Title: State Aware Neural Stochastic Differential Equations for Multi-Modal Dynamics
Primary area: learning on time series and dynamical systems
Keywords: Time series Modeling, Sequential Modeling, Stochastic Differential Equations

Abstract: Neural Stochastic Differential Equations (NSDEs) are emerging as a powerful tool for modeling temporal data generation processes (DGPs). However, existing NSDEs frameworks encounter significant challenges when it comes to modeling multimodal densities, which are common in real-world datasets. These challenges often arise from the inherent ambiguities present in real-world DGPs. In this paper, we first provide a theoretical analysis explaining why current NSDEs frameworks struggle to effectively model these scenarios. We then introduce the Multimodal NSDEs (MM-NSDE) framework, a novel and intuitive approach designed to capture system states and dynamically adapt NSDEs to state transitions. Additionally, we conduct extensive experiments on both simulated and real-world datasets to demonstrate the robustness and effectiveness of our proposed method. MM-NSDEs achieves groundbreaking parameter efficiency, outperforming previous state-of-the-art approaches (e.g., Mamba) using only 1\% of their parameters, all while maintaining superior performance in temporal pattern recognition.