A smoothing interval neural networks-based Caputo fractional-order gradient learning algorithm

Smoothing interval neural networks (SINNs) are widely recognized for their effectiveness in handling uncertain data across various domains. However, training SINNs using the integer-order gradient method usually leads to lower computational accuracy and instability during parameter updating, which adversely affects the convergence and accuracy of the model. Fractional-order derivatives, in contrast, offer superior non-local memory properties and broader data fitting capabilities, providing more accurate descriptions of complex system dynamics. Therefore, this paper introduces a fractional-order gradient descent (FGD) method that utilizes Caputo fractional-order derivatives to train SINNs. Theoretical validation of the FGD method is achieved by rigorously proving the monotonicity of the error function and the strong convergence theorem of the algorithm. Additionally, various simulations are conducted to assess the enhanced algorithm’s performance on different approximation functions and classification datasets. The experimental results demonstrate that the FGD method significantly accelerates the convergence rate, enhances generalization ability, and improves the overall performance of SINNs.