RI-Loss: A Learnable Residual-Informed Loss for Time Series Forecasting

• URL: http://arxiv.org/abs/2511.10130v1
• Date: Fri, 14 Nov 2025 01:34:00 GMT
• Title: RI-Loss: A Learnable Residual-Informed Loss for Time Series Forecasting
• Authors: Jieting Wang, Xiaolei Shang, Feijiang Li, Furong Peng,
• Abstract summary: Time series forecasting relies on predicting future values from historical data.<n>MSE has two fundamental weaknesses: its point-wise error fails to capture temporal relationships, and it does not account for inherent noise in the data.<n>We introduce the Residual-Informed Loss (RI-Loss), a novel objective function based on the Hilbert-Schmidt Independence Criterion (HSIC)
• Score: 13.117430904377905
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Time series forecasting relies on predicting future values from historical data, yet most state-of-the-art approaches-including transformer and multilayer perceptron-based models-optimize using Mean Squared Error (MSE), which has two fundamental weaknesses: its point-wise error computation fails to capture temporal relationships, and it does not account for inherent noise in the data. To overcome these limitations, we introduce the Residual-Informed Loss (RI-Loss), a novel objective function based on the Hilbert-Schmidt Independence Criterion (HSIC). RI-Loss explicitly models noise structure by enforcing dependence between the residual sequence and a random time series, enabling more robust, noise-aware representations. Theoretically, we derive the first non-asymptotic HSIC bound with explicit double-sample complexity terms, achieving optimal convergence rates through Bernstein-type concentration inequalities and Rademacher complexity analysis. This provides rigorous guarantees for RI-Loss optimization while precisely quantifying kernel space interactions. Empirically, experiments across eight real-world benchmarks and five leading forecasting models demonstrate improvements in predictive performance, validating the effectiveness of our approach. Code will be made publicly available to ensure reproducibility.

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