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We study the fundamental limits to the expressive power of neural networks. Given two sets $F$, $G$ of real-valued functions, we first prove a general lower bound on how well functions in $F$ can be approximated in $L^p(\mu)$ norm by functions in $G$, for any $p \geq 1$ and any probability measure $\mu$. The lower bound depends on the packing number of $F$, the range of $F$, and the fat-shattering dimension of $G$. We then instantiate this bound to the case where $G$ corresponds to a piecewise-polynomial feed-forward neural network, and describe in details the application to two sets $F$: H{\"o}lder balls and multivariate monotonic functions. Beside matching (known or new) upper bounds up to log factors, our lower bounds shed some light on the similarities or differences between approximation in $L^p$ norm or in sup norm, solving an open question by DeVore et al. (2021). Our proof strategy differs from the sup norm case and uses a key probability result of Mendelson (2002).

This work considers mitigation of information leakage between communication and sensing operations in joint communication and sensing systems. Specifically, a discrete memoryless state-dependent broadcast channel model is studied in which (i) the presence of feedback enables a transmitter to simultaneously achieve reliable communication and channel state estimation; (ii) one of the receivers is treated as an eavesdropper whose state should be estimated but which should remain oblivious to a part of the transmitted information. The model abstracts the challenges behind security for joint communication and sensing if one views the channel state as a characteristic of the receiver, e.g., its location. For independent identically distributed (i.i.d.) states, perfect output feedback, and when part of the transmitted message should be kept secret, a partial characterization of the secrecy-distortion region is developed. The characterization is exact when the broadcast channel is either physically-degraded or reversely-physically-degraded. The characterization is also extended to the situation in which the entire transmitted message should be kept secret. The benefits of a joint approach compared to separation-based secure communication and state-sensing methods are illustrated with a binary joint communication and sensing model.

We consider the problem of kernel classification. Works on kernel regression have shown that the rate of decay of the prediction error with the number of samples for a large class of data-sets is well characterized by two quantities: the capacity and source of the data-set. In this work, we compute the decay rates for the misclassification (prediction) error under the Gaussian design, for data-sets satisfying source and capacity assumptions. We derive the rates as a function of the source and capacity coefficients for two standard kernel classification settings, namely margin-maximizing Support Vector Machines (SVM) and ridge classification, and contrast the two methods. As a consequence, we find that the known worst-case rates are loose for this class of data-sets. Finally, we show that the rates presented in this work are also observed on real data-sets.

Cell-free massive MIMO is a variant of multiuser MIMO and massive MIMO, in which the total number of antennas $LM$ is distributed among the $L$ remote radio units (RUs) in the system, enabling macrodiversity and joint processing. Due to pilot contamination and system scalability, each RU can only serve a limited number of users. Obtaining the optimal number of users simultaneously served on one resource block (RB) by the $L$ RUs regarding the sum spectral efficiency (SE) is not a simple challenge though, as many of the system parameters are intertwined. For example, the dimension $\tau_p$ of orthogonal Demodulation Reference Signal (DMRS) pilots limits the number of users that an RU can serve. Thus, depending on $\tau_p$, the optimal user load yielding the maximum sum SE will vary. Another key parameter is the users' uplink transmit power $P^{\rm ue}_{\rm tx}$, where a trade-off between users in outage, interference and energy inefficiency exists. We study the effect of multiple parameters in cell-free massive MIMO on the sum SE and user outage, as well as the performance of different levels of RU antenna distribution. We provide extensive numerical investigations to illuminate the behavior of the system SE with respect to the various parameters, including the effect of the system load, i.e., the number of active users to be served on any RB. The results show that in general a system with many RUs and few RU antennas yields the largest sum SE, where the benefits of distributed antennas reduce in very dense networks.

Unmanned aerial vehicle (UAV)-enabled integrated sensing and communication (ISAC) has attracted growing research interests towards sixth-generation (6G) wireless networks, in which UAVs are exploited as aerial wireless platforms to provide better coverage and enhanced sensing and communication (S\&C) services. However, due to the UAVs' size, weight, and power (SWAP) constraints, controllable mobility, and strong line-of-sight (LoS) air-ground channels, the UAV-enabled ISAC introduces both new opportunities and challenges. This article provides an overview on UAV-enabled ISAC, by presenting various solutions for optimizing the S\&C performance. In particular, we first present the UAV-enabled joint sensing and communication, and discuss the UAV maneuver control, wireless resource allocation, and interference management in the cases with single and multiple UAVs. Then, we present two application scenarios to exploit the mutual assistance between S\&C, namely sensing-assisted UAV communication and communication-assisted UAV sensing. Finally, we highlight several interesting research directions to motivate future work.

