Gegenbauer Graph Neural Networks for Time-varying Signal Reconstruction

Reconstructing time-varying graph signals (or graph time-series imputation) is a critical problem in machine learning and signal processing with broad applications, ranging from missing data imputation in sensor networks to time-series forecasting. Accurately capturing the spatio-temporal information inherent in these signals is crucial for effectively addressing these tasks. However, existing approaches relying on smoothness assumptions of temporal differences and simple convex optimization techniques have inherent limitations. To address these challenges, we propose a novel approach that incorporates a learning module to enhance the accuracy of the downstream task. To this end, we introduce the Gegenbauer-based graph convolutional (GegenConv) operator, which is a generalization of the conventional Chebyshev graph convolution by leveraging the theory of Gegenbauer polynomials. By deviating from traditional convex problems, we expand the complexity of the model and offer a more accurate solution for recovering time-varying graph signals. Building upon GegenConv, we design the Gegenbauer-based time Graph Neural Network (GegenGNN) architecture, which adopts an encoder-decoder structure. Likewise, our approach also utilizes a dedicated loss function that incorporates a mean squared error component alongside Sobolev smoothness regularization. This combination enables GegenGNN to capture both the fidelity to ground truth and the underlying smoothness properties of the signals, enhancing the reconstruction performance. We conduct extensive experiments on real datasets to evaluate the effectiveness of our proposed approach. The experimental results demonstrate that GegenGNN outperforms state-of-the-art methods, showcasing its superior capability in recovering time-varying graph signals.

Dealing with Missing Modalities in Multimodal Recommendation: a Feature Propagation-based Approach

Multimodal recommender systems work by augmenting the representation of the products in the catalogue through multimodal features extracted from images, textual descriptions, or audio tracks characterising such products. Nevertheless, in real-world applications, only a limited percentage of products come with multimodal content to extract meaningful features from, making it hard to provide accurate recommendations. To the best of our knowledge, very few attention has been put into the problem of missing modalities in multimodal recommendation so far. To this end, our paper comes as a preliminary attempt to formalise and address such an issue. Inspired by the recent advances in graph representation learning, we propose to re-sketch the missing modalities problem as a problem of missing graph node features to apply the state-of-the-art feature propagation algorithm eventually. Technically, we first project the user-item graph into an item-item one based on co-interactions. Then, leveraging the multimodal similarities among co-interacted items, we apply a modified version of the feature propagation technique to impute the missing multimodal features. Adopted as a pre-processing stage for two recent multimodal recommender systems, our simple approach performs better than other shallower solutions on three popular datasets.

Graph Neural Networks for Treatment Effect Prediction

Estimating causal effects in e-commerce tends to involve costly treatment assignments which can be impractical in large-scale settings. Leveraging machine learning to predict such treatment effects without actual intervention is a standard practice to diminish the risk. However, existing methods for treatment effect prediction tend to rely on training sets of substantial size, which are built from real experiments and are thus inherently risky to create. In this work we propose a graph neural network to diminish the required training set size, relying on graphs that are common in e-commerce data. Specifically, we view the problem as node regression with a restricted number of labeled instances, develop a two-model neural architecture akin to previous causal effect estimators, and test varying message-passing layers for encoding. Furthermore, as an extra step, we combine the model with an acquisition function to guide the creation of the training set in settings with extremely low experimental budget. The framework is flexible since each step can be used separately with other models or policies. The experiments on real large-scale networks indicate a clear advantage of our methodology over the state of the art, which in many cases performs close to random underlining the need for models that can generalize with limited labeled samples to reduce experimental risks.

A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems

Recent advances in computational modelling of atomic systems, spanning molecules, proteins, and materials, represent them as geometric graphs with atoms embedded as nodes in 3D Euclidean space. In these graphs, the geometric attributes transform according to the inherent physical symmetries of 3D atomic systems, including rotations and translations in Euclidean space, as well as node permutations. In recent years, Geometric Graph Neural Networks have emerged as the preferred machine learning architecture powering applications ranging from protein structure prediction to molecular simulations and material generation. Their specificity lies in the inductive biases they leverage -- such as physical symmetries and chemical properties -- to learn informative representations of these geometric graphs. In this opinionated paper, we provide a comprehensive and self-contained overview of the field of Geometric GNNs for 3D atomic systems. We cover fundamental background material and introduce a pedagogical taxonomy of Geometric GNN architectures:(1) invariant networks, (2) equivariant networks in Cartesian basis, (3) equivariant networks in spherical basis, and (4) unconstrained networks. Additionally, we outline key datasets and application areas and suggest future research directions. The objective of this work is to present a structured perspective on the field, making it accessible to newcomers and aiding practitioners in gaining an intuition for its mathematical abstractions.

