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Reconfigurable intelligent surface (RIS)-aided terahertz (THz) communications have been regarded as a promising candidate for future 6G networks because of its ultra-wide bandwidth and ultra-low power consumption. However, there exists the beam split problem, especially when the base station (BS) or RIS owns the large-scale antennas, which may lead to serious array gain loss. Therefore, in this paper, we investigate the beam split and beamforming design problems in the THz RIS communications. Specifically, we first analyze the beam split effect caused by different RIS sizes, shapes and deployments. On this basis, we apply the fully connected time delayer phase shifter hybrid beamforming architecture at the BS and deploy distributed RISs to cooperatively mitigate the beam split effect. We aim to maximize the achievable sum rate by jointly optimizing the hybrid analog/digital beamforming, time delays at the BS and reflection coefficients at the RISs. To solve the formulated problem, we first design the analog beamforming and time delays based on different RISs physical directions, and then it is transformed into an optimization problem by jointly optimizing the digital beamforming and reflection coefficients. Next, we propose an alternatively iterative optimization algorithm to deal with it. Specifically, for given the reflection coefficients, we propose an iterative algorithm based on the minimum mean square error technique to obtain the digital beamforming. After, we apply LDR and MCQT methods to transform the original problem to a QCQP, which can be solved by ADMM technique to obtain the reflection coefficients. Finally, the digital beamforming and reflection coefficients are obtained via repeating the above processes until convergence. Simulation results verify that the proposed scheme can effectively alleviate the beam split effect and improve the system capacity.

Rate-Splitting Multiple Access (RSMA) is a robust multiple access scheme for multi-antenna wireless networks. In this work, we study the performance of RSMA in downlink overloaded networks, where the number of transmit antennas is smaller than the number of users. We provide analysis and closed-form solutions for optimal power and rate allocations that maximize max-min fairness when low-complexity precoding schemes are employed. The derived closed-form solutions are used to propose a low-complexity RSMA system design for precoder selection and resource allocation for arbitrary number of users and antennas under perfect Channel State Information at the Transmitter (CSIT). We compare the performance of the proposed design with benchmark designs based on Space Division Multiple Access (SDMA) to show that the proposed low-complexity RSMA design achieves a significantly higher performance gain in overloaded networks.

We propose to use L\'evy {\alpha}-stable distributions for constructing priors for Bayesian inverse problems. The construction is based on Markov fields with stable-distributed increments. Special cases include the Cauchy and Gaussian distributions, with stability indices {\alpha} = 1, and {\alpha} = 2, respectively. Our target is to show that these priors provide a rich class of priors for modelling rough features. The main technical issue is that the {\alpha}-stable probability density functions do not have closed-form expressions in general, and this limits their applicability. For practical purposes, we need to approximate probability density functions through numerical integration or series expansions. Current available approximation methods are either too time-consuming or do not function within the range of stability and radius arguments needed in Bayesian inversion. To address the issue, we propose a new hybrid approximation method for symmetric univariate and bivariate {\alpha}-stable distributions, which is both fast to evaluate, and accurate enough from a practical viewpoint. Then we use approximation method in the numerical implementation of {\alpha}-stable random field priors. We demonstrate the applicability of the constructed priors on selected Bayesian inverse problems which include the deconvolution problem, and the inversion of a function governed by an elliptic partial differential equation. We also demonstrate hierarchical {\alpha}-stable priors in the one-dimensional deconvolution problem. We employ maximum-a-posterior-based estimation at all the numerical examples. To that end, we exploit the limited-memory BFGS and its bounded variant for the estimator.

One cannot make truly fair decisions using integer linear programs unless one controls the selection probabilities of the (possibly many) optimal solutions. For this purpose, we propose a unified framework when binary decision variables represent agents with dichotomous preferences, who only care about whether they are selected in the final solution. We develop several general-purpose algorithms to fairly select optimal solutions, for example, by maximizing the Nash product or the minimum selection probability, or by using a random ordering of the agents as a selection criterion (Random Serial Dictatorship). As such, we embed the black-box procedure of solving an integer linear program into a framework that is explainable from start to finish. Moreover, we study the axiomatic properties of the proposed methods by embedding our framework into the rich literature of cooperative bargaining and probabilistic social choice. Lastly, we evaluate the proposed methods on a specific application, namely kidney exchange. We find that while the methods maximizing the Nash product or the minimum selection probability outperform the other methods on the evaluated welfare criteria, methods such as Random Serial Dictatorship perform reasonably well in computation times that are similar to those of finding a single optimal solution.

A pooling operation is essential for effective graph-level representation learning, where the node drop pooling has become one mainstream graph pooling technology. However, current node drop pooling methods usually keep the top-k nodes according to their significance scores, which ignore the graph diversity in terms of the node features and the graph structures, thus resulting in suboptimal graph-level representations. To address the aforementioned issue, we propose a novel plug-and-play score scheme and refer to it as MID, which consists of a \textbf{M}ultidimensional score space with two operations, \textit{i.e.}, fl\textbf{I}pscore and \textbf{D}ropscore. Specifically, the multidimensional score space depicts the significance of nodes through multiple criteria; the flipscore encourages the maintenance of dissimilar node features; and the dropscore forces the model to notice diverse graph structures instead of being stuck in significant local structures. To evaluate the effectiveness of our proposed MID, we perform extensive experiments by applying it to a wide variety of recent node drop pooling methods, including TopKPool, SAGPool, GSAPool, and ASAP. Specifically, the proposed MID can efficiently and consistently achieve about 2.8\% average improvements over the above four methods on seventeen real-world graph classification datasets, including four social datasets (IMDB-BINARY, IMDB-MULTI, REDDIT-BINARY, and COLLAB), and thirteen biochemical datasets (D\&D, PROTEINS, NCI1, MUTAG, PTC-MR, NCI109, ENZYMES, MUTAGENICITY, FRANKENSTEIN, HIV, BBBP, TOXCAST, and TOX21). Code is available at~\url{//github.com/whuchuang/mid}.

