While message passing neural networks (MPNNs) have convincing success in a range of applications, they exhibit limitations such as the oversquashing problem and their inability to capture long-range interactions. Augmenting MPNNs with a virtual node (VN) removes the locality constraint of the layer aggregation and has been found to improve performance on a range of benchmarks. We provide a comprehensive theoretical analysis of the role of VNs and benefits thereof, through the lenses of oversquashing and sensitivity analysis. First, we characterize, precisely, how the improvement afforded by VNs on the mixing abilities of the network and hence in mitigating oversquashing, depends on the underlying topology. We then highlight that, unlike Graph-Transformers (GTs), classical instantiations of the VN are often constrained to assign uniform importance to different nodes. Consequently, we propose a variant of VN with the same computational complexity, which can have different sensitivity to nodes based on the graph structure. We show that this is an extremely effective and computationally efficient baseline for graph-level tasks.

Subgraph GNNs have emerged as promising architectures that overcome the expressiveness limitations of Graph Neural Networks (GNNs) by processing bags of subgraphs. Despite their compelling empirical performance, these methods are afflicted by a high computational complexity: they process bags whose size grows linearly in the number of nodes, hindering their applicability to larger graphs. In this work, we propose an effective and easy-to-implement approach to dramatically alleviate the computational cost of Subgraph GNNs and unleash broader applications thereof. Our method, dubbed HyMN, leverages walk-based centrality measures to sample a small number of relevant subgraphs and drastically reduce the bag size. By drawing a connection to perturbation analysis, we highlight the strength of the proposed centrality-based subgraph sampling, and further prove that these walk-based centralities can be additionally used as Structural Encodings for improved discriminative power. A comprehensive set of experimental results demonstrates that HyMN provides an effective synthesis of expressiveness, efficiency, and downstream performance, unlocking the application of Subgraph GNNs to dramatically larger graphs. Not only does our method outperform more sophisticated subgraph sampling approaches, it is also competitive, and sometimes better, than other state-of-the-art approaches for a fraction of their runtime.

Graph generative model evaluation necessitates understanding differences between graphs on the distributional level. This entails being able to harness salient attributes of graphs in an efficient manner. Curvature constitutes one such property of graphs, and has recently started to prove useful in characterising graphs. Its expressive properties, stability, and practical utility in model evaluation remain largely unexplored, however. We combine graph curvature descriptors with emerging methods from topological data analysis to obtain robust, expressive descriptors for evaluating graph generative models.

Automatic prediction of emotion promises to revolutionise human-computer interaction. Recent trends involve fusion of multiple data modalities$-$-audio, visual, and physiological$-$-to classify emotional state. However, in practice, collection of physiological data ‘in the wild’ is currently limited to heartbeat time series of the kind generated by affordable wearable heart monitors. Furthermore, real-world applications of emotion prediction often require some measure of uncertainty over model output, in order to inform downstream decision-making. We present here an end-to-end deep learning model for classifying emotional valence from unimodal heartbeat time series. We further propose a Bayesian framework for modelling uncertainty over these valence predictions, and describe a probabilistic procedure for choosing to accept or reject model output according to the intended application. We benchmarked our framework against two established datasets and achieved peak classification accuracy of 90 percent. These results lay the foundation for applications of affective computing in real-world domains such as healthcare, where a high premium is placed on non-invasive collection of data, and predictive certainty.

Automatic detection of emotion has the potential to revolutionize mental health and wellbeing. Recent work has been successful in predicting affect from unimodal electrocardiogram (ECG) data. However, to be immediately relevant for real-world applications, physiology-based emotion detection must make use of ubiquitous photoplethysmogram (PPG) data collected by affordable consumer fitness trackers. Additionally, applications of emotion detection in healthcare settings will require some measure of uncertainty over model predictions. We present here a Bayesian deep learning model for end-to-end classification of emotional valence, using only the unimodal heartbeat time series collected by a consumer fitness tracker (Garmin Vivosmart 3). We collected a new dataset for this task, and report a peak F1 score of 0.7. This demonstrates a practical relevance of physiology-based emotion detection `in the wild' today.