within this framework, we reveal the optimal number of candidate GLPs serving as activation functions for hidden neurons, the optimal number of hidden neurons that should be set in the GLNN, and the optimal activation criterion for candidate GLPs, under energy constraint. We also establish the root-exponentially decay convergence of the minimum approximation error under energy constraint. An algorithm based on our discovered results is proposed for the GLNN to minimize the approximation error under the acceptable level of energy consumption. Theoretical analysis and experiments jointly demonstrate its performance.