Incommensurate fractional recurrent neural networks

This paper introduces a novel class of neural networks called Incommensurate Fractional Recurrent Neural Networks (FRNNs) , inspired by incommensurate fractional difference systems. Unlike classical RNNs, FRNNs incorporate learnable fractional orders to capture heterogeneous temporal dependencies. To address the failure of back-propagation caused by cross-layer and cross-time coupling, we propose a forward-forward recursive gradient computation method combined with mini-batch SGD and ADAM optimization. Extensive experiments on multiple time-series datasets, including synthetic sinusoidal sequences, chaotic sequences, and real-world financial and energy data, demonstrate that FRNN achieves lower prediction error compared to RNN. These results confirm the effectiveness of fractional memory dynamics for sequential data processing. • Innovative FRNN Design : FRNNs inspired by IFDSs utilize diverse fractional orders to model complex and heterogeneous temporal dynamics. • Gradient Computation Solution : A forward-forward recursive method resolves the limitations of back-propagation in FRNNs. • Robust Training Approach : Mini-batch SGD combined with ADAM effectively tunes weights, biases, and the fractional memory vector . • Strong Empirical Results : FRNNs perform well on time-series tasks, reducing MSE and maintaining stable ordering. • Cross-Disciplinary Integration : Bridges fractional calculus and artificial intelligence to capture.