We analyze the relation between spectral initializers and theoretical limits of \emph{descending} phase retrieval algorithms (dPR). In companion paper [104], for any sample complexity ratio, $α$, \emph{parametric manifold}, ${\mathcal {PM}}(α)$, is recognized as a critically important structure that generically determines dPRs abilities to solve phase retrieval (PR). Moreover, overlap between the algorithmic solution and the true signal is positioned as a key ${\mathcal {PM}}$'s component. We here consider the so-called \emph{overlap optimal} spectral initializers (OptSpins) as dPR's starting points and develop a generic \emph{Random duality theory} (RDT) based program to statistically characterize them. In particular, we determine the functional structure of OptSpins and evaluate the starting overlaps that they provide for the dPRs. Since ${\mathcal {PM}}$'s so-called \emph{flat regions} are highly susceptible to \emph{local jitteriness} and as such are key obstacles on dPR's path towards PR's global optimum, a precise characterization of the starting overlap allows to determine if such regions can be successfully circumvented. Through the presented theoretical analysis we observe two key points in that regard: \textbf{\emph{(i)}} dPR's theoretical phase transition (critical $α$ above which they solve PR) might be difficult to practically achieve as the ${\mathcal {PM}}$'s flat regions are large causing the associated OptSpins to fall exactly within them; and \textbf{\emph{(ii)}} Opting for so-called ``\emph{safer compression}'' and slightly increasing $α$ (by say $15\%$) shrinks flat regions and allows OptSpins to fall outside them and dPRs to ultimately solve PR. Numerical simulations are conducted as well and shown to be in an excellent agreement with theoretical predictions.

Representation learning methods are an important tool for addressing the challenges posed by complex observations spaces in sequential decision making problems. Recently, many methods have used a wide variety of types of approaches for learning meaningful state representations in reinforcement learning, allowing better sample efficiency, generalization, and performance. This survey aims to provide a broad categorization of these methods within a model-free online setting, exploring how they tackle the learning of state representations differently. We categorize the methods into six main classes, detailing their mechanisms, benefits, and limitations. Through this taxonomy, our aim is to enhance the understanding of this field and provide a guide for new researchers. We also discuss techniques for assessing the quality of representations, and detail relevant future directions.

We study theoretical limits of \emph{descending} phase retrieval algorithms. Utilizing \emph{Random duality theory} (RDT) we develop a generic program that allows statistical characterization of various algorithmic performance metrics. Through these we identify the concepts of \emph{parametric manifold} and its \emph{funneling points} as key mathematical objects that govern the underlying algorithms' behavior. An isomorphism between single funneling point manifolds and global convergence of descending algorithms is established. The structure and shape of the parametric manifold as well as its dependence on the sample complexity are studied through both plain and lifted RDT. Emergence of a phase transition is observed. Namely, as sample complexity increases, parametric manifold transitions from a multi to a single funneling point structure. This in return corresponds to a transition from the scenarios where descending algorithms generically fail to the scenarios where they succeed in solving phase retrieval. We also develop and implement a practical algorithmic variant that in a hybrid alternating fashion combines a barrier and a plain gradient descent. Even though the theoretical results are obtained for infinite dimensional scenarios (and consequently non-jittery parametric manifolds), we observe a strong agrement between theoretical and simulated phase transitions predictions for fairly small dimensions on the order of a few hundreds.

Progress of AI has led to a creation of very successful, but by no means humble models and tools, especially regarding (i) the huge and further exploding costs and resources they demand, and (ii) the over-confidence of these tools with the answers they provide. Here we introduce a novel mathematical framework for a non-equilibrium entropy-optimizing reformulation of Boltzmann machines based on the exact law of total probability. It results in the highly-performant, but much cheaper, gradient-descent-free learning framework with mathematically-justified existence and uniqueness criteria, and answer confidence/reliability measures. Comparisons to state-of-the-art AI tools in terms of performance, cost and the model descriptor lengths on a set of synthetic problems with varying complexity reveal that the proposed method results in more performant and slim models, with the descriptor lengths being very close to the intrinsic complexity scaling bounds for the underlying problems. Applying this framework to historical climate data results in models with systematically higher prediction skills for the onsets of La Niña and El Niño climate phenomena, requiring just few years of climate data for training - a small fraction of what is necessary for contemporary climate prediction tools.

We consider optimal resource allocation for restless multi-armed bandits (RMABs) in unknown, non-stationary settings. RMABs are PSPACE-hard to solve optimally, even when all parameters are known. The Whittle index policy is known to achieve asymptotic optimality for a large class of such problems, while remaining computationally efficient. In many practical settings, however, the transition kernels required to compute the Whittle index are unknown and non-stationary. In this work, we propose an online learning algorithm for Whittle indices in this setting. Our algorithm first predicts current transition kernels by solving a linear optimization problem based on upper confidence bounds and empirical transition probabilities calculated from data over a sliding window. Then, it computes the Whittle index associated with the predicted transition kernels. We design these sliding windows and upper confidence bounds to guarantee sub-linear dynamic regret on the number of episodes $T$, under the condition that transition kernels change slowly over time (rate upper bounded by $ε=1/T^k$ with $k>0$). Furthermore, our proposed algorithm and regret analysis are designed to exploit prior domain knowledge and structural information of the RMABs to accelerate the learning process. Numerical results validate that our algorithm achieves superior performance in terms of lowest cumulative regret relative to baselines in non-stationary environments.

