Representation Learning on Graphs: A Reinforcement Learning Application

In this work, we study value function approximation in reinforcement learning (RL) problems with high dimensional state or action spaces via a generalized version of representation policy iteration (RPI). We consider the limitations of proto-value functions (PVFs) at accurately approximating the value function in low dimensions and we highlight the importance of features learning for an improved low-dimensional value function approximation. Then, we adopt different representation learning algorithm on graphs to learn the basis functions that best represent the value function. We empirically show that node2vec, an algorithm for scalable feature learning in networks, and the Variational Graph Auto-Encoder constantly outperform the commonly used smooth proto-value functions in low-dimensional feature space

Contrastive Learning for Non-Local Graphs with Multi-Resolution Structural Views

Learning node-level representations of heterophilic graphs is crucial for various applications, including fraudster detection and protein function prediction. In such graphs, nodes share structural similarity identified by the equivalence of their connectivity which is implicitly encoded in the form of higher-order hierarchical information in the graphs. The contrastive methods are popular choices for learning the representation of nodes in a graph. However, existing contrastive methods struggle to capture higher-order graph structures. To address this limitation, we propose a novel multiview contrastive learning approach that integrates diffusion filters on graphs. By incorporating multiple graph views as augmentations, our method captures the structural equivalence in heterophilic graphs, enabling the discovery of hidden relationships and similarities not apparent in traditional node representations. Our approach outperforms baselines on synthetic and real structural datasets, surpassing the best baseline by $16.06\%$ on Cornell, $3.27\%$ on Texas, and $8.04\%$ on Wisconsin. Additionally, it consistently achieves superior performance on proximal tasks, demonstrating its effectiveness in uncovering structural information and improving downstream applications

Multiresolution Graph Transformers and Wavelet Positional Encoding for Learning Hierarchical Structures

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-Transforme