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Artificial neural networks (ANNs) are powerful machine learning methods used in many modern applications such as facial recognition, machine translation, and cancer diagnostics. A common issue with ANNs is that they usually have millions or billions of trainable parameters, and therefore tend to overfit to the training data. This is especially problematic in applications where it is important to have reliable uncertainty estimates. Bayesian neural networks (BNN) can improve on this, since they incorporate parameter uncertainty. In addition, latent binary Bayesian neural networks (LBBNN) also take into account structural uncertainty by allowing the weights to be turned on or off, enabling inference in the joint space of weights and structures. In this paper, we will consider two extensions to the LBBNN method: Firstly, by using the local reparametrization trick (LRT) to sample the hidden units directly, we get a more computationally efficient algorithm. More importantly, by using normalizing flows on the variational posterior distribution of the LBBNN parameters, the network learns a more flexible variational posterior distribution than the mean field Gaussian. Experimental results show that this improves predictive power compared to the LBBNN method, while also obtaining more sparse networks. We perform two simulation studies. In the first study, we consider variable selection in a logistic regression setting, where the more flexible variational distribution leads to improved results. In the second study, we compare predictive uncertainty based on data generated from two-dimensional Gaussian distributions. Here, we argue that our Bayesian methods lead to more realistic estimates of predictive uncertainty.

There are plenty of applications and analysis for time-independent elliptic partial differential equations in the literature hinting at the benefits of overtesting by using more collocation conditions than the number of basis functions. Overtesting not only reduces the problem size, but is also known to be necessary for stability and convergence of widely used unsymmetric Kansa-type strong-form collocation methods. We consider kernel-based meshfree methods, which is a method of lines with collocation and overtesting spatially, for solving parabolic partial differential equations on surfaces without parametrization. In this paper, we extend the time-independent convergence theories for overtesting techniques to the parabolic equations on smooth and closed surfaces.

Random graphs are increasingly becoming objects of interest for modeling networks in a wide range of applications. Latent position random graph models posit that each node is associated with a latent position vector, and that these vectors follow some geometric structure in the latent space. In this paper, we consider random dot product graphs, in which an edge is formed between two nodes with probability given by the inner product of their respective latent positions. We assume that the latent position vectors lie on an unknown one-dimensional curve and are coupled with a response covariate via a regression model. Using the geometry of the underlying latent position vectors, we propose a manifold learning and graph embedding technique to predict the response variable on out-of-sample nodes, and we establish convergence guarantees for these responses. Our theoretical results are supported by simulations and an application to Drosophila brain data.

In strong line-of-sight millimeter-wave (mmWave) wireless systems, the rank-deficient channel severely hampers spatial multiplexing. To address this inherent deficiency, multiple reconfigurable-intelligent-surfaces (RISs) are introduced in this study to customize the wireless channel. Utilizing the RIS to reshape electromagnetic waves, we theoretically show that a favorable channel with an arbitrary tunable rank and a minimized truncated condition number can be established by elaborately designing the placement and reflection matrix of RISs. Different from existing works on multi-RISs, the number of elements needed for each RIS to combat the path loss and the limited phase control is also considered. On the basis of the proposed channel customization, a joint transmitter-RISs-receiver (Tx-RISs-Rx) design under a hybrid mmWave system is investigated to maximize the spectral efficiency. Using the proposed scheme, the optimal singular value decomposition-based hybrid beamforming at the Tx and Rx can be obtained without matrix decomposition for the digital and analog beamforming. The bottoms of the sub-channel mode in the water-filling algorithm, which are conventionally uncontrollable, are proven to be independently adjustable by RISs. Moreover, the transmit power required for realizing multi-stream transmission is derived. Numerical results are presented to verify our theoretical analysis and exhibit substantial gains over systems without RISs.

In this paper we address the numerical solution of the quadratic optimal transport problem in its dynamical form, the so-called Benamou-Brenier formulation. When solved using interior point methods, the main computational bottleneck is the solution of large saddle point linear systems arising from the associated Newton-Raphson scheme. The main purpose of this paper is to design efficient preconditioners to solve these linear systems via iterative methods. Among the proposed preconditioners, we introduce one based on the partial commutation of the operators that compose the dual Schur complement of these saddle point linear systems, which we refer as $\boldsymbol{B}\boldsymbol{B}$-preconditioner. A series of numerical tests show that the $\boldsymbol{B}\boldsymbol{B}$-preconditioner is the most efficient among those presented, with a CPU-time scaling only slightly more than linearly with respect to the number of unknowns used to discretize the problem.

