Over-the-air federated learning (OTA-FL) reduces uplink latency by aggregating client updates directly over the wireless multiple-access channel. Coherent analog aggregation realizes this idea by aligning the phases and amplitudes of simultaneously transmitted waveforms, which typically requires synchronization, instantaneous channel-state information (CSI), phase compensation, and power control. Noncoherent energy detection removes the need for phase-coherent combining, but a single energy measurement is nonnegative and, therefore, cannot represent signed model updates. This paper introduces resource-element energy difference (REED), a noncoherent physical-layer primitive for continuous signed aggregation. REED maps the positive and negative parts of each real-valued update to transmit energies on paired orthogonal resource elements and estimates the signed sum by subtracting the corresponding received energies. The construction uses slow-timescale calibration of average channel powers, but does not require instantaneous transmitter- or receiver-side CSI or channel inversion. For independent Rayleigh fading, we derive exact first- and second-moment expressions for single-shot REED and for a chip-diverse extension that spreads each coordinate over multiple independently faded paired chips. The resulting variance laws separate fading-induced self-noise, signal-noise interaction, and receiver-noise fluctuation, giving an explicit diversity-resource tradeoff. More->The rest of abstract is in the paper.

Artificial intelligence-generated content (AIGC) has emerged as a transformative paradigm for automating the creation of diverse and customized content, giving rise to rapidly growing computational workloads in cloud data centers. It is imperative for AIGC service providers (ASPs) to strategically schedule AIGC workloads to reduce data center energy costs while guaranteeing high-quality content generation. However, the distinctive characteristics of AIGC services pose critical challenges, including model heterogeneity across ASPs, implicit service quality evaluation, and complex inference process control. To tackle these challenges, we propose a joint energy management and coordinated AIGC workload scheduling framework, which introduces an explicit mathematical characterization of service quality to promote both job transfer among ASPs and fine-grained inference process configuration. Moreover, various energy resources within data centers are jointly considered to enhance power usage flexibility. Subsequently, a system utility maximization problem is formulated to balance AIGC service revenue with operational penalties and costs. Nevertheless, the strong coupling among job scheduling decisions induces severe reward sparsity, which limits the effectiveness of existing deep reinforcement learning (DRL) algorithms. To address this issue, we develop a diffusion model-aided reward shaping approach to synthesize complementary reward signals through a multi-step denoising process. This approach is seamlessly integrated with DRL to enable efficient learning of scheduling policies under sparse environmental feedback. Experiments based on real-world models and datasets demonstrate that our scheme effectively accommodates electricity price fluctuations and AIGC model heterogeneity, while achieving superior learning convergence and system utility compared with benchmark methods.

The plug-and-play priors (PnP) and regularization by denoising (RED) methods have become widely used for solving inverse problems by leveraging pre-trained deep denoisers as image priors. While the empirical imaging performance and the theoretical convergence properties of these algorithms have been widely investigated, their recovery properties have not previously been theoretically analyzed. We address this gap by showing how to establish theoretical recovery guarantees for PnP/RED by assuming that the solution of these methods lies near the fixedpoints of a deep neural network. We also present numerical results comparing the recovery performance of PnP/RED in compressive sensing against that of recent compressive sensing algorithms based on generative models. Our numerical results suggest that PnP with a pre-trained artifact removal network provides significantly better results compared to the existing state-of-the-art methods.

Commonly used in many applications, robust PCA represents an algorithmic attempt to reduce the sensitivity of classical PCA to outliers. The basic idea is to learn a decomposition of some data matrix of interest into low rank and sparse components, the latter representing unwanted outliers. Although the resulting problem is typically NP-hard, convex relaxations provide a computationally-expedient alternative with theoretical support. However, in practical regimes performance guarantees break down and a variety of non-convex alternatives, including Bayesian-inspired models, have been proposed to boost estimation quality. Unfortunately though, without additional a priori knowledge none of these methods can significantly expand the critical operational range such that exact principal subspace recovery is possible. Into this mix we propose a novel pseudo-Bayesian algorithm that explicitly compensates for design weaknesses in many existing non-convex approaches leading to state-of-the-art performance with a sound analytical foundation.

The restricted isometry property (RIP) for design matrices gives guarantees for optimal recovery in sparse linear models. It is of high interest in compressed sensing and statistical learning. This property is particularly important for computationally efficient recovery methods. As a consequence, even though it is in general NP-hard to check that RIP holds, there have been substantial efforts to find tractable proxies for it. These would allow the construction of RIP matrices and the polynomial-time verification of RIP given an arbitrary matrix. We consider the framework of average-case certifiers, that never wrongly declare that a matrix is RIP, while being often correct for random instances. While there are such functions which are tractable in a suboptimal parameter regime, we show that this is a computationally hard task in any better regime. Our results are based on a new, weaker assumption on the problem of detecting dense subgraphs.

We study downlink beam and rate adaptation in a multi-user mmWave MISO system where multiple base stations (BSs), each using analog beamforming from finite codebooks, serve multiple single-antenna user equipments (UEs) with a unique beam per UE and discrete data transmission rates. BSs learn about transmission success based on ACK/NACK feedback. To encode service goals, we introduce a satisficing throughput threshold $τ_r$ and cast joint beam and rate adaptation as a combinatorial semi-bandit over beam-rate tuples. Within this framework, we propose SAT-CTS, a lightweight, threshold-aware policy that blends conservative confidence estimates with posterior sampling, steering learning toward meeting $τ_r$ rather than merely maximizing. Our main theoretical contribution provides the first finite-time regret bounds for combinatorial semi-bandits with satisficing objective: when $τ_r$ is realizable, we upper bound the cumulative satisficing regret to the target with a time-independent constant, and when $τ_r$ is non-realizable, we show that SAT-CTS incurs only a finite expected transient outside committed CTS rounds, after which its regret is governed by the sum of the regret contributions of restarted CTS rounds, yielding an $O((\log T)^2)$ standard regret bound. On the practical side, we evaluate the performance via cumulative satisficing regret to $τ_r$ alongside standard regret and fairness. Experiments with time-varying sparse multipath channels show that SAT-CTS consistently reduces satisficing regret and maintains competitive standard regret, while achieving favorable average throughput and fairness across users, indicating that feedback-efficient learning can equitably allocate beams and rates to meet QoS targets without channel state knowledge.

