用签名编码器捕捉历史依赖，让连续系统模型更真实。
Learning non-Markovian Dynamical Systems with Signature-based Encoders
- 用签名变换替代RNN，实现连续时间历史编码
- 在合成数据上性能超越传统RNN编码器
- 适合建模带延迟和记忆效应的复杂动态系统
神经微分方程为建模动态系统提供了有效框架，通过学习连续时间向量场实现。然而，它们依赖马尔可夫假设——未来状态仅取决于当前状态——这在现实场景中常不成立，尤其在存在延迟和记忆效应的复杂系统连续控制中更为明显。现有方法多采用基于循环神经网络（RNN）的编码器来捕捉历史依赖，但其本质离散，难以适应连续建模，且训练表现不佳。本文研究将签名变换作为编码器用于学习非马尔可夫动态系统，在连续时间框架下实现。签名变换具备坚实的理论基础，能高效总结多维时间信息。我们将基于签名的编码方案融入编码器-解码器动态模型，实验表明其在合成基准测试中优于RNN基线模型。
原文摘要 · Abstract (English)
Neural ordinary differential equations offer an effective framework for modeling dynamical systems by learning a continuous-time vector field. However, they rely on the Markovian assumption - that future states depend only on the current state - which is often untrue in real-world scenarios where the dynamics may depend on the history of past states. This limitation becomes especially evident in settings involving the continuous control of complex systems with delays and memory effects. To capture historical dependencies, existing approaches often rely on recurrent neural network (RNN)-based encoders, which are inherently discrete and struggle with continuous modeling. In addition, they may exhibit poor training behavior. In this work, we investigate the use of the signature transform as an encoder for learning non-Markovian dynamics in a continuous-time setting. The signature transform offers a continuous-time alternative with strong theoretical foundations and proven efficiency in summarizing multidimensional information in time. We integrate a signature-based encoding scheme into encoder-decoder dynamics models and demonstrate that it outperforms RNN-based alternatives in test performance on synthetic benchmarks.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。