On the Stability of Expressive Positional Encodings for Graph Neural Networks

Designing effective positional encodings for graphs is key to building powerful graph transformers and enhancing message-passing graph neural networks. Although widespread, using Laplacian eigenvectors as positional encodings faces two fundamental challenges: (1) \emph{Non-uniqueness}: there are many different eigendecompositions of the same Laplacian, and (2) \emph{Instability}: small perturbations to the Laplacian could result in completely different eigenspaces, leading to unpredictable changes in positional encoding. Despite many attempts to address non-uniqueness, most methods overlook stability, leading to poor generalization on unseen graph structures. We identify the cause of instability to be a "hard partition" of eigenspaces. Hence, we introduce Stable and Expressive Positional Encodings (SPE), an architecture for processing eigenvectors that uses eigenvalues to "softly partition" eigenspaces. SPE is the first architecture that is (1) provably stable, and (2) universally expressive for basis invariant functions whilst respecting all symmetries of eigenvectors. Besides guaranteed stability, we prove that SPE is at least as expressive as existing methods, and highly capable of counting graph structures. Finally, we evaluate the effectiveness of our method on molecular property prediction, and out-of-distribution generalization tasks, finding improved generalization compared to existing positional encoding methods.

Deep object detection for waterbird monitoring using aerial imagery

Monitoring of colonial waterbird nesting islands is essential to tracking waterbird population trends, which are used for evaluating ecosystem health and informing conservation management decisions. Recently, unmanned aerial vehicles, or drones, have emerged as a viable technology to precisely monitor waterbird colonies. However, manually counting waterbirds from hundreds, or potentially thousands, of aerial images is both difficult and time-consuming. In this work, we present a deep learning pipeline that can be used to precisely detect, count, and monitor waterbirds using aerial imagery collected by a commercial drone. By utilizing convolutional neural network-based object detectors, we show that we can detect 16 classes of waterbird species that are commonly found in colonial nesting islands along the Texas coast. Our experiments using Faster R-CNN and RetinaNet object detectors give mean interpolated average precision scores of 67.9% and 63.1% respectively.