For solving combinatorial optimisation problems with metaheuristics, different search operators are applied for sampling new solutions in the neighbourhood of a given solution. It is important to understand the relationship between operators for various purposes, e.g., adaptively deciding when to use which operator to find optimal solutions efficiently. However, it is difficult to theoretically analyse this relationship, especially in the complex solution space of combinatorial optimisation problems. In this paper, we propose to empirically analyse the relationship between operators in terms of the correlation between their local optima and develop a measure for quantifying their relationship. The comprehensive analyses on a wide range of capacitated vehicle routing problem benchmark instances show that there is a consistent pattern in the correlation between commonly used operators. Based on this newly proposed local optima correlation metric, we propose a novel approach for adaptively selecting among the operators during the search process. The core intention is to improve search efficiency by preventing wasting computational resources on exploring neighbourhoods where the local optima have already been reached. Experiments on randomly generated instances and commonly used benchmark datasets are conducted. Results show that the proposed approach outperforms commonly used adaptive operator selection methods.

Three-dimensional (3-D) synthetic aperture radar (SAR) is widely used in many security and industrial applications requiring high-resolution imaging of concealed or occluded objects. The ability to resolve intricate 3-D targets is essential to the performance of such applications and depends directly on system bandwidth. However, because high-bandwidth systems face several prohibitive hurdles, an alternative solution is to operate multiple radars at distinct frequency bands and fuse the multiband signals. Current multiband signal fusion methods assume a simple target model and a small number of point reflectors, which is invalid for realistic security screening and industrial imaging scenarios wherein the target model effectively consists of a large number of reflectors. To the best of our knowledge, this study presents the first use of deep learning for multiband signal fusion. The proposed network, called kR-Net, employs a hybrid, dual-domain complex-valued convolutional neural network (CV-CNN) to fuse multiband signals and impute the missing samples in the frequency gaps between subbands. By exploiting the relationships in both the wavenumber domain and wavenumber spectral domain, the proposed framework overcomes the drawbacks of existing multiband imaging techniques for realistic scenarios at a fraction of the computation time of existing multiband fusion algorithms. Our method achieves high-resolution imaging of intricate targets previously impossible using conventional techniques and enables finer resolution capacity for concealed weapon detection and occluded object classification using multiband signaling without requiring more advanced hardware. Furthermore, a fully integrated multiband imaging system is developed using commercially available millimeter-wave (mmWave) radars for efficient multiband imaging.

Multiple instance learning (MIL) is a powerful tool to solve the weakly supervised classification in whole slide image (WSI) based pathology diagnosis. However, the current MIL methods are usually based on independent and identical distribution hypothesis, thus neglect the correlation among different instances. To address this problem, we proposed a new framework, called correlated MIL, and provided a proof for convergence. Based on this framework, we devised a Transformer based MIL (TransMIL), which explored both morphological and spatial information. The proposed TransMIL can effectively deal with unbalanced/balanced and binary/multiple classification with great visualization and interpretability. We conducted various experiments for three different computational pathology problems and achieved better performance and faster convergence compared with state-of-the-art methods. The test AUC for the binary tumor classification can be up to 93.09% over CAMELYON16 dataset. And the AUC over the cancer subtypes classification can be up to 96.03% and 98.82% over TCGA-NSCLC dataset and TCGA-RCC dataset, respectively.

Graph Neural Networks (GNNs) have recently become increasingly popular due to their ability to learn complex systems of relations or interactions arising in a broad spectrum of problems ranging from biology and particle physics to social networks and recommendation systems. Despite the plethora of different models for deep learning on graphs, few approaches have been proposed thus far for dealing with graphs that present some sort of dynamic nature (e.g. evolving features or connectivity over time). In this paper, we present Temporal Graph Networks (TGNs), a generic, efficient framework for deep learning on dynamic graphs represented as sequences of timed events. Thanks to a novel combination of memory modules and graph-based operators, TGNs are able to significantly outperform previous approaches being at the same time more computationally efficient. We furthermore show that several previous models for learning on dynamic graphs can be cast as specific instances of our framework. We perform a detailed ablation study of different components of our framework and devise the best configuration that achieves state-of-the-art performance on several transductive and inductive prediction tasks for dynamic graphs.

We propose a Bayesian convolutional neural network built upon Bayes by Backprop and elaborate how this known method can serve as the fundamental construct of our novel, reliable variational inference method for convolutional neural networks. First, we show how Bayes by Backprop can be applied to convolutional layers where weights in filters have probability distributions instead of point-estimates; and second, how our proposed framework leads with various network architectures to performances comparable to convolutional neural networks with point-estimates weights. In the past, Bayes by Backprop has been successfully utilised in feedforward and recurrent neural networks, but not in convolutional ones. This work symbolises the extension of the group of Bayesian neural networks which encompasses all three aforementioned types of network architectures now.