The robust low-rank tensor completion problem addresses the challenge of recovering corrupted high-dimensional tensor data with missing entries, outliers, and sparse noise commonly found in real-world applications. Existing methodologies have encountered fundamental limitations due to their reliance on uniform regularization schemes, particularly the tensor nuclear norm and $\ell_1$ norm regularization approaches, which indiscriminately apply equal shrinkage to all singular values and sparse components, thereby compromising the preservation of critical tensor structures. The proposed tensor weighted correlated total variation (TWCTV) regularizer addresses these shortcomings through an $M$-product framework that combines a weighted Schatten-$p$ norm on gradient tensors for low-rankness with smoothness enforcement and weighted sparse components for noise suppression. The proposed weighting scheme adaptively reduces the thresholding level to preserve both dominant singular values and sparse components, thus improving the reconstruction of critical structural elements and nuanced details in the recovered signal. Through a systematic algorithmic approach, we introduce an enhanced alternating direction method of multipliers (ADMM) that offers both computational efficiency and theoretical substantiation, with convergence properties comprehensively analyzed within the $M$-product framework.Comprehensive numerical evaluations across image completion, denoising, and background subtraction tasks validate the superior performance of this approach relative to established benchmark methods.

Nonrigid registration is conventionally divided into point set registration, which aligns sparse geometries, and image registration, which aligns continuous intensity fields on regular grids. However, this dichotomy creates a critical bottleneck for emerging scientific data, such as spatial transcriptomics, where high-dimensional vector-valued functions, e.g., gene expression, are defined on irregular, sparse manifolds. Consequently, researchers currently face a forced choice: either sacrifice single-cell resolution via voxelization to utilize image-based tools, or ignore the critical functional signal to utilize geometric tools. To resolve this dilemma, we propose Domain Elastic Transform (DET), a grid-free probabilistic framework that unifies geometric and functional alignment. By treating data as functions on irregular domains, DET registers high-dimensional signals directly without binning. We formulate the problem within a rigorous Bayesian framework, modeling domain deformation as an elastic motion guided by a joint spatial-functional likelihood. The method is fully unsupervised and scalable, utilizing feature-sensitive downsampling to handle massive atlases. We demonstrate that DET achieves 92\% topological preservation on MERFISH data where state-of-the-art optimal transport methods struggle ($<$5\%), and successfully registers whole-embryo Stereo-seq atlases across developmental stages -- a task involving massive scale and complex nonrigid growth. The implementation of DET is available on {https://github.com/ohirose/bcpd} (since Mar, 2025).

Autocorrelation is a defining characteristic of time-series data, where each observation is statistically dependent on its predecessors. In the context of deep time-series forecasting, autocorrelation arises in both the input history and the label sequences, presenting two central research challenges: (1) designing neural architectures that model autocorrelation in history sequences, and (2) devising learning objectives that model autocorrelation in label sequences. Recent studies have made strides in tackling these challenges, but a systematic survey examining both aspects remains lacking. To bridge this gap, this paper provides a comprehensive review of deep time-series forecasting from the perspective of autocorrelation modeling. In contrast to existing surveys, this work makes two distinctive contributions. First, it proposes a novel taxonomy that encompasses recent literature on both model architectures and learning objectives -- whereas prior surveys neglect or inadequately discuss the latter aspect. Second, it offers a thorough analysis of the motivations, insights, and progression of the surveyed literature from a unified, autocorrelation-centric perspective, providing a holistic overview of the evolution of deep time-series forecasting. The full list of papers and resources is available at https://github.com/Master-PLC/Awesome-TSF-Papers.

Channel state information (CSI) feedback in frequency-division duplex (FDD) massive multiple-input multiple-output (MIMO) systems is fundamentally limited by the high dimensionality of wideband channels. In this paper, we model the stacked wideband CSI vector as a Gaussian-mixture source with a latent geometry state that represents different propagation environments. Each component corresponds to a locally stationary regime characterized by a correlated proper complex Gaussian distribution with its own covariance matrix. This representation captures the multimodal nature of practical CSI datasets while preserving the analytical tractability of Gaussian models. Motivated by this structure, we propose Gaussian-mixture transform coding (GMTC), a practical CSI feedback architecture that combines state inference with state-adaptive TC. The mixture parameters are learned offline from channel samples and stored as a shared statistical dictionary at both the user equipment (UE) and the base station. For each CSI realization, the UE identifies the most likely geometry state, encodes the corresponding label using a lossless source code, and compresses the CSI using the Karhunen-Loeve transform matched to that state. We further characterize the fundamental limits of CSI compression under this model by deriving analytical converse and achievability bounds on the rate-distortion (RD) function. A key structural result is that the optimal bit allocation across all mixture components is governed by a single global reverse-waterfilling level. Simulations on the COST2100 dataset show that GMTC significantly improves the RD tradeoff relative to neural transform coding approaches while requiring substantially smaller model memory and lower inference complexity. These results indicate that near-optimal CSI compression can be achieved through state-adaptive TC without relying on large neural encoders.