A lattice of integers is the collection of all linear combinations of a set of vectors for which all entries of the vectors are integers and all coefficients in the linear combinations are also integers. Lattice reduction refers to the problem of finding a set of vectors in a given lattice such that the collection of all integer linear combinations of this subset is still the entire original lattice and so that the Euclidean norms of the subset are reduced. The present paper proposes simple, efficient iterations for lattice reduction which are guaranteed to reduce the Euclidean norms of the basis vectors (the vectors in the subset) monotonically during every iteration. Each iteration selects the basis vector for which projecting off (with integer coefficients) the components of the other basis vectors along the selected vector minimizes the Euclidean norms of the reduced basis vectors. Each iteration projects off the components along the selected basis vector and efficiently updates all information required for the next iteration to select its best basis vector and perform the associated projections.

Pre-trained language models have recently emerged as a powerful tool for fine-tuning a variety of language tasks. Ideally, when models are pre-trained on large amount of data, they are expected to gain implicit knowledge. In this paper, we investigate the ability of pre-trained language models to generalize to different non-language tasks. In particular, we test them on tasks from different domains such as computer vision, reasoning on hierarchical data, and protein fold prediction. The four pre-trained models that we used, T5, BART, BERT, and GPT-2 achieve outstanding results. They all have similar performance and they outperform transformers that are trained from scratch by a large margin. For instance, pre-trained language models perform better on the Listops dataset, with an average accuracy of 58.7\%, compared to transformers trained from scratch, which have an average accuracy of 29.0\%. The significant improvement demonstrated across three types of datasets suggests that pre-training on language helps the models to acquire general knowledge, bringing us a step closer to general AI. We also showed that reducing the number of parameters in pre-trained language models does not have a great impact as the performance drops slightly when using T5-Small instead of T5-Base. In fact, when using only 2\% of the parameters, we achieved a great improvement compared to training from scratch. Finally, in contrast to prior work, we find out that using pre-trained embeddings for the input layer is necessary to achieve the desired results.

Stochastic optimization has found wide applications in minimizing objective functions in machine learning, which motivates a lot of theoretical studies to understand its practical success. Most of existing studies focus on the convergence of optimization errors, while the generalization analysis of stochastic optimization is much lagging behind. This is especially the case for nonconvex and nonsmooth problems often encountered in practice. In this paper, we initialize a systematic stability and generalization analysis of stochastic optimization on nonconvex and nonsmooth problems. We introduce novel algorithmic stability measures and establish their quantitative connection on the gap between population gradients and empirical gradients, which is then further extended to study the gap between the Moreau envelope of the empirical risk and that of the population risk. To our knowledge, these quantitative connection between stability and generalization in terms of either gradients or Moreau envelopes have not been studied in the literature. We introduce a class of sampling-determined algorithms, for which we develop bounds for three stability measures. Finally, we apply these discussions to derive error bounds for stochastic gradient descent and its adaptive variant, where we show how to achieve an implicit regularization by tuning the step sizes and the number of iterations.

This paper presents the vision of multi-band communication networks (MBN) in 6G, where optical and TeraHertz (THz) transmissions will coexist with the conventional radio frequency (RF) spectrum. This paper will first pin-point the fundamental challenges in MBN architectures at the PHYsical (PHY) and Medium Access (MAC) layer, such as unique channel propagation and estimation issues, user offloading and resource allocation, multi-band transceiver design and antenna systems, mobility and handoff management, backhauling, etc. We then perform a quantitative performance assessment of the two fundamental MBN architectures, i.e., {stand-alone MBN} and {integrated MBN} considering critical factors like achievable rate, and capital/operational deployment cost. {Our results show that stand-alone deployment is prone to higher capital and operational expenses for a predefined data rate requirement. Stand-alone deployment, however, offers flexibility and enables controlling the number of access points in different transmission bands.} In addition, we propose a molecular absorption-aware user offloading metric for MBNs and demonstrate its performance gains over conventional user offloading schemes. Finally, open research directions are presented.

Behaviors of the synthetic characters in current military simulations are limited since they are generally generated by rule-based and reactive computational models with minimal intelligence. Such computational models cannot adapt to reflect the experience of the characters, resulting in brittle intelligence for even the most effective behavior models devised via costly and labor-intensive processes. Observation-based behavior model adaptation that leverages machine learning and the experience of synthetic entities in combination with appropriate prior knowledge can address the issues in the existing computational behavior models to create a better training experience in military training simulations. In this paper, we introduce a framework that aims to create autonomous synthetic characters that can perform coherent sequences of believable behavior while being aware of human trainees and their needs within a training simulation. This framework brings together three mutually complementary components. The first component is a Unity-based simulation environment - Rapid Integration and Development Environment (RIDE) - supporting One World Terrain (OWT) models and capable of running and supporting machine learning experiments. The second is Shiva, a novel multi-agent reinforcement and imitation learning framework that can interface with a variety of simulation environments, and that can additionally utilize a variety of learning algorithms. The final component is the Sigma Cognitive Architecture that will augment the behavior models with symbolic and probabilistic reasoning capabilities. We have successfully created proof-of-concept behavior models leveraging this framework on realistic terrain as an essential step towards bringing machine learning into military simulations.