# Continuous-Time SO(3) Forecasting with Savitzky--Golay Neural Controlled Differential Equations

arXiv: https://arxiv.org/abs/2506.06780 · HTML: https://mlsanity.com/paper/2506.06780/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 49 references that are in the map.
- First posted on arXiv 7 Jun 2025.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [ORB-SLAM: a Versatile and Accurate Monocular SLAM System](https://mlsanity.com/paper/1502.00956/) (2015)
- [Large Scale Interactive Motion Forecasting for Autonomous Driving : The Waymo Open Motion Dataset](https://mlsanity.com/paper/2104.10133/) (2021)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [An Analysis of SVD for Deep Rotation Estimation](https://mlsanity.com/paper/2006.14616/) (2020)
- [Deep Regression on Manifolds: A 3D Rotation Case Study](https://mlsanity.com/paper/2103.16317/) (2021)
- [The Double Sphere Camera Model](https://mlsanity.com/paper/1807.08957/) (2018)
- [SE3-Nets: Learning Rigid Body Motion using Deep Neural Networks](https://mlsanity.com/paper/1606.02378/) (2016)
- [Learning with 3D rotations, a hitchhiker's guide to SO(3)](https://mlsanity.com/paper/2404.11735/) (2024)
- [Tangent Space Backpropagation for 3D Transformation Groups](https://mlsanity.com/paper/2103.12032/) (2021)
- [Benchmarks and Challenges in Pose Estimation for Egocentric Hand Interactions with Objects](https://mlsanity.com/paper/2403.16428/) (2024)
- [Projective Manifold Gradient Layer for Deep Rotation Regression](https://mlsanity.com/paper/2110.11657/) (2021)
- [A Smooth Representation of Belief over SO(3) for Deep Rotation Learning with Uncertainty](https://mlsanity.com/paper/2006.01031/) (2020)
- [Efficient Derivative Computation for Cumulative B-Splines on Lie Groups](https://mlsanity.com/paper/1911.08860/) (2019)
- [The Oxford Multimotion Dataset: Multiple SE(3) Motions with Ground Truth](https://mlsanity.com/paper/1901.01445/) (2019)
- [Continuous-Time State Estimation Methods in Robotics: A Survey](https://mlsanity.com/paper/2411.03951/) (2024)
- [Camera Pose Filtering with Local Regression Geodesics on the Riemannian Manifold of Dual Quaternions](https://mlsanity.com/paper/1704.07072/) (2017)
- [GraspARL: Dynamic Grasping via Adversarial Reinforcement Learning](https://mlsanity.com/paper/2203.02119/) (2022)
- [Learning to Predict 3D Rotational Dynamics from Images of a Rigid Body with Unknown Mass Distribution](https://mlsanity.com/paper/2308.14666/) (2023)
- [A White-Noise-On-Jerk Motion Prior for Continuous-Time Trajectory Estimation on SE(3)](https://mlsanity.com/paper/1809.06518/) (2018)

## Built on by (most cited first, 2 of 2)

- [Explicit and Effectively Symmetric Schemes for Neural SDEs on Lie Groups](https://mlsanity.com/paper/2509.20599/) (2025)
- [Learning Manifold and Ito Dynamics with Branched Neural Rough Differential Equations](https://mlsanity.com/paper/2606.05272/) (2026)

## Abstract (arXiv)

Tracking and forecasting the rotation of objects is fundamental in computer vision and robotics, yet SO(3) extrapolation remains challenging as (1) sensor observations can be noisy and sparse, (2) motion patterns can be governed by complex dynamics, and (3) application settings can demand long-term forecasting. This work proposes modeling continuous-time rotational object dynamics on SO(3) using Neural Controlled Differential Equations guided by Savitzky-Golay paths. Unlike existing methods that rely on simplified motion assumptions, our method learns a general latent dynamical system of the underlying object trajectory while respecting the geometric structure of rotations. Experimental results on real-world data demonstrate compelling forecasting capabilities compared to existing approaches.