FAENet: Frame Averaging Equivariant GNN for Materials Modeling

Applications of machine learning techniques for materials modeling typically involve functions known to be equivariant or invariant to specific symmetries. While graph neural networks (GNNs) have proven successful in such tasks, they enforce symmetries via the model architecture, which often reduces their expressivity, scalability and comprehensibility. In this paper, we introduce (1) a flexible framework relying on stochastic frame-averaging (SFA) to make any model E(3)-equivariant or invariant through data transformations. (2) FAENet: a simple, fast and expressive GNN, optimized for SFA, that processes geometric information without any symmetrypreserving design constraints. We prove the validity of our method theoretically and empirically demonstrate its superior accuracy and computational scalability in materials modeling on the OC20 dataset (S2EF, IS2RE) as well as common molecular modeling tasks (QM9, QM7-X). A package implementation is available at https://faenet.readthedocs.io.

Time-varying Signals Recovery via Graph Neural Networks

The recovery of time-varying graph signals is a fundamental problem with numerous applications in sensor networks and forecasting in time series. Effectively capturing the spatio-temporal information in these signals is essential for the downstream tasks. Previous studies have used the smoothness of the temporal differences of such graph signals as an initial assumption. Nevertheless, this smoothness assumption could result in a degradation of performance in the corresponding application when the prior does not hold. In this work, we relax the requirement of this hypothesis by including a learning module. We propose a Time Graph Neural Network (TimeGNN) for the recovery of time-varying graph signals. Our algorithm uses an encoder-decoder architecture with a specialized loss composed of a mean squared error function and a Sobolev smoothness operator.TimeGNN shows competitive performance against previous methods in real datasets.

Higher-order Sparse Convolutions in Graph Neural Networks

Graph Neural Networks (GNNs) have been applied to many problems in computer sciences. Capturing higher-order relationships between nodes is crucial to increase the expressive power of GNNs. However, existing methods to capture these relationships could be infeasible for large-scale graphs. In this work, we introduce a new higher-order sparse convolution based on the Sobolev norm of graph signals. Our Sparse Sobolev GNN (S-SobGNN) computes a cascade of filters on each layer with increasing Hadamard powers to get a more diverse set of functions, and then a linear combination layer weights the embeddings of each filter. We evaluate S-SobGNN in several applications of semi-supervised learning. S-SobGNN shows competitive performance in all applications as compared to several state-of-the-art methods.

Understanding the Relationship between Over-smoothing and Over-squashing in Graph Neural Networks

Graph Neural Networks (GNNs) have been successfully applied in many applications in computer sciences. Despite the success of deep learning architectures in other domains, deep GNNs still underperform their shallow counterparts. There are many open questions about deep GNNs, but over-smoothing and over-squashing are perhaps the most intriguing issues. When stacking multiple graph convolutional layers, the over-smoothing and over-squashing problems arise and have been defined as the inability of GNNs to learn deep representations and propagate information from distant nodes, respectively. Even though the widespread definitions of both problems are similar, these phenomena have been studied independently. This work strives to understand the underlying relationship between over-smoothing and over-squashing from a topological perspective. We show that both problems are intrinsically related to the spectral gap of the Laplacian of the graph. Therefore, there is a trade-off between these two problems, i.e., we cannot simultaneously alleviate both over-smoothing and over-squashing. We also propose a Stochastic Jost and Liu curvature Rewiring (SJLR) algorithm based on a bound of the Ollivier's Ricci curvature. SJLR is less expensive than previous curvature-based rewiring methods while retaining fundamental properties. Finally, we perform a thorough comparison of SJLR with previous techniques to alleviate over-smoothing or over-squashing, seeking to gain a better understanding of both problems.

Multiple Similarity Drug-Target Interaction Prediction with Random Walks and Matrix Factorization

The discovery of drug-target interactions (DTIs) is a very promising area of research with great potential. In general, the identification of reliable interactions among drugs and proteins can boost the development of effective pharmaceuticals. In this work, we leverage random walks and matrix factorization techniques towards DTI prediction. In particular, we take a multi-layered network perspective, where different layers correspond to different similarity metrics between drugs and targets. To fully take advantage of topology information captured in multiple views, we develop an optimization framework, called MDMF, for DTI prediction. The framework learns vector representations of drugs and targets that not only retain higher-order proximity across all hyper-layers and layer-specific local invariance, but also approximates the interactions with their inner product. Furthermore, we propose an ensemble method, called MDMF2A, which integrates two instantiations of the MDMF model that optimize surrogate losses of the area under the precision-recall curve (AUPR) and the area under the receiver operating characteristic curve (AUC), respectively. The empirical study on real-world DTI datasets shows that our method achieves significant improvement over current state-of-the-art approaches in four different settings. Moreover, the validation of highly ranked non-interacting pairs also demonstrates the potential of MDMF2A to discover novel DTIs.