The paper introduces local coordinate frames for each node in geometric graphs to enforce roto‑translation (Galilean) invariance in modeling interacting dynamical systems. By aligning each node’s frame with its local geometry, the method enables anisotropic filtering in graph neural networks and improves learning of highly non‑linear, time‑dependent behaviors. Experiments on traffic scenes, 3D motion capture, and colliding particles show that this approach outperforms recent state‑of‑the‑art methods.
arXiv:2608.28853v1 Announce Type: cross Abstract: Equivariant graph neural networks provide a principled way to model geometric systems, but efficient first-order architectures remain limited in how...
arXiv:2606. 09432v1 Announce Type: new Abstract: Modeling interacting dynamical systems requires capturing spatial interactions alongside long-range temporal dependencies.
arXiv:2607. 09741v1 Announce Type: cross Abstract: Accurate trajectory prediction in autonomous driving hinges on modeling dynamic and context-dependent interactions among traffic agents.
arXiv:2608.31045v1 Announce Type: new Abstract: Rotational symmetry is one of the most important structural principles in machine learning on 3D data. In applications ranging from physics and materia...
arXiv:2606. 14956v1 Announce Type: new Abstract: Autonomous driving systems rely on precise trajectory prediction to plan safe and efficient movement.
arXiv:2604. 07126v2 Announce Type: replace-cross Abstract: Predicting vehicle trajectories plays an important role in autonomous driving, transportation safety analysis, traffic operations, etc.
The paper introduces the Invariant-Conditioned Isotropic Kernel Neural Operator (IKNO), a compact graph model designed to predict vector-valued partial differential equations in a rotation‑robust manner. IKNO constructs local interactions from rotation‑invariant scalar quantities and vector directions that transform consistently with the data, ensuring that rotating input positions and velocities results in a correspondingly rotated predicted velocity change. Experiments on three‑dimensional Navier–Stokes dynamics show that IKNO achieves numerical precision consistency, matches the forecasting accuracy of a larger rotation‑aware Tensor Field Network, and outperforms a parameter‑matched graph simulator.
arXiv:2607. 05167v1 Announce Type: new Abstract: Many real-world systems are organized as networks where spatio-temporal dynamics unfold along connections and not discretely between nodes.
arXiv:2602.06859v3 Announce Type: replace-cross Abstract: Graph Anomaly Detection (GAD) aims to identify irregular patterns in graph data, and recent works have explored zero-shot generalist GAD to e...
The paper introduces a promptable localized motion representation that generates persistent embeddings for user-specified regions in a video, without cropping or masking the input. By conditioning motion encoding directly on spatial masks while processing the full video, the method produces temporally consistent, region-addressable embeddings that capture local dynamics while preserving global context. These embeddings enable object-level motion transfer for dynamic scene composition and improve localized action classification in multi-actor videos, outperforming global representations that rely on cropping or post-hoc masking.
arXiv:2604.04554v3 Announce Type: replace Abstract: We demonstrate Graph Representation Learning to address challenges that arise in visual odometry. In this context, the change in pose of a camera i...
The paper introduces the Motion Equivariant Convolutional LSTM (MELSTM), a neural network that treats motion as a gauge symmetry and is equivariant to any motion, including time‑varying velocities. MELSTM extends previous flow‑equivariant recurrent networks by moving from simple recurrent units to convolutional LSTMs, allowing velocity estimation rather than enumeration. Experiments on future‑frame prediction, motion‑only digit classification, and action recognition with camera shake show that MELSTM outperforms both standard convolutional LSTMs and flow‑equivariant counterparts while using fewer parameters and generalizing to longer horizons and unseen motions.