By 2050, people aged 65 and over are projected to make up 16 percent of the global population. As aging is closely associated with increased fall risk, particularly in wet and confined environments such as bathrooms where over 80 percent of falls occur. Although recent research has increasingly focused on non-intrusive, privacy-preserving approaches that do not rely on wearable devices or video-based monitoring, these efforts have not fully overcome the limitations of existing unimodal systems (e.g., WiFi-, infrared-, or mmWave-based), which are prone to reduced accuracy in complex environments. These limitations stem from fundamental constraints in unimodal sensing, including system bias and environmental interference, such as multipath fading in WiFi-based systems and drastic temperature changes in infrared-based methods. To address these challenges, we propose a Privacy-Preserving Multimodal Fall Detection System for Elderly People in Bathroom Environments. First, we develop a sensor evaluation framework to select and fuse millimeter-wave radar with 3D vibration sensing, and use it to construct and preprocess a large-scale, privacy-preserving multimodal dataset in real bathroom settings, which will be released upon publication. Second, we introduce P2MFDS, a dual-stream network combining a CNN-BiLSTM-Attention branch for radar motion dynamics with a multi-scale CNN-SEBlock-Self-Attention branch for vibration impact detection. By uniting macro- and micro-scale features, P2MFDS delivers significant gains in accuracy and recall over state-of-the-art approaches. Code and pretrained models will be made available at: https://github.com/HaitianWang/P2MFDS-A-Privacy-Preserving-Multimodal-Fall-Detection-Network-for-Elderly-Individuals-in-Bathroom.

Industrial Cyber-Physical Systems (ICPS) technologies are foundational in driving maritime autonomy, particularly for Unmanned Surface Vehicles (USVs). However, onboard computational constraints and communication latency significantly restrict real-time data processing, analysis, and predictive modeling, hence limiting the scalability and responsiveness of maritime ICPS. To overcome these challenges, we propose a distributed Cloud-Edge-IoT architecture tailored for maritime ICPS by leveraging design principles from the recently proposed Cloud-Fog Automation paradigm. Our proposed architecture comprises three hierarchical layers: a Cloud Layer for centralized and decentralized data aggregation, advanced analytics, and future model refinement; an Edge Layer that executes localized AI-driven processing and decision-making; and an IoT Layer responsible for low-latency sensor data acquisition. Our experimental results demonstrated improvements in computational efficiency, responsiveness, and scalability. When compared with our conventional approaches, we achieved a classification accuracy of 86\%, with an improved latency performance. By adopting Cloud-Fog Automation, we address the low-latency processing constraints and scalability challenges in maritime ICPS applications. Our work offers a practical, modular, and scalable framework to advance robust autonomy and AI-driven decision-making and autonomy for intelligent USVs in future maritime ICPS.

Telerobotics is a key foundation in autonomous Industrial Cyber-Physical Systems (ICPS), enabling remote operations across various domains. However, conventional cloud-based telerobotics suffers from latency, reliability, scalability, and resilience issues, hindering real-time performance in critical applications. Cloud-Fog Telerobotics (CFTel) builds on the Cloud-Fog Automation (CFA) paradigm to address these limitations by leveraging a distributed Cloud-Edge-Robotics computing architecture, enabling deterministic connectivity, deterministic connected intelligence, and deterministic networked computing. This paper synthesizes recent advancements in CFTel, aiming to highlight its role in facilitating scalable, low-latency, autonomous, and AI-driven telerobotics. We analyze architectural frameworks and technologies that enable them, including 5G Ultra-Reliable Low-Latency Communication, Edge Intelligence, Embodied AI, and Digital Twins. The study demonstrates that CFTel has the potential to enhance real-time control, scalability, and autonomy while supporting service-oriented solutions. We also discuss practical challenges, including latency constraints, cybersecurity risks, interoperability issues, and standardization efforts. This work serves as a foundational reference for researchers, stakeholders, and industry practitioners in future telerobotics research.

Supporting decision-making has long been a central vision in the field of spatio-temporal intelligence. While prior work has improved the timeliness and accuracy of spatio-temporal forecasting, converting these forecasts into actionable strategies remains a key challenge. A main limitation is the decoupling of the prediction and the downstream decision phases, which can significantly degrade the downstream efficiency. For example, in emergency response, the priority is successful resource allocation and intervention, not just incident prediction. To this end, it is essential to propose an Adaptive Spatio-Temporal Early Decision model (ASTER) that reforms the forecasting paradigm from event anticipation to actionable decision support. This framework ensures that information is directly used for decision-making, thereby maximizing overall effectiveness. Specifically, ASTER introduces a new Resource-aware Spatio-Temporal interaction module (RaST) that adaptively captures long- and short-term dependencies under dynamic resource conditions, producing context-aware spatiotemporal representations. To directly generate actionable decisions, we further design a Preference-oriented decision agent (Poda) based on multi-objective reinforcement learning, which transforms predictive signals into resource-efficient intervention strategies by deriving optimal actions under specific preferences and dynamic constraints. Experimental results on four benchmark datasets demonstrate the state-of-the-art performance of ASTER in improving both early prediction accuracy and resource allocation outcomes across six downstream metrics.

Amazon delivery can be tough, unglamorous work. Workers must often reckon with complicated geography, demanding bosses, ever more biblical weather, and schedules that force time-conscious drivers to urinate in bottles. Surprising, then, that this is effectively the role in which one of the year's most anticipated video games casts the player. In Death Stranding 2, you arrange packages into swaying towers on your back, nudge the controller's left- and right-shoulder buttons to keep your weight balanced as you trip down rocky hills, and incur financial penalties for scuffing the merchandise if you take a tumble. The premise is a long trek from the super-soldier games, such as Call of Duty and Helldivers, that dominate the sales charts--even if you must occasionally battle the odd spectral marauder from a parallel dimension to clear the way to the next address on your delivery sheet.