Topological Neural Networks go Persistent, Equivariant, and Continuous

Topological Neural Networks (TNNs) incorporate higher-order relational information beyond pairwise interactions, enabling richer representations than Graph Neural Networks (GNNs). Concurrently, topological descriptors based on persistent homology (PH) are being increasingly employed to augment the GNNs. We investigate the benefits of integrating these two paradigms. Specifically, we introduce TopNets as a broad framework that subsumes and unifies various methods in the intersection of GNNs/TNNs and PH such as (generalizations of) RePHINE and TOGL. TopNets can also be readily adapted to handle (symmetries in) geometric complexes, extending the scope of TNNs and PH to spatial settings. Theoretically, we show that PH descriptors can provably enhance the expressivity of simplicial message-passing networks. Empirically, (continuous and E(n)-equivariant extensions of) TopNets achieve strong performance across diverse tasks, including antibody design, molecular dynamics simulation, and drug property prediction.

In-n-Out: Calibrating Graph Neural Networks for Link Prediction

Deep neural networks are notoriously miscalibrated, i.e., their outputs do not reflect the true probability of the event we aim to predict. While networks for tabular or image data are usually overconfident, recent works have shown that graph neural networks (GNNs) show the opposite behavior for node-level classification. But what happens when we are predicting links? We show that, in this case, GNNs often exhibit a mixed behavior. More specifically, they may be overconfident in negative predictions while being underconfident in positive ones. Based on this observation, we propose IN-N-OUT, the first-ever method to calibrate GNNs for link prediction. IN-N-OUT is based on two simple intuitions: i) attributing true/false labels to an edge while respecting a GNNs prediction should cause but small fluctuations in that edge's embedding; and, conversely, ii) if we label that same edge contradicting our GNN, embeddings should change more substantially. An extensive experimental campaign shows that IN-N-OUT significantly improves the calibration of GNNs in link prediction, consistently outperforming the baselines available -- which are not designed for this specific task.