arXiv:2606. 06344v1 Announce Type: new Abstract: Probabilistic inference over spatially embedded variables requires beliefs that respect $SE(3)$ symmetry, yet existing equivariant networks produce only scalars and vectors -- not the rank-2 precision tensors needed for anisotropic uncertainty, and single-component messages collapse multi-modal energy landscapes to physically meaningless averages.
arXiv:2608.24386v1 Announce Type: cross Abstract: Tensor-valued prediction is fundamental to geometric deep learning, yet uncertainty quantification (UQ) for such outputs remains an open challenge. W...
arXiv:2609. 21085v1 Announce Type: cross Abstract: Gaussian processes (GPs) provide principled probabilistic predictions while encoding prior knowledge, including equivariances.
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:2505. 19809v3 Announce Type: replace-cross Abstract: In many real-world applications of regression, conditional probability estimation, and uncertainty quantification, exploiting symmetries rooted in physics or geometry can dramatically improve generalization and sample efficiency.
arXiv:2606. 05042v1 Announce Type: new Abstract: Marginal inference in discrete graphical models forces a choice between exactness and scalability: exact algorithms are intractable for high-treewidth graphs, while iterative approximations (Belief Propagation, variational methods) sacrifice convergence guarantees on frustrated topologies.
arXiv:2607. 03809v1 Announce Type: new Abstract: Normalising flows provide a powerful variational family for approximate inference, yet individual architectures often fail to generalise across heterogeneous posterior geometries.
The paper introduces an end‑to‑end equivariant surrogate model for three‑dimensional Rayleigh‑Bénard convection, combining an equivariant convolutional autoencoder with an equivariant convolutional LSTM that employs $G$‑steerable kernels. The architecture exploits $D_4$‑steerable kernels in vertically stacked layers and partial kernel sharing in the vertical direction to respect the system’s E(2) equivariance in the horizontal plane while handling broken translational symmetry vertically. Experiments show notable improvements in sample and parameter efficiency and better scaling to more complex dynamics.
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. 01443v1 Announce Type: cross Abstract: A central difficulty in training Joint-Embedding Predictive Architectures (JEPAs) is preventing representation collapse.
arXiv:2512. 04954v3 Announce Type: replace Abstract: We present a novel technique for amortized posterior estimation using Normalizing Flows trained with likelihood-weighted importance sampling.
EquiReg introduces an equivariance‑regularized diffusion framework that penalises sampling trajectories deviating from the data manifold, thereby improving posterior sampling for inverse problems. By formalising manifold‑preferential equivariant functions—naturally arising from data augmentation or inherent symmetries—EquiReg guides diffusion steps toward symmetry‑preserving regions of the solution space. The method shows consistent gains in both linear and nonlinear image restoration tasks and partial differential equation solving, especially under reduced sampling and measurement consistency steps, and is available as open‑source code.
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.