QAAR-SIREN: quantum-augmented attention and residual SIREN for time-series forecasting

Abstract

Time series forecasting remains challenging in the presence of nonstationarity, regime changes, and observation noise. Many existing machine learning approaches rely on complex architectures that often lead to unstable training and limited robustness. To address these limitations, we propose QAAR-SIREN, a compact forecasting framework that improves stability through residual learning and complementary feature representations. Instead of predicting absolute values, the model forecasts temporal increments, mitigating nonstationarity effects. It integrates three information sources: raw temporal lags, attention-based contextual summarization, and lightweight nonlinear features extracted from a shallow variational quantum circuit applied to the most recent observation. The quantum component functions as a compact nonlinear feature extractor that enriches the input representation without increasing architectural complexity. Experiments on synthetic signals with regime transitions and heterogeneous noise, as well as real-world datasets from climate, energy demand, finance, and transportation, demonstrate that QAAR-SIREN achieves strong and stable predictive performance. The model attains coefficients of determination up to approximately 0.985 with low mean squared error. Ablation studies confirm that observed gains arise from the complementary effects of residual learning, attention-based context aggregation, and quantum feature extraction.