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Quadratic minimization problems with orthogonality constraints (QMPO) play an important role in many applications of science and engineering. However, some existing methods may suffer from low accuracy or heavy workload for large-scale QMPO. Krylov subspace methods are popular for large-scale optimization problems. In this work, we propose a block Lanczos method for solving the large-scale QMPO. In the proposed method, the original problem is projected into a small-sized one, and the Riemannian Trust-Region method is employed to solve the reduced QMPO. Convergence results on the optimal solution, the optimal objective function value, the multiplier and the KKT error are established. Moreover, we give the convergence speed of optimal solution, and show that if the block Lanczos process terminates, then an exact KKT solution is derived. Numerical experiments illustrate the numerical behavior of the proposed algorithm, and demonstrate that it is more powerful than many state-of-the-art algorithms for large-scale quadratic minimization problems with orthogonality constraints.

Limited intra-session information is the performance bottleneck of the early GNN based SBR models. Therefore, some GNN based SBR models have evolved to introduce additional inter-session information to facilitate the next-item prediction. However, we found that the introduction of inter-session information may bring interference to these models. The possible reasons are twofold. First, inter-session dependencies are not differentiated at the factor-level. Second, measuring inter-session weight by similarity is not enough. In this paper, we propose DEISI to solve the problems. For the first problem, DEISI differentiates the types of inter-session dependencies at the factor-level with the help of DRL technology. For the second problem, DEISI introduces stability as a new metric for weighting inter-session dependencies together with the similarity. Moreover, CL is used to improve the robustness of the model. Extensive experiments on three datasets show the superior performance of the DEISI model compared with the state-of-the-art models.

Session-based recommendation systems(SBRS) are more suitable for the current e-commerce and streaming media recommendation scenarios and thus have become a hot topic. The data encountered by SBRS is typically highly sparse, which also serves as one of the bottlenecks limiting the accuracy of recommendations. So Contrastive Learning(CL) is applied in SBRS owing to its capability of improving embedding learning under the condition of sparse data. However, existing CL strategies are limited in their ability to enforce finer-grained (e.g., factor-level) comparisons and, as a result, are unable to capture subtle differences between instances. More than that, these strategies usually use item or segment dropout as a means of data augmentation which may result in sparser data and thus ineffective self-supervised signals. By addressing the two aforementioned limitations, we introduce a novel multi-granularity CL framework. Specifically, two extra augmented embedding convolution channels with different granularities are constructed and the embeddings learned by them are compared with those learned from original view to complete the CL tasks. At factor-level, we employ Disentangled Representation Learning to obtain finer-grained data(e.g. factor-level embeddings), with which we can construct factor-level convolution channels. At item-level, the star graph is deployed as the augmented data and graph convolution on it can ensure the effectiveness of self-supervised signals. Compare the learned embeddings of these two views with the learned embeddings of the basic view to achieve CL at two granularities. Finally, the more precise item-level and factor-level embeddings obtained are referenced to generate personalized recommendations for the user. The proposed model is validated through extensive experiments on two benchmark datasets, showcasing superior performance compared to existing methods.

In recent years, the use of large convolutional kernels has become popular in designing convolutional neural networks due to their ability to capture long-range dependencies and provide large receptive fields. However, the increase in kernel size also leads to a quadratic growth in the number of parameters, resulting in heavy computation and memory requirements. To address this challenge, we propose a neighborhood attention (NA) module that upgrades the standard convolution with a self-attention mechanism. The NA module efficiently extracts long-range dependencies in a sliding window pattern, thereby achieving similar performance to large convolutional kernels but with fewer parameters. Building upon the NA module, we propose a lightweight single image super-resolution (SISR) network named TCSR. Additionally, we introduce an enhanced feed-forward network (EFFN) in TCSR to improve the SISR performance. EFFN employs a parameter-free spatial-shift operation for efficient feature aggregation. Our extensive experiments and ablation studies demonstrate that TCSR outperforms existing lightweight SISR methods and achieves state-of-the-art performance. Our codes are available at \url{https://github.com/Aitical/TCSR}., Comment: 9 pages, 9 figures

