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We propose a computationally efficient $G$-invariant neural network that approximates functions invariant to the action of a given permutation subgroup $G \leq S_n$ of the symmetric group on input data. The key element of the proposed…

Geometric deep learning enables the encoding of physical symmetries in modeling 3D objects. Despite rapid progress in encoding 3D symmetries into Graph Neural Networks (GNNs), a comprehensive evaluation of the expressiveness of these…

Neural operators approximate PDE solution maps, but they need not respect the symmetries of the governing equation. In out-of-distribution (OOD) regimes, a standard neural operator must often learn coordinate alignment and physical…

The classical universal approximation (UA) theorem for neural networks establishes mild conditions under which a feedforward neural network can approximate a continuous function $f$ with arbitrary accuracy. A recent result shows that neural…

Long-range correlations are essential across numerous machine learning tasks, especially for data embedded in Euclidean space, where the relative positions and orientations of distant components are often critical for accurate predictions.…

Face presentation attacks (PA), also known as spoofing attacks, pose a substantial threat to biometric systems that rely on facial recognition systems, such as access control systems, mobile payments, and identity verification systems. To…

Recently, deep neural network has shown promising performance in face image recognition. The inputs of most networks are face images, and there is hardly any work reported in literature on network with face videos as input. To sufficiently…

This paper presents a novel framework combining group equivariant convolutional neural networks (G-CNNs) with equivariant-aware structured pruning to produce compact, transformation-invariant models for resource-constrained environments.…

The success of neural networks such as convolutional neural networks (CNNs) has been largely attributed to their effective and widespread deployment on customised computing platforms, including field-programmable gate arrays (FPGAs) and…

Many learning problems involve symmetries, and while invariance can be built into neural architectures, it can also emerge implicitly when training on group-structured data. We study this phenomenon in classical Hopfield networks and show…

Learning representations of nodes has been a crucial area of the graph machine learning research area. A well-defined node embedding model should reflect both node features and the graph structure in the final embedding. In the case of…

Federated Learning (FL) has revolutionized how we train deep neural networks by enabling decentralized collaboration while safeguarding sensitive data and improving model performance. However, FL faces two crucial challenges: the diverse…

The notion of group invariance helps neural networks in recognizing patterns and features under geometric transformations. Group convolutional neural networks enhance traditional convolutional neural networks by incorporating group-based…

Equivariant Graph Neural Networks (GNNs) have achieved remarkable success across diverse scientific applications. However, existing approaches face critical efficiency challenges when scaling to large geometric graphs and suffer significant…

Foreground segmentation is an essential task in the field of image understanding. Under unsupervised conditions, different images and instances always have variable expressions, which make it difficult to achieve stable segmentation…

In subsurface imaging, learning the mapping from velocity maps to seismic waveforms (forward problem) and waveforms to velocity (inverse problem) is important for several applications. While traditional techniques for solving forward and…

Local gauge symmetry underlies fundamental interactions and strongly correlated quantum matter, yet existing machine-learning approaches lack a general, principled framework for learning under site-dependent symmetries, particularly for…

Graph neural networks (GNNs) have become a workhorse approach for learning from data defined over irregular domains, typically by implicitly assuming that the data structure is represented by a homophilic graph. However, recent works have…

Graph-structured data jointly contain discrete topology and continuous geometry, which poses fundamental challenges for generative modeling due to heterogeneous distributions, incompatible noise dynamics, and the need for equivariant…

Computational materials discovery is limited by the high cost of first-principles calculations. Machine learning (ML) potentials that predict energies from crystal structures are promising, but existing methods face computational…