Resilient State-Space Network: A dynamically adaptive framework for non-linear modelling of temporal dependencies

Abstract Time-series modelling plays a central role in machine learning applications such as speech processing, biosignal analysis, and emotion recognition. Despite recent advances, existing models still face fundamental challenges in capturing complex temporal patterns, especially in scenarios involving non-linear dynamics, time-varying behaviours, and long-range dependencies. Recurrent Neural Networks and transformers are limited by their reliance on discrete updates and fixed positional encodings, while classical state-space models are constrained by static system parameters and linear assumptions. To address these limitations, we propose a Resilient State-Space Network, a unified framework that integrates zero-order hold discretization to maintain continuity in state evolution, complex-valued eigendecomposition to capture frequency-phase dynamics, and a dynamic parameter network based on the Kolmogorov-Arnold representation theorem, which generates time-varying gain matrices and adaptive sampling intervals—thereby overcoming the linear time-invariant constraints of traditional State Space Models. Resilient State-Space Network is validated on three benchmark datasets: RAVDESS, SAVEE, and DISFA. The model is compared against strong baselines, including deep state space models, attention-based architectures, and temporal convolutional networks. Experimental results demonstrate that Resilient State-Space Network consistently outperforms existing methods, achieving accuracy improved from 89.5% to 90.8% on RAVDESS, 88.7% to 95.4% on SAVEE, and 79.1% to 80.8% on DISFA. Resilient State-Space Network establishes a unified modelling framework that combines physical modelling with deep learning. This approach introduces a new paradigm for time-series modelling and opens new directions for the design of physics-inspired neural networks, carrying significant theoretical implications and potential for practical applications. The code will be available at https://github.com/SWU1111/RSN.