{"ID":2842180,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.10130","arxiv_id":"2511.10130","title":"RI-Loss: A Learnable Residual-Informed Loss for Time Series Forecasting","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. The code is publicly available at: https://github.com/shang-xl/RI-Loss.","short_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 rel...","url_abs":"https://arxiv.org/abs/2511.10130","url_pdf":"https://arxiv.org/pdf/2511.10130v2","authors":"[\"Jieting Wang\",\"Xiaolei Shang\",\"Feijiang Li\",\"Furong Peng\"]","published":"2025-11-13T09:36:00Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[\"Transformer\"]","has_code":false,"code_links":[{"ID":607109,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_id":2842180,"paper_url":"https://arxiv.org/abs/2511.10130","paper_title":"RI-Loss: A Learnable Residual-Informed Loss for Time Series Forecasting","repo_url":"https://github.com/shang-xl/RI-Loss","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}