Technical Report: The Graph Spectral Token -- Enhancing Graph Transformers with Spectral Information

Graph Transformers have emerged as a powerful alternative to Message-Passing Graph Neural Networks (MP-GNNs) to address limitations such as over-squashing of information exchange. However, incorporating graph inductive bias into transformer architectures remains a significant challenge. In this report, we propose the Graph Spectral Token, a novel approach to directly encode graph spectral information, which captures the global structure of the graph, into the transformer architecture. By parameterizing the auxiliary [CLS] token and leaving other tokens representing graph nodes, our method seamlessly integrates spectral information into the learning process. We benchmark the effectiveness of our approach by enhancing two existing graph transformers, GraphTrans and SubFormer. The improved GraphTrans, dubbed GraphTrans-Spec, achieves over 10% improvements on large graph benchmark datasets while maintaining efficiency comparable to MP-GNNs. SubFormer-Spec demonstrates strong performance across various datasets.

Transformers are efficient hierarchical chemical graph learners

Transformers, adapted from natural language processing, are emerging as a leading approach for graph representation learning. Contemporary graph transformers often treat nodes or edges as separate tokens. This approach leads to computational challenges for even moderately-sized graphs due to the quadratic scaling of self-attention complexity with token count. In this paper, we introduce SubFormer, a graph transformer that operates on subgraphs that aggregate information by a message-passing mechanism. This approach reduces the number of tokens and enhances learning long-range interactions. We demonstrate SubFormer on benchmarks for predicting molecular properties from chemical structures and show that it is competitive with state-of-the-art graph transformers at a fraction of the computational cost, with training times on the order of minutes on a consumer-grade graphics card. We interpret the attention weights in terms of chemical structures. We show that SubFormer exhibits limited over-smoothing and avoids over-squashing, which is prevalent in traditional graph neural networks.

xxMD: Benchmarking Neural Force Fields Using Extended Dynamics beyond Equilibrium

Neural force fields (NFFs) have gained prominence in computational chemistry as surrogate models, superseding quantum-chemistry calculations in ab initio molecular dynamics. The prevalent benchmark for NFFs has been the MD17 dataset and its subsequent extension. These datasets predominantly comprise geometries from the equilibrium region of the ground electronic state potential energy surface, sampling from direct adiabatic dynamics. However, many chemical reactions entail significant molecular deformations, notably bond breaking. We demonstrate the constrained distribution of internal coordinates and energies in the MD17 datasets, underscoring their inadequacy for representing systems undergoing chemical reactions. Addressing this sampling limitation, we introduce the xxMD (Extended Excited-state Molecular Dynamics) dataset, derived from non-adiabatic dynamics. This dataset encompasses energies and forces ascertained from both multireference wave function theory and density functional theory. Furthermore, its nuclear configuration spaces authentically depict chemical reactions, making xxMD a more chemically relevant dataset. Our re-assessment of equivariant models on the xxMD datasets reveals notably higher mean absolute errors than those reported for MD17 and its variants. This observation underscores the challenges faced in crafting a generalizable NFF model with extrapolation capability. Our proposed xxMD-CASSCF and xxMD-DFT datasets are available at https://github.com/zpengmei/xxMD.