arXiv:2510. 03511v3 Announce Type: replace-cross Abstract: While widespread, Transformers lack inductive biases for geometric symmetries common in science and computer vision.
arXiv:2606. 04108v1 Announce Type: cross Abstract: Single-view 3D generative models have achieved impressive visual quality, yet they are not designed to satisfy structural or functional requirements, and in practice, often fall short.
arXiv:2505. 15441v5 Announce Type: replace-cross Abstract: Natural images exhibit strong geometric regularities: local structures, such as edges, corners, and textures, appear in many orientations and mirror configurations.
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:2606.23489v2 Announce Type: replace-cross Abstract: Meshes are among the most common 3D scene representations, but directly generating meshes is challenging because the representation contains...
arXiv:2312. 08230v2 Announce Type: replace-cross Abstract: Detecting partial extrinsic symmetry in 3D geometry is a fundamental yet persistent challenge in computer vision and graphics, critical for tasks ranging from shape completion to procedural generation.
While recent advancements like the Poincaré ResNet have demonstrated the potential of learning visual representations directly in hyperbolic space, their optimisation remains hampered by the computationally intensive nature of Riemannian gradients and the strict boundaries of the manifold. Furthermore, standard hyperbolic networks treat spatial transformations of the same object as distinct hierarchical concepts, leading to redundant parameter usage and vanishing signals.
arXiv:2509. 11218v2 Announce Type: replace-cross Abstract: Spatial transformations such as rotation and scale obscure the morphological cues needed for accurate image classification.
arXiv:2606. 03260v1 Announce Type: cross Abstract: Deep learning surrogates for 3D Partial Differential Equations (PDEs) often fail to generalize across geometric transformations because they depend heavily on specific coordinate systems.
arXiv:2602. 18948v2 Announce Type: replace Abstract: Transformer models contain substantial internal redundancy arising from coordinate-dependent representations and continuous symmetries, in model space and in head space, respectively.
arXiv:2607. 00556v1 Announce Type: cross Abstract: While recent advancements like the Poincar\'e ResNet have demonstrated the potential of learning visual representations directly in hyperbolic space, their optimisation remains hampered by the computationally intensive nature of Riemannian gradients and the strict boundaries of the manifold.
arXiv:2602. 11626v3 Announce Type: replace-cross Abstract: Learning solution operators on arbitrary geometries remains a central challenge in scientific machine learning, especially for many-query simulation, physics-informed learning, and evolving geometries requiring accurate, geometry-aware predictions at arbitrary spatial locations.
arXiv:2608.29819v1 Announce Type: new Abstract: Accurate stereo matching remains challenging in ill-posed regions such as fine structures, reflective, or transparent objects, where appearance cues ar...