Equivariant Neural
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Related Articles from SNS
Theoretical Aspects of Lie Groupoid and Lie Algebroid Equivariant Convolutional Neural Networks
Announce Type: cross Abstract: We introduce Lie groupoid equivariant neural networks as a specialization of recently proposed topological category-equivariant neural networks to the differentiable setting. Lie groupoid equivariant neural networks are composed from Lie groupoid lifting convolutions and Lie groupoid convolution layers, and we show how for suitable Lie groupoids they are equivalent to certain Lie algebroid-equivariant neural networks. We additionally describe groupoid invariant...
Equivariant Neural Belief Propagation
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. We introduce Equivariant Neural Belief Propagation (ENBP), a factor-graph framework whose messages are equivariant...
Separation Power of Equivariant Neural Networks
arXiv:2406.08966v3 Announce Type: replace Abstract: The separation power of a machine learning model refers to its ability to distinguish between different inputs and is often used as a proxy for its expressivity. Indeed, knowing the separation power of a family of models is a necessary condition to obtain fine-grained universality results. In this paper, we analyze the separation power of equivariant neural networks, such as convolutional and permutation-invariant networks.
Turbulence teaches equivariance to neural networks
Announce Type: replace Abstract: We show that the rotational nature of turbulence affects how neural networks learn mappings between quantities governed by the Navier-Stokes equations. We train super-resolution models at different wall-normal locations in a turbulent channel flow, where anisotropy varies naturally, and test their generalization to new coordinate frames, new anisotropy regimes, and a higher Reynolds number. Our findings inform both the design of equivariant machine learning...
EqGINO: Equivariant Geometry-Informed Fourier Neural Operators for 3D PDEs
Announce Type: new 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. While equivariant networks offer a solution, they typically rely on local operations in the spatial domain, making the global receptive field, which is essential for PDE dynamics, computationally expensive. Conversely, Fourier Neural Operators (FNOs) efficiently capture global...
Identifiable Equivariant Networks are Layerwise Equivariant
Announce Type: replace Abstract: We investigate the relation between end-to-end equivariance and layerwise equivariance in deep neural networks. We prove the following: For a network whose end-to-end function is equivariant with respect to group actions on the input and output spaces, there is a parameter choice yielding the same end-to-end function such that its layers are equivariant with respect to some group actions on the latent spaces. Our result assumes that the parameters of the...
On Universality of Deep Equivariant Networks
arXiv:2510.15814v2 Announce Type: replace-cross Abstract: Universality results for equivariant neural networks remain rare. Those that do exist typically hold only in restrictive settings: either they rely on regular or higher-order tensor representations, leading to impractically high-dimensional hidden spaces, or they target specialized architectures, often confined to the invariant setting. This work develops a more general account.
E2Former-V2: On-the-Fly Equivariant Attention with Linear Activation Memory
arXiv:2601.16622v2 Announce Type: replace Abstract: Equivariant Graph Neural Networks (EGNNs) have become a widely used approach for modeling 3D atomistic systems. However, mainstream architectures face critical scalability bottlenecks due to the explicit construction of geometric features or dense tensor products on \textit{every} edge. To overcome this, we introduce \textbf{E2Former-V2}, a scalable architecture that integrates algebraic sparsity with hardware-aware execution.
Multi-objective optimization and quantum hybridization of equivariant deep learning interatomic potentials
arXiv:2602.16908v2 Announce Type: replace-cross Abstract: Allegro is a machine learning interatomic potential model designed to predict atomic properties in molecules using E(3) equivariant neural networks. When training this model, there tends to be a trade-off between accuracy and inference time. For this reason, we apply multi-objective hyperparameter optimization to both objectives.
A Hypertoroidal Covering for Perfect Color Equivariance
arXiv:2603.04256v3 Announce Type: replace Abstract: When the color distribution of input images changes at inference, the performance of conventional neural network architectures drops considerably. A few researchers have begun to incorporate prior knowledge of color geometry in neural network design. These color equivariant architectures have modeled hue variation with 2D rotations, and saturation and luminance transformations as 1D translations.