So3krates – Self-attention for higher-order geometric interactions on arbitrary length-scales
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The application of machine learning methods in quantum chemistry has enabled the study of numerous chemical phenomena, which are computationally intractable with traditional ab-initio methods. However, some quantum mechanical properties of molecules and materials depend on non-local electronic effects, which are often neglected due to the difficulty of modeling them efficiently. This work proposes a modified attention mechanism adapted to the underlying physics, which allows to recover the relevant non-local effects. Namely, we introduce spherical harmonic coordinates (SPHCs) to reflect higher-order geometric information for each atom in a molecule, enabling a non-local formulation of attention in the SPHC space. Our proposed model So3krates – a self-attention based message passing neural network – uncouples geometric information from atomic features, making them independently amenable to attention mechanisms. We show that in contrast to other published methods, So3krates is able to describe non-local quantum mechanical effects over arbitrary length scales. Further, we find evidence that the inclusion of higher-order geometric correlations increases data efficiency and improves generalization. So3krates matches or exceeds state-of-the-art performance on popular benchmarks, notably, requiring a significantly lower number of parameters (0.25–0.4x) while at the same time giving a substantial speedup (6–14x for training and 2–11x for inference) compared to other models.
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