用平滑核方法降低神经微分方程推理成本，提升效率与精度。
Efficient Neural Controlled Differential Equations via Attentive Kernel Smoothing
- 用核函数和高斯过程平滑控制路径，减少高频抖动
- 多视角注意力机制恢复平滑损失的细节，提升建模能力
- 在保持精度前提下，大幅降低函数求值次数和推理时间
神经控制微分方程（Neural CDEs）提供强大的连续时间序列建模框架，但驱动控制路径的粗糙性常限制其效率。标准样条插值引入高频波动，迫使自适应求解器采用极小步长，导致函数求值次数（NFE）过高。本文提出一种新路径构建方法，以核函数与高斯过程（GP）平滑替代精确插值，实现轨迹平滑度的显式控制。为恢复平滑过程丢失的细节，提出基于注意力的多视图CDE（MV-CDE）及其卷积扩展（MVC-CDE），通过可学习查询信息重构路径。该框架使模型能在多个轨迹间分配表征能力，分别捕捉不同时间模式。实验表明，使用GP的MVC-CDE在保持最佳准确率的同时，显著降低NFE和总推理时间，优于基于样条的基线方法。
原文摘要 · Abstract (English)
Neural Controlled Differential Equations (Neural CDEs) provide a powerful continuous-time framework for sequence modeling, yet the roughness of the driving control path often restricts their efficiency. Standard splines introduce high-frequency variations that force adaptive solvers to take excessively small steps, driving up the Number of Function Evaluations (NFE). We propose a novel approach to Neural CDE path construction that replaces exact interpolation with Kernel and Gaussian Process (GP) smoothing, enabling explicit control over trajectory regularity. To recover details lost during smoothing, we propose an attention-based Multi-View CDE (MV-CDE) and its convolutional extension (MVC-CDE), which employ learnable queries to inform path reconstruction. This framework allows the model to distribute representational capacity across multiple trajectories, each capturing distinct temporal patterns. Empirical results demonstrate that our method, MVC-CDE with GP, achieves state-of-the-art accuracy while significantly reducing NFEs and total inference time compared to spline-based baselines.
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