Osteoporosis is a widespread and chronic metabolic bone disease that often remains undiagnosed and untreated due to limited access to bone mineral density (BMD) tests like Dual-energy X-ray absorptiometry (DXA). In response to this challenge, current advancements are pivoting towards detecting osteoporosis by examining alternative indicators from peripheral bone areas, with the goal of increasing screening rates without added expenses or time. In this paper, we present a method to predict osteoporosis using hand and wrist X-ray images, which are both widely accessible and affordable, though their link to DXA-based data is not thoroughly explored. We employ a sophisticated image segmentation model that utilizes a mixture of probabilistic U-Net decoders, specifically designed to capture predictive uncertainty in the segmentation of the ulna, radius, and metacarpal bones. This model is formulated as an optimal transport (OT) problem, enabling it to handle the inherent uncertainties in image segmentation more effectively. Further, we adopt a self-supervised learning (SSL) approach to extract meaningful representations without the need for explicit labels, and move on to classify osteoporosis in a supervised manner. Our method is evaluated on a dataset with 192 individuals, cross-referencing their verified osteoporosis conditions against the standard DXA test. With a notable classification score, this integration of uncertainty-aware segmentation and self-supervised learning represents a pioneering effort in leveraging vision-based techniques for the early detection of osteoporosis from peripheral skeletal sites.

Multivariate time series is prevalent in many scientific and industrial domains. Modeling multivariate signals is challenging due to their long-range temporal dependencies and intricate interactions--both direct and indirect. To confront these complexities, we introduce a method of representing multivariate signals as nodes in a graph with edges indicating interdependency between them. Specifically, we leverage graph neural networks (GNN) and attention mechanisms to efficiently learn the underlying relationships within the time series data. Moreover, we suggest employing hierarchical signal decompositions running over the graphs to capture multiple spatial dependencies. The effectiveness of our proposed model is evaluated across various real-world benchmark datasets designed for long-term forecasting tasks. The results consistently showcase the superiority of our model, achieving an average 23\% reduction in mean squared error (MSE) compared to existing models.

Graph neural networks (GNNs) have become compelling models designed to perform learning and inference on graph-structured data. However, little work has been done to understand the fundamental limitations of GNNs for scaling to larger graphs and generalizing to out-of-distribution (OOD) inputs. In this paper, we use a random graph generator to systematically investigate how the graph size and structural properties affect the predictive performance of GNNs. We present specific evidence that the average node degree is a key feature in determining whether GNNs can generalize to unseen graphs, and that the use of multiple node update functions can improve the generalization performance of GNNs when dealing with graphs of multimodal degree distributions. Accordingly, we propose a multi-module GNN framework that allows the network to adapt flexibly to new graphs by generalizing a single canonical nonlinear transformation over aggregated inputs. Our results show that the multi-module GNNs improve the OOD generalization on a variety of inference tasks in the direction of diverse structural features.

Neurons in the brain are complex machines with distinct functional compartments that interact nonlinearly. In contrast, neurons in artificial neural networks abstract away this complexity, typically down to a scalar activation function of a weighted sum of inputs. Here we emulate more biologically realistic neurons by learning canonical activation functions with two input arguments, analogous to basal and apical dendrites. We use a network-in-network architecture where each neuron is modeled as a multilayer perceptron with two inputs and a single output. This inner perceptron is shared by all units in the outer network. Remarkably, the resultant nonlinearities often produce soft XOR functions, consistent with recent experimental observations about interactions between inputs in human cortical neurons. When hyperparameters are optimized, networks with these nonlinearities learn faster and perform better than conventional ReLU nonlinearities with matched parameter counts, and they are more robust to natural and adversarial perturbations.