Multiresolution Graph Transformers and Wavelet Positional Encoding for Learning Hierarchical Structures

TL;DR

This paper introduces Multiresolution Graph Transformers and Wavelet Positional Encoding to effectively learn hierarchical structures in large molecules, enabling accurate property prediction and capturing long-range interactions.

Contribution

The work presents the first graph transformer architecture capable of multi-scale representation of large molecules and introduces Wavelet Positional Encoding for improved localization.

Findings

Achieves chemical accuracy in molecular property estimation.

Outperforms state-of-the-art methods on multiple datasets.

Demonstrates effective learning of hierarchical and long-range structures.

Abstract

Contemporary graph learning algorithms are not well-defined for large molecules since they do not consider the hierarchical interactions among the atoms, which are essential to determine the molecular properties of macromolecules. In this work, we propose Multiresolution Graph Transformers (MGT), the first graph transformer architecture that can learn to represent large molecules at multiple scales. MGT can learn to produce representations for the atoms and group them into meaningful functional groups or repeating units. We also introduce Wavelet Positional Encoding (WavePE), a new positional encoding method that can guarantee localization in both spectral and spatial domains. Our proposed model achieves competitive results on two macromolecule datasets consisting of polymers and peptides, and one drug-like molecule dataset. Importantly, our model outperforms other state-of-the-art methods and achieves chemical accuracy in estimating molecular properties (e.g., GAP, HOMO and LUMO) calculated by Density Functional Theory (DFT) in the polymers dataset. Furthermore, the visualizations, including clustering results on macromolecules and low-dimensional spaces of their representations, demonstrate the capability of our methodology in learning to represent long-range and hierarchical structures. Our PyTorch implementation is publicly available at https://github.com/HySonLab/Multires-Graph-Transformer