Efficient Neural Controlled Differential Equations via Attentive Kernel Smoothing
About
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.
Related benchmarks
| Task | Dataset | Result | Rank | |
|---|---|---|---|---|
| Probabilistic time series forecasting | ETTm2 Regular (test) | Avg NCRPS0.434 | 11 | |
| Probabilistic time series forecasting | ETTm2 Irregular (test) | Average NCRPS0.46 | 11 | |
| Probabilistic time series forecasting | ETTm1 Regular (test) | Avg NCRPS0.299 | 11 | |
| Probabilistic time series forecasting | Weather Regular (test) | Avg NCRPS0.42 | 11 | |
| Probabilistic time series forecasting | ETTm1 Irregular (test) | Avg NCRPS0.326 | 11 | |
| Probabilistic time series forecasting | Weather Irregular (test) | Average NCRPS0.469 | 11 | |
| Probabilistic time series forecasting | Electricity Irregular (test) | Average NCRPS0.22 | 10 | |
| Probabilistic time series forecasting | Electricity (test) | Average NCRPS0.214 | 10 | |
| Probabilistic time series forecasting | Traffic Regular (test) | Average NCRPS0.432 | 10 | |
| Probabilistic time series forecasting | Traffic Irregular (test) | Avg NCRPS0.436 | 10 |