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We derive a new parallel-in-time approach for solving large-scale optimization problems constrained by time-dependent partial differential equations arising from fluid dynamics. The solver involves the use of a block circulant approximation of the original matrices, enabling parallelization-in-time via the use of fast Fourier transforms, and we devise bespoke matrix approximations which may be applied within this framework. These make use of permutations, saddle-point approximations, commutator arguments, as well as inner solvers such as the Uzawa method, Chebyshev semi-iteration, and multigrid. Theoretical results underpin our strategy of applying a block circulant strategy, and numerical experiments demonstrate the effectiveness and robustness of our approach on Stokes and Oseen problems. Noteably, satisfying results for the strong and weak scaling of our methods are provided within a fully parallel architecture.

Annotated datasets are an essential ingredient to train, evaluate, compare and productionalize supervised machine learning models. It is therefore imperative that annotations are of high quality. For their creation, good quality management and thereby reliable quality estimates are needed. Then, if quality is insufficient during the annotation process, rectifying measures can be taken to improve it. Quality estimation is often performed by having experts manually label instances as correct or incorrect. But checking all annotated instances tends to be expensive. Therefore, in practice, usually only subsets are inspected; sizes are chosen mostly without justification or regard to statistical power and more often than not, are relatively small. Basing estimates on small sample sizes, however, can lead to imprecise values for the error rate. Using unnecessarily large sample sizes costs money that could be better spent, for instance on more annotations. Therefore, we first describe in detail how to use confidence intervals for finding the minimal sample size needed to estimate the annotation error rate. Then, we propose applying acceptance sampling as an alternative to error rate estimation We show that acceptance sampling can reduce the required sample sizes up to 50% while providing the same statistical guarantees.

We propose a new approach for non-Cartesian magnetic resonance image reconstruction. While unrolled architectures provide robustness via data-consistency layers, embedding measurement operators in Deep Neural Network (DNN) can become impractical at large scale. Alternative Plug-and-Play (PnP) approaches, where the denoising DNNs are blind to the measurement setting, are not affected by this limitation and have also proven effective, but their highly iterative nature also affects scalability. To address this scalability challenge, we leverage the "Residual-to-Residual DNN series for high-Dynamic range imaging (R2D2)" approach recently introduced in astronomical imaging. R2D2's reconstruction is formed as a series of residual images, iteratively estimated as outputs of DNNs taking the previous iteration's image estimate and associated data residual as inputs. The method can be interpreted as a learned version of the Matching Pursuit algorithm. We demonstrate R2D2 in simulation, considering radial k-space sampling acquisition sequences. Our preliminary results suggest that R2D2 achieves: (i) suboptimal performance compared to its unrolled incarnation R2D2-Net, which is however non-scalable due to the necessary embedding of NUFFT-based data-consistency layers; (ii) superior reconstruction quality to a scalable version of R2D2-Net embedding an FFT-based approximation for data consistency; (iii) superior reconstruction quality to PnP, while only requiring few iterations.

Intelligent vision control systems for surgical robots should adapt to unknown and diverse objects while being robust to system disturbances. Previous methods did not meet these requirements due to mainly relying on pose estimation and feature tracking. We propose a world-model-based deep reinforcement learning framework "Grasp Anything for Surgery" (GAS), that learns a pixel-level visuomotor policy for surgical grasping, enhancing both generality and robustness. In particular, a novel method is proposed to estimate the values and uncertainties of depth pixels for a rigid-link object's inaccurate region based on the empirical prior of the object's size; both depth and mask images of task objects are encoded to a single compact 3-channel image (size: 64x64x3) by dynamically zooming in the mask regions, minimizing the information loss. The learned controller's effectiveness is extensively evaluated in simulation and in a real robot. Our learned visuomotor policy handles: i) unseen objects, including 5 types of target grasping objects and a robot gripper, in unstructured real-world surgery environments, and ii) disturbances in perception and control. Note that we are the first work to achieve a unified surgical control system that grasps diverse surgical objects using different robot grippers on real robots in complex surgery scenes (average success rate: 69%). Our system also demonstrates significant robustness across 6 conditions including background variation, target disturbance, camera pose variation, kinematic control error, image noise, and re-grasping after the gripped target object drops from the gripper. Videos and codes can be found on our project page: //linhongbin.github.io/gas/.

