Compensation-Balanced Recurrent Neural Architecture Based on Nonlinear Spiking Neural Membrane Systems

Nonlinear spiking neural P (NSNP) systems offer a biologically inspired framework for modeling nonlinear temporal dynamics via spike consumption and generation. Existing NSNP-based recurrent architectures, such as the long short-term memory model inspired from spiking neural P systems (LSTM-SNP), primarily rely on implicit gating mechanisms and lack explicit state correction during recurrent propagation, which can lead to unstable state evolution and excessive information decay in long-term temporal modeling. To address this limitation, a compensation-balanced LSTM-SNP (CBLSTM-SNP) architecture is proposed. The model introduces a compensation-driven regulation mechanism, comprising a regulation branch and an adaptive compensation branch, to dynamically adjust hidden state evolution. From a nonlinear dynamical systems perspective, CBLSTM-SNP establishes a balanced recurrent state transition integrating memory preservation, nonlinear spike processing, and adaptive state restoration. Theoretical analysis confirms the boundedness and Lipschitz continuity of the proposed recurrent dynamics. Empirical evaluations on five benchmark time series datasets demonstrate that CBLSTM-SNP produces smoother hidden state trajectories and achieves comparable forecasting performance compared with several representative recurrent and hybrid models.