Predictive tasks on relational databases are critical in real-world applications spanning e-commerce, healthcare, and social media. To address these tasks effectively, Relational Deep Learning (RDL) encodes relational data as graphs, enabling Graph Neural Networks (GNNs) to exploit relational structures for improved predictions. However, existing RDL methods often overlook the intrinsic structural properties of the graphs built from relational databases, leading to modeling inefficiencies, particularly in handling many-to-many relationships. Here we introduce RelGNN, a novel GNN framework specifically designed to leverage the unique structural characteristics of the graphs built from relational databases. At the core of our approach is the introduction of atomic routes, which are simple paths that enable direct single-hop interactions between the source and destination nodes. Building upon these atomic routes, RelGNN designs new composite message passing and graph attention mechanisms that reduce redundancy, highlight key signals, and enhance predictive accuracy. RelGNN is evaluated on 30 diverse real-world tasks from Relbench (Fey et al., 2024), and achieves state-of-the-art performance on the vast majority of tasks, with improvements of up to 25%.

Developing equivariant neural networks for the E(3) group plays an important role in modeling 3D data across real-world applications. Enforcing this equivariance primarily involves the tensor products of irreducible representations (irreps). However, the computational complexity of such operations increases significantly as higher-order tensors are used. In this work, we propose a systematic approach to substantially accelerate the computation of the tensor products of irreps. We mathematically connect the commonly used Clebsch-Gordan coefficients to the Gaunt coefficients, which are integrals of products of three spherical harmonics. Through Gaunt coefficients, the tensor product of irreps becomes equivalent to the multiplication between spherical functions represented by spherical harmonics. This perspective further allows us to change the basis for the equivariant operations from spherical harmonics to a 2D Fourier basis. Consequently, the multiplication between spherical functions represented by a 2D Fourier basis can be efficiently computed via the convolution theorem and Fast Fourier Transforms. This transformation reduces the complexity of full tensor products of irreps from $\mathcal{O}(L^6)$ to $\mathcal{O}(L^3)$, where $L$ is the max degree of irreps. Leveraging this approach, we introduce the Gaunt Tensor Product, which serves as a new method to construct efficient equivariant operations across different model architectures. Our experiments on the Open Catalyst Project and 3BPA datasets demonstrate both the increased efficiency and improved performance of our approach. The code and models will be made publicly available at https://github.com/lsj2408/Gaunt-Tensor-Product.

Molecular modeling, a central topic in quantum mechanics, aims to accurately calculate the properties and simulate the behaviors of molecular systems. The molecular model is governed by physical laws, which impose geometric constraints such as invariance and equivariance to coordinate rotation and translation. While numerous deep learning approaches have been developed to learn molecular representations under these constraints, most of them are built upon heuristic and costly modules. We argue that there is a strong need for a general and flexible framework for learning both invariant and equivariant features. In this work, we introduce a novel Transformer-based molecular model called GeoMFormer to achieve this goal. Using the standard Transformer modules, two separate streams are developed to maintain and learn invariant and equivariant representations. Carefully designed cross-attention modules bridge the two streams, allowing information fusion and enhancing geometric modeling in each stream. As a general and flexible architecture, we show that many previous architectures can be viewed as special instantiations of GeoMFormer. Extensive experiments are conducted to demonstrate the power of GeoMFormer. All empirical results show that GeoMFormer achieves strong performance on both invariant and equivariant tasks of different types and scales. Code and models will be made publicly available at https://github.com/c-tl/GeoMFormer.