This letter studies a vertical federated edge learning (FEEL) system for collaborative objects/human motion recognition by exploiting the distributed integrated sensing and communication (ISAC). In this system, distributed edge devices first send wireless signals to sense targeted objects/human, and then exchange intermediate computed vectors (instead of raw sensing data) for collaborative recognition while preserving data privacy. To boost the spectrum and hardware utilization efficiency for FEEL, we exploit ISAC for both target sensing and data exchange, by employing dedicated frequency-modulated continuous-wave (FMCW) signals at each edge device. Under this setup, we propose a vertical FEEL framework for realizing the recognition based on the collected multi-view wireless sensing data. In this framework, each edge device owns an individual local L-model to transform its sensing data into an intermediate vector with relatively low dimensions, which is then transmitted to a coordinating edge device for final output via a common downstream S-model. By considering a human motion recognition task, experimental results show that our vertical FEEL based approach achieves recognition accuracy up to 98\% with an improvement up to 8\% compared to the benchmarks, including on-device training and horizontal FEEL.

Recommender systems, a pivotal tool to alleviate the information overload problem, aim to predict user's preferred items from millions of candidates by analyzing observed user-item relations. As for tackling the sparsity and cold start problems encountered by recommender systems, uncovering hidden (indirect) user-item relations by employing side information and knowledge to enrich observed information for the recommendation has been proven promising recently; and its performance is largely determined by the scalability of recommendation models in the face of the high complexity and large scale of side information and knowledge. Making great strides towards efficiently utilizing complex and large-scale data, research into graph embedding techniques is a major topic. Equipping recommender systems with graph embedding techniques contributes to outperforming the conventional recommendation implementing directly based on graph topology analysis and has been widely studied these years. This article systematically retrospects graph embedding-based recommendation from embedding techniques for bipartite graphs, general graphs, and knowledge graphs, and proposes a general design pipeline of that. In addition, comparing several representative graph embedding-based recommendation models with the most common-used conventional recommendation models, on simulations, manifests that the conventional models overall outperform the graph embedding-based ones in predicting implicit user-item interactions, revealing the relative weakness of graph embedding-based recommendation in these tasks. To foster future research, this article proposes constructive suggestions on making a trade-off between graph embedding-based recommendation and the conventional recommendation in different tasks as well as some open questions.

Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.

Recently, neural networks have been widely used in e-commerce recommender systems, owing to the rapid development of deep learning. We formalize the recommender system as a sequential recommendation problem, intending to predict the next items that the user might be interacted with. Recent works usually give an overall embedding from a user's behavior sequence. However, a unified user embedding cannot reflect the user's multiple interests during a period. In this paper, we propose a novel controllable multi-interest framework for the sequential recommendation, called ComiRec. Our multi-interest module captures multiple interests from user behavior sequences, which can be exploited for retrieving candidate items from the large-scale item pool. These items are then fed into an aggregation module to obtain the overall recommendation. The aggregation module leverages a controllable factor to balance the recommendation accuracy and diversity. We conduct experiments for the sequential recommendation on two real-world datasets, Amazon and Taobao. Experimental results demonstrate that our framework achieves significant improvements over state-of-the-art models. Our framework has also been successfully deployed on the offline Alibaba distributed cloud platform.

Recent years have witnessed the emerging success of graph neural networks (GNNs) for modeling structured data. However, most GNNs are designed for homogeneous graphs, in which all nodes and edges belong to the same types, making them infeasible to represent heterogeneous structures. In this paper, we present the Heterogeneous Graph Transformer (HGT) architecture for modeling Web-scale heterogeneous graphs. To model heterogeneity, we design node- and edge-type dependent parameters to characterize the heterogeneous attention over each edge, empowering HGT to maintain dedicated representations for different types of nodes and edges. To handle dynamic heterogeneous graphs, we introduce the relative temporal encoding technique into HGT, which is able to capture the dynamic structural dependency with arbitrary durations. To handle Web-scale graph data, we design the heterogeneous mini-batch graph sampling algorithm---HGSampling---for efficient and scalable training. Extensive experiments on the Open Academic Graph of 179 million nodes and 2 billion edges show that the proposed HGT model consistently outperforms all the state-of-the-art GNN baselines by 9%--21% on various downstream tasks.