{"ID":2827632,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.16723","arxiv_id":"2512.16723","title":"KOSS: Kalman-Optimal Selective State Spaces for Long-Term Sequence Modeling","abstract":"Recent selective state space models (SSMs), such as Mamba and Mamba-2, have demonstrated strong performance in sequence modeling owing to input-dependent selection mechanisms. However, these mechanisms lack theoretical grounding and cannot support context-aware selection from latent state dynamics. To address these limitations, we propose KOSS, a Kalman-optimal Selective State Space model that formulates selection as latent state uncertainty minimization. Derived from estimation theory, KOSS adopts a continuous-time latent update driven by a Kalman gain that dynamically modulates information propagation based on content and context, enabling a closed-loop, context-aware selectivity mechanism. To ensure stable computation and near-linear scalability, KOSS employs global spectral differentiation for frequency-domain derivative estimation, along with a segment-wise scan for hardware-efficient processing. On a selective copying task with distractors, KOSS achieves over 79\\% accuracy while baselines drop below 20\\%, demonstrating robust context-aware selection. Furthermore, across nine long-term forecasting benchmarks, KOSS reduces MSE by 2.92--36.23\\% and consistently outperforms state-of-the-art models in both accuracy and stability. To assess real-world applicability, a case study on secondary surveillance radar (SSR) tracking confirms KOSS's robustness under irregular intervals and noisy conditions and demonstrates its effectiveness in real-world applications. Finally, supplementary experiments verify Kalman gain convergence and the frequency response of spectral differentiation, providing theoretical support for the proposed closed-loop design.","short_abstract":"Recent selective state space models (SSMs), such as Mamba and Mamba-2, have demonstrated strong performance in sequence modeling owing to input-dependent selection mechanisms. However, these mechanisms lack theoretical grounding and cannot support context-aware selection from latent state dynamics. To address these lim...","url_abs":"https://arxiv.org/abs/2512.16723","url_pdf":"https://arxiv.org/pdf/2512.16723v1","authors":"[\"Lei Wang\",\"Xin Tan\",\"Mingwei Wang\",\"Ying Zhang\"]","published":"2025-12-18T16:25:21Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false}