We present a novel synthetically generated multi-modal dataset, SCaRL, to enable the training and validation of autonomous driving solutions. Multi-modal datasets are essential to attain the robustness and high accuracy required by autonomous systems in applications such as autonomous driving. As deep learning-based solutions are becoming more prevalent for object detection, classification, and tracking tasks, there is great demand for datasets combining camera, lidar, and radar sensors. Existing real/synthetic datasets for autonomous driving lack synchronized data collection from a complete sensor suite. SCaRL provides synchronized Synthetic data from RGB, semantic/instance, and depth Cameras; Range-Doppler-Azimuth/Elevation maps and raw data from Radar; and 3D point clouds/2D maps of semantic, depth and Doppler data from coherent Lidar. SCaRL is a large dataset based on the CARLA Simulator, which provides data for diverse, dynamic scenarios and traffic conditions. SCaRL is the first dataset to include synthetic synchronized data from coherent Lidar and MIMO radar sensors. The dataset can be accessed here: //fhr-ihs-sva.pages.fraunhofer.de/asp/scarl/

This paper studies minimax optimization problems defined over infinite-dimensional function classes of overparameterized two-layer neural networks. In particular, we consider the minimax optimization problem stemming from estimating linear functional equations defined by conditional expectations, where the objective functions are quadratic in the functional spaces. We address (i) the convergence of the stochastic gradient descent-ascent algorithm and (ii) the representation learning of the neural networks. We establish convergence under the mean-field regime by considering the continuous-time and infinite-width limit of the optimization dynamics. Under this regime, the stochastic gradient descent-ascent corresponds to a Wasserstein gradient flow over the space of probability measures defined over the space of neural network parameters. We prove that the Wasserstein gradient flow converges globally to a stationary point of the minimax objective at a $O(T^{-1} + \alpha^{-1})$ sublinear rate, and additionally finds the solution to the functional equation when the regularizer of the minimax objective is strongly convex. Here $T$ denotes the time and $\alpha$ is a scaling parameter of the neural networks. In terms of representation learning, our results show that the feature representation induced by the neural networks is allowed to deviate from the initial one by the magnitude of $O(\alpha^{-1})$, measured in terms of the Wasserstein distance. Finally, we apply our general results to concrete examples including policy evaluation, nonparametric instrumental variable regression, asset pricing, and adversarial Riesz representer estimation.

Finding the best solution is a common objective in combinatorial optimization (CO). In practice, directly handling constraints is often challenging, incorporating them into the objective function as the penalties. However, balancing these penalties to achieve the desired solution is time-consuming. Additionally, formulated objective functions and constraints often only approximate real-world scenarios, where the optimal solution is not necessarily the best solution for the original real-world problem. One solution is to obtain (i) penalty-diversified solutions with varying penalty strengths for the former issue and (ii) variation-diversified solutions with different characteristics for the latter issue. Users can then post-select the desired solution from these diverse solutions. However, efficiently finding these diverse solutions is more difficult than identifying one. This study introduces Continual Tensor Relaxation Annealing (CTRA) for unsupervised-learning (UL)-based CO solvers, a computationally efficient framework for finding these diverse solutions in a single training run. The key idea is to leverage representation learning capability to automatically and efficiently learn common representations and parallelization. Numerical experiments show that CTRA enables UL-based solvers to find these diverse solutions much faster than repeatedly running existing UL-based solvers.

This paper presents a novel and efficient wireless channel estimation scheme based on a tapped delay line (TDL) model of wireless signal propagation, where a data-driven machine learning approach is used to estimate the path delays and gains. The key motivation for our novel channel estimation model is to gain environment awareness, i.e., detecting changes in path delays and gains related to interesting objects and events in the field. The estimated channel state provides a more detailed measure to sense the field than the single-tap channel state indicator (CSI) in current OFDM systems. Advantages of this approach also include low computation time and training data requirements, making it suitable for environment awareness applications. We evaluate this model's performance using Matlab's ray-tracing tool under static and dynamic conditions for increased realism instead of the standard evaluation approaches that rely on classical statistical channel models. Our results show that our TDL-based model can accurately estimate the path delays and associated gains for a broad-range of locations and operating conditions. Root-mean-square estimation error was less than $10^{-4}$, or $-40$dB, for SNR $\geq 60$dB in all of our experiments. Our results show that interference of a flying drone on signal multipaths, in a preliminary experiment, can be detected in estimated channel states which, otherwise, remains obscured in conventional CSI.

High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.

In this paper, we propose the joint learning attention and recurrent neural network (RNN) models for multi-label classification. While approaches based on the use of either model exist (e.g., for the task of image captioning), training such existing network architectures typically require pre-defined label sequences. For multi-label classification, it would be desirable to have a robust inference process, so that the prediction error would not propagate and thus affect the performance. Our proposed model uniquely integrates attention and Long Short Term Memory (LSTM) models, which not only addresses the above problem but also allows one to identify visual objects of interests with varying sizes without the prior knowledge of particular label ordering. More importantly, label co-occurrence information can be jointly exploited by our LSTM model. Finally, by advancing the technique of beam search, prediction of multiple labels can be efficiently achieved by our proposed network model.