Intelligent wireless networks have long been expected to have self-configuration and self-optimization capabilities to adapt to various environments and demands. In this paper, we develop a novel distributed hierarchical deep reinforcement learning (DHDRL) framework with two-tier control networks in different timescales to optimize the long-term spectrum efficiency (SE) of the downlink cell-free multiple-input single-output (MISO) network, consisting of multiple distributed access points (AP) and user terminals (UT). To realize the proposed two-tier control strategy, we decompose the optimization problem into two sub-problems, AP-UT association (AUA) as well as beamforming and power allocation (BPA), resulting in a Markov decision process (MDP) and Partially Observable MDP (POMDP). The proposed method consists of two neural networks. At the system level, a distributed high-level neural network is introduced to optimize wireless network structure on a large timescale. While at the link level, a distributed low-level neural network is proposed to mitigate inter-AP interference and improve the transmission performance on a small timescale. Numerical results show that our method is effective for high-dimensional problems, in terms of spectrum efficiency, signaling overhead as well as satisfaction probability, and generalize well to diverse multi-object problems., Comment: The paper has some updated

This paper investigates downlink power adaptation for the suborbital node in suborbital-ground communication systems, which are subject to extremely high reliability and ultra-low latency communications requirements. The problem is formulated as a power threshold-minimization problem, where interference from satellites is modeled as an accumulation of stochastic point processes on different orbit planes, and hybrid beamforming (HBF) is considered. To ensure Quality of Service (QoS) constraints, the finite blocklength regime is adopted. Numerical results show that the required transmit power of the suborbital node decreases as the elevation angle at the receiving station increases.

Graphic layout designs play an essential role in visual communication. Yet handcrafting layout designs is skill-demanding, time-consuming, and non-scalable to batch production. Generative models emerge to make design automation scalable but it remains non-trivial to produce designs that comply with designers' multimodal desires, i.e., constrained by background images and driven by foreground content. We propose LayoutDETR that inherits the high quality and realism from generative modeling, while reformulating content-aware requirements as a detection problem: we learn to detect in a background image the reasonable locations, scales, and spatial relations for multimodal foreground elements in a layout. Our solution sets a new state-of-the-art performance for layout generation on public benchmarks and on our newly-curated ad banner dataset. We integrate our solution into a graphical system that facilitates user studies, and show that users prefer our designs over baselines by significant margins. Code, models, dataset, and demos are available at https://github.com/salesforce/LayoutDETR., Comment: Accepted to ECCV'24

Randomized block Kaczmraz method plays an important role in solving large-scale linear system. One of the key points of this type of methods is how to effectively select working rows. However, in most of the state-of-the-art randomized block Kaczmarz-type methods, one has to scan all the rows of the coefficient matrix in advance for computing probabilities or paving, or to compute the residual vector of the linear system in each iteration to determine the working rows. Thus, we have to access all the rows of the data matrix in these methods, which are unfavorable for big-data problems. Moreover, to the best of our knowledge, how to efficiently choose working rows in randomized block Kaczmarz-type methods for multiple linear systems is still an open problem. In order to deal with these problems, we propose semi-randomized block Kaczmarz methods with simple random sampling for linear systems with single and multiple right-hand sides, respectively. In these methods, there is no need to scan or pave all the rows of the coefficient matrix, nor to compute probabilities and the residual vector of the linear system in each step. Specifically, one can update all the solutions of a large-scale linear system with multiple right-hand sides simultaneously. The convergence of the proposed methods is considered. Numerical experiments on both real-world and synthetic data sets show that the proposed methods are superior to many state-of-the-art randomized Kaczmarz-type methods for large-scale linear systems.

Trust-region subproblem (TRS) is an important problem arising in many applications such as numerical optimization, Tikhonov regularization of ill-posed problems, and constrained eigenvalue problems. In recent decades, extensive works focus on how to solve the trust-region subproblem efficiently. To the best of our knowledge, there are few results on perturbation analysis of the trust-region subproblem. In order to fill in this gap, we focus on first-order perturbation theory of the trust-region subproblem. The main contributions of this paper are three-fold. First, suppose that the TRS is in \emph{easy case}, we give a sufficient condition under which the perturbed TRS is still in easy case. Second, with the help of the structure of the TRS and the classical eigenproblem perturbation theory, we perform first-order perturbation analysis on the Lagrange multiplier and the solution of the TRS, and define their condition numbers. Third, we point out that the solution and the Lagrange multiplier could be well-conditioned even if TRS is in {\it nearly hard case}. The established results are computable, and are helpful to evaluate ill-conditioning of the TRS problem beforehand. Numerical experiments show the sharpness of the established bounds and the effectiveness of the proposed strategies.

Natural language understanding (NLU) has two core tasks: intent classification and slot filling. The success of pre-training language models resulted in a significant breakthrough in the two tasks. One of the promising solutions called BERT can jointly optimize the two tasks. We note that BERT-based models convert each complex token into multiple sub-tokens by wordpiece algorithm, which generates a mismatch between the lengths of the tokens and the labels. This leads to BERT-based models do not do well in label prediction which limits model performance improvement. Many existing models can be compatible with this issue but some hidden semantic information is discarded in the fine-tuning process. We address the problem by introducing a novel joint method on top of BERT which explicitly models the multiple sub-tokens features after wordpiece tokenization, thereby contributing to the two tasks. Our method can well extract the contextual features from complex tokens by the proposed sub-words attention adapter (SAA), which preserves overall utterance information. Additionally, we propose an intent attention adapter (IAA) to obtain the full sentence features to aid users to predict intent. Experimental results confirm that our proposed model is significantly improved on two public benchmark datasets. In particular, the slot filling F1 score is improved from 96.1 to 98.2 (2.1% absolute) on the Airline Travel Information Systems (ATIS) dataset.

We present BotSIM, a data-efficient end-to-end Bot SIMulation toolkit for commercial text-based task-oriented dialog (TOD) systems. BotSIM consists of three major components: 1) a Generator that can infer semantic-level dialog acts and entities from bot definitions and generate user queries via model-based paraphrasing; 2) an agenda-based dialog user Simulator (ABUS) to simulate conversations with the dialog agents; 3) a Remediator to analyze the simulated conversations, visualize the bot health reports and provide actionable remediation suggestions for bot troubleshooting and improvement. We demonstrate BotSIM's effectiveness in end-to-end evaluation, remediation and multi-intent dialog generation via case studies on two commercial bot platforms. BotSIM's "generation-simulation-remediation" paradigm accelerates the end-to-end bot evaluation and iteration process by: 1) reducing manual test cases creation efforts; 2) enabling a holistic gauge of the bot in terms of NLU and end-to-end performance via extensive dialog simulation; 3) improving the bot troubleshooting process with actionable suggestions. A demo of our system can be found at https://tinyurl.com/mryu74cd and a demo video at https://youtu.be/qLi5iSoly30. We have open-sourced the toolkit at https://github.com/salesforce/botsim, Comment: Paper accepted by the EMNLP 2022 System Demo Track; We have open-sourced the toolkit at https://github.com/salesforce/botsim

In this paper, we adopt a three-stage based uplink channel estimation protocol with reduced pilot overhead for an reconfigurable intelligent surface (RIS)-aided multi-user (MU) millimeter wave (mmWave) communication system, in which both the base station (BS) and the RIS are equipped with a uniform planar array (UPA). Specifically, in Stage I, the channel state information (CSI) of a typical user is estimated. To address the power leakage issue for the common angles-of-arrival (AoAs) estimation in this stage, we develop a low-complexity one-dimensional search method. In Stage II, a re-parameterized common BS-RIS channel is constructed with the estimated information from Stage I to estimate other users' CSI. In Stage III, only the rapidly varying channel gains need to re-estimated. Furthermore, the proposed method can be extended to multi-antenna UPA-type users, by decomposing the estimation of a multi-antenna channel with $J$ scatterers into estimating $J$ single-scatterer channels for a virtual single-antenna user. An orthogonal matching pursuit (OMP)-based method is proposed to estimate the angles-of-departure (AoDs) at the users. Simulation results demonstrate that the proposed algorithm significantly achieves high channel estimation accuracy, which approaches the genie-aided upper bound in the high SNR regime., Comment: 20 pages, 7 figures, 4 Appendices

The main objective of this paper is to answer the questions posed by Robinson and Sadowski [21, p. 505, Comm. Math. Phys., 2010]{[RS3]} for the Navier-Stokes equations. Firstly, we prove that the upper box dimension of the potential singular points set $\mathcal{S}$ of suitable weak solution $u$ belonging in $ L^{q}(0,T;L^{p}(\mathbb{R}^{3}))$ for $1\leq\frac{2}{q}+\frac{ 3}{p}\leq\frac32$ with $2\leq q<\infty$ and $2

The generalized Lanczos trust-region (GLTR) method is one of the most popular approaches for solving large-scale trust-region subproblem (TRS). Recently, Jia and Wang [Z. Jia and F. Wang, \emph{SIAM J. Optim., 31 (2021), pp. 887--914}] considered the convergence of this method and established some {\it a prior} error bounds on the residual, the solution and the Largrange multiplier. In this paper, we revisit the convergence of the GLTR method and try to improve these bounds. First, we establish a sharper upper bound on the residual. Second, we give a new bound on the distance between the approximation and the exact solution, and show that the convergence of the approximation has nothing to do with the associated spectral separation. Third, we present some non-asymptotic bounds for the convergence of the Largrange multiplier, and define a factor that plays an important role on the convergence of the Largrange multiplier. Numerical experiments demonstrate the effectiveness of our theoretical results., Comment: 28 pages, 17 figures

We propose a method to detect individualized highlights for users on given target videos based on their preferred highlight clips marked on previous videos they have watched. Our method explicitly leverages the contents of both the preferred clips and the target videos using pre-trained features for the objects and the human activities. We design a multi-head attention mechanism to adaptively weigh the preferred clips based on their object- and human-activity-based contents, and fuse them using these weights into a single feature representation for each user. We compute similarities between these per-user feature representations and the per-frame features computed from the desired target videos to estimate the user-specific highlight clips from the target videos. We test our method on a large-scale highlight detection dataset containing the annotated highlights of individual users. Compared to current baselines, we observe an absolute improvement of 2-4% in the mean average precision of the detected highlights. We also perform extensive ablation experiments on the number of preferred highlight clips associated with each user as well as on the object- and human-activity-based feature representations to validate that our method is indeed both content-based and user-specific., Comment: 14 pages, 5 figures, 7 tables

We studied the cloud-cloud collision candidate G323.18+0.15 based on signatures of induced filaments, clumps, and star formation. We used archival molecular spectrum line data from the SEDIGISM $^{13}$CO($J$\,=\,2--1) survey, from the Mopra southern Galactic plane CO survey, and infrared to radio data from the GLIMPSE, MIPS, Hi-GAL, and SGPS surveys. Our new result shows that the G323.18+0.15 complex is 3.55kpc away from us and consists of three cloud components, G323.18a, G323.18b, and G323.18c. G323.18b shows a perfect U-shape structure, which can be fully complemented by G323.18a, suggesting a collision between G323.18a and the combined G323.18bc filamentary structure. One dense compressed layer (filament) is formed at the bottom of G323.18b, where we detect a greatly increased velocity dispersion. The bridge with an intermediate velocity in a position-velocity diagram appears between G323.18a and G323.18b, which corresponds to the compressed layer. G323.18a plus G323.18b as a whole are probably not gravitationally bound. This indicates that high-mass star formation in the compressed layer may have been caused by an accidental event. The column density in the compressed layer of about $1.36 \times 10^{22}$cm$^{-2}$ and most of the dense clumps and high-mass stars are located there. The average surface density of classI and classII young stellar objects (YSOs) inside the G323.18+0.15 complex is much higher than the density in the surroundings. The timescale of the collision between G323.18a and G323.18b is $1.59$Myr. This is longer than the typical lifetime of classI YSOs and is comparable to the lifetime of classII YSOs.