Solving differential equations is a critical challenge across a host of domains. While many software packages efficiently solve these equations using classical numerical approaches, there has been less effort in developing a library for researchers interested in solving such systems using neural networks. With PyTorch as its backend, NeuroDiffEq is a software library that exploits neural networks to solve differential equations. In this paper, we highlight the latest features of the NeuroDiffEq library since its debut. We show that NeuroDiffEq can solve complex boundary value problems in arbitrary dimensions, tackle boundary conditions at infinity, and maintain flexibility for dynamic injection at runtime.

Offline meta-reinforcement learning (meta-RL) methods, which adapt to unseen target tasks with prior experience, are essential in robot control tasks. Current methods typically utilize task contexts and skills as prior experience, where task contexts are related to the information within each task and skills represent a set of temporally extended actions for solving subtasks. However, these methods still suffer from limited performance when adapting to unseen target tasks, mainly because the learned prior experience lacks generalization, i.e., they are unable to extract effective prior experience from meta-training tasks by exploration and learning of continuous latent spaces. We propose a framework called decoupled meta-reinforcement learning (DCMRL), which (1) contrastively restricts the learning of task contexts through pulling in similar task contexts within the same task and pushing away different task contexts of different tasks, and (2) utilizes a Gaussian quantization variational autoencoder (GQ-VAE) for clustering the Gaussian distributions of the task contexts and skills respectively, and decoupling the exploration and learning processes of their spaces. These cluster centers which serve as representative and discrete distributions of task context and skill are stored in task context codebook and skill codebook, respectively. DCMRL can acquire generalizable prior experience and achieve effective adaptation to unseen target tasks during the meta-testing phase. Experiments in the navigation and robot manipulation continuous control tasks show that DCMRL is more effective than previous meta-RL methods with more generalizable prior experience.

Accurate understanding and prediction of human behaviors are critical prerequisites for autonomous vehicles, especially in highly dynamic and interactive scenarios such as intersections in dense urban areas. In this work, we aim at identifying crossing pedestrians and predicting their future trajectories. To achieve these goals, we not only need the context information of road geometry and other traffic participants but also need fine-grained information of the human pose, motion and activity, which can be inferred from human keypoints. In this paper, we propose a novel multi-task learning framework for pedestrian crossing action recognition and trajectory prediction, which utilizes 3D human keypoints extracted from raw sensor data to capture rich information on human pose and activity. Moreover, we propose to apply two auxiliary tasks and contrastive learning to enable auxiliary supervisions to improve the learned keypoints representation, which further enhances the performance of major tasks. We validate our approach on a large-scale in-house dataset, as well as a public benchmark dataset, and show that our approach achieves state-of-the-art performance on a wide range of evaluation metrics. The effectiveness of each model component is validated in a detailed ablation study.

The K-means algorithm is arguably the most popular data clustering method, commonly applied to processed datasets in some "feature spaces", as is in spectral clustering. Highly sensitive to initializations, however, K-means encounters a scalability bottleneck with respect to the number of clusters K as this number grows in big data applications. In this work, we promote a closely related model called K-indicators model and construct an efficient, semi-convex-relaxation algorithm that requires no randomized initializations. We present extensive empirical results to show advantages of the new algorithm when K is large. In particular, using the new algorithm to start the K-means algorithm, without any replication, can significantly outperform the standard K-means with a large number of currently state-of-the-art random replications.

Compressed sensing in MRI enables high subsampling factors while maintaining diagnostic image quality. This technique enables shortened scan durations and/or improved image resolution. Further, compressed sensing can increase the diagnostic information and value from each scan performed. Overall, compressed sensing has significant clinical impact in improving the diagnostic quality and patient experience for imaging exams. However, a number of challenges exist when moving compressed sensing from research to the clinic. These challenges include hand-crafted image priors, sensitive tuning parameters, and long reconstruction times. Data-driven learning provides a solution to address these challenges. As a result, compressed sensing can have greater clinical impact. In this tutorial, we will review the compressed sensing formulation and outline steps needed to transform this formulation to a deep learning framework. Supplementary open source code in python will be used to demonstrate this approach with open databases. Further, we will discuss considerations in applying data-driven compressed sensing in the clinical setting.