Understanding Virtual Nodes: Oversmoothing, Oversquashing, and Node Heterogeneity

Message passing neural networks (MPNNs) have been shown to have limitations in terms of expressivity and modeling 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 oversmoothing, oversquashing, and sensitivity analysis. First, in contrast to prior belief, we find that VNs typically avoid replicating anti-smoothing approaches to maintain expressive power. Second, 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. Finally, we highlight that, unlike Graph-Transformers (GT), 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 on graph-level tasks.

Curvature Filtrations for Graph Generative Model Evaluation

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 cutting-edge methods from topological data analysis to obtain robust, expressive descriptors for evaluating graph generative models.

End-To-End Prediction of Emotion From Heartbeat Data Collected by a Consumer Fitness Tracker

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 V\'ivosmart 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.

A Bayesian Deep Learning Framework for End-To-End Prediction of Emotion from Heartbeat

Automatic prediction of emotion promises to revolutionise human-computer interaction. Recent trends involve fusion of multiple modalities - audio, visual, and physiological - to classify emotional state. However, practical considerations 'in the wild' limit collection of this physiological data to commoditised heartbeat sensors. Furthermore, real-world applications often require some measure of uncertainty over model output. We present here an end-to-end deep learning model for classifying emotional valence from unimodal heartbeat data. We further propose a Bayesian framework for modelling uncertainty over valence predictions, and describe a procedure for tuning output according to varying demands on confidence. We benchmarked our framework against two established datasets within the field and achieved peak classification accuracy of 90%. 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.