We revisit online binary classification by shifting the focus from competing with the best-in-class binary loss to competing against relaxed benchmarks that capture smoothed notions of optimality. Instead of measuring regret relative to the exact minimal binary error -- a standard approach that leads to worst-case bounds tied to the Littlestone dimension -- we consider comparing with predictors that are robust to small input perturbations, perform well under Gaussian smoothing, or maintain a prescribed output margin. Previous examples of this were primarily limited to the hinge loss. Our algorithms achieve regret guarantees that depend only on the VC dimension and the complexity of the instance space (e.g., metric entropy), and notably, they incur only an $O(\log(1/\gamma))$ dependence on the generalized margin $\gamma$. This stands in contrast to most existing regret bounds, which typically exhibit a polynomial dependence on $1/\gamma$. We complement this with matching lower bounds. Our analysis connects recent ideas from adversarial robustness and smoothed online learning.

AI and ML enable rapid processing of large datasets, and offer advanced feature extraction and pattern recognition capabilities that deliver meaningful insights, enhancing human analysts' ability to identify correlations within complex, multi - variable datasets. This is especially needed for astrobiology, where m odels must distinguish complex biotic patterns fro m intricate abiotic backgrounds. As data volume outpaces the capacity for timely data analysis, AI and ML become essential for data processing. They could also prove invaluable for the complex data analysis that will accompany flight instruments ' advancements. ML has been widely applied in image processing of large datasets in astrophysics and Earth observation ( e.g., crater identification [2 - 4], sample targeting [5]). Similar techniques that share methodology but are improved for onboard computational rest rictions could be leveraged for astrobiology missions to identify key features [6].

Cybersecurity demands rigorous and scalable techniques to ensure system correctness, robustness, and resilience against evolving threats. Automated reasoning, encompassing formal logic, theorem proving, model checking, and symbolic analysis, provides a foundational framework for verifying security properties across diverse domains such as access control, protocol design, vulnerability detection, and adversarial modeling. This survey presents a comprehensive overview of the role of automated reasoning in cybersecurity, analyzing how logical systems, including temporal, deontic, and epistemic logics are employed to formalize and verify security guarantees. We examine SOTA tools and frameworks, explore integrations with AI for neural-symbolic reasoning, and highlight critical research gaps, particularly in scalability, compositionality, and multi-layered security modeling. The paper concludes with a set of well-grounded future research directions, aiming to foster the development of secure systems through formal, automated, and explainable reasoning techniques.

Object Goal Navigation (OGN) is a fundamental task for robot s and AI, with key applications such as mobile robot image databases (MRID). In particular, mapless OGN is essential i n scenarios involving unknown or dynamic environments. Thi s study aims to enhance recent modular mapless OGN systems by l everaging the commonsense reasoning capabilities of large language models (LLMs). Specifically, we address the challe nge of determining the visiting order in frontier-based exp loration by framing it as a frontier ranking problem. Our approach is g rounded in recent findings that, while LLMs cannot determine the absolute value of a frontier, they excel at evaluating the re lative value between multiple frontiers viewed within a sin gle image using the view image as context. We dynamically manage the fr ontier list by adding and removing elements, using an LLM as a ranking model. The ranking results are represented as re ciprocal rank vectors, which are ideal for multi-view, mult i-query information fusion. Object Goal Navigation (OGN) is a task in which a robot explor es and locates a user-specified object within a workspace, widely studied in robotics and artificial intelligence [1]. If object locations are pre-recorded on a map, the most effici ent method is to retrieve the object from the mobile robot image d atabase [2]-[4]. However, in unknown environments or when map information is unreliable, mapless OGN is essential. Ex isting OGN methods include end-to-end approaches, which directly generate action commands from sensor data [5], but these require extensive training data and high computation al costs.

Multi-robot coordination is fundamental to various applications, including autonomous exploration, search and rescue, and cooperative transportation. This paper presents an optimal consensus framework for multi-robot systems (MRSs) that ensures efficient rendezvous while minimizing energy consumption and addressing actuator constraints. A critical challenge in real-world deployments is actuator limitations, particularly wheel velocity saturation, which can significantly degrade control performance. To address this issue, we incorporate Pontryagin Minimum Principle (PMP) into the control design, facilitating constrained optimization while ensuring system stability and feasibility. The resulting optimal control policy effectively balances coordination efficiency and energy consumption, even in the presence of actuation constraints. The proposed framework is validated through extensive numerical simulations and real-world experiments conducted using a team of Robotarium mobile robots. The experimental results confirm that our control strategies achieve reliable and efficient coordinated rendezvous while addressing real-world challenges such as communication delays, sensor noise, and packet loss.

Neural architecture search (NAS) provides a systematic framework for automating the design of neural network architectures, yet its widespread adoption is hindered by prohibitive computational requirements. Existing zero-cost proxy methods, while reducing search overhead, demonstrate inadequate performance in architecture ranking tasks, particularly for Transformer-based models where they often underperform simple parameter counting metrics. Current automated proxy discovery approaches suffer from extended search times, susceptibility to data overfitting, and structural complexity. This paper introduces a novel zero-cost proxy methodology that quantifies model capacity through efficient weight statistics computation while decomposing Transformer architectures into functionally distinct sub-modules, thereby optimizing the balance of their contributions to overall performance. Our comprehensive evaluation demonstrates the superiority of this approach, achieving a Spearman's rho of 0.76 and Kendall's tau of 0.53 on the FlexiBERT benchmark. The proposed method exhibits exceptional computational efficiency while maintaining robust performance across diverse NAS benchmark tasks, offering a practical solution for large-scale architecture search.

Recent advancements in ophthalmology foundation models such as RetFound have demonstrated remarkable diagnostic capabilities but require massive datasets for effective pre-training, creating significant barriers for development and deployment. To address this critical challenge, we propose FundusGAN, a novel hierarchical feature-aware generative framework specifically designed for high-fidelity fundus image synthesis. Our approach leverages a Feature Pyramid Network within its encoder to comprehensively extract multi-scale information, capturing both large anatomical structures and subtle pathological features. The framework incorporates a modified StyleGAN-based generator with dilated convolutions and strategic upsampling adjustments to preserve critical retinal structures while enhancing pathological detail representation. Comprehensive evaluations on the DDR, DRIVE, and IDRiD datasets demonstrate that FundusGAN consistently outperforms state-of-the-art methods across multiple metrics (SSIM: 0.8863, FID: 54.2, KID: 0.0436 on DDR). Furthermore, disease classification experiments reveal that augmenting training data with FundusGAN-generated images significantly improves diagnostic accuracy across multiple CNN architectures (up to 6.49\% improvement with ResNet50). These results establish FundusGAN as a valuable foundation model component that effectively addresses data scarcity challenges in ophthalmological AI research, enabling more robust and generalizable diagnostic systems while reducing dependency on large-scale clinical data collection.

In this paper, we develop a novel online federated learning framework for classification, designed to handle streaming data from multiple clients while ensuring data privacy and computational efficiency. Our method leverages the generalized distance-weighted discriminant technique, making it robust to both homogeneous and heterogeneous data distributions across clients. In particular, we develop a new optimization algorithm based on the Majorization-Minimization principle, integrated with a renewable estimation procedure, enabling efficient model updates without full retraining. We provide a theoretical guarantee for the convergence of our estimator, proving its consistency and asymptotic normality under standard regularity conditions. In addition, we establish that our method achieves Bayesian risk consistency, ensuring its reliability for classification tasks in federated environments. We further incorporate differential privacy mechanisms to enhance data security, protecting client information while maintaining model performance. Extensive numerical experiments on both simulated and real-world datasets demonstrate that our approach delivers high classification accuracy, significant computational efficiency gains, and substantial savings in data storage requirