William W. Lu

Yinan Huang, William Lu, Joshua Robinson et al.

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. Our code is available at \url{https://github.com/Graph-COM/SPE}.

Krish Kabra, Alexander Xiong, Wenbin Li et al.

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.

Chentian Li, Chi Ma, William W. Lu

The shapes and morphology of the organs and tissues are important prior knowledge in medical imaging recognition and segmentation. The morphological operation is a well-known method for morphological feature extraction. As the morphological operation is performed well in hand-crafted image segmentation techniques, it is also promising to design an approach to approximate morphological operation in the convolutional networks. However, using the traditional convolutional neural network as a black-box is usually hard to specify the morphological operation action. Here, we introduced a 3D morphological operation residual block to extract morphological features in end-to-end deep learning models for semantic segmentation. This study proposed a novel network block architecture that embedded the morphological operation as an infinitely strong prior in the convolutional neural network. Several 3D deep learning models with the proposed morphological operation block were built and compared in different medical imaging segmentation tasks. Experimental results showed the proposed network achieved a relatively higher performance in the segmentation tasks comparing with the conventional approach. In conclusion, the novel network block could be easily embedded in traditional networks and efficiently reinforce the deep learning models for medical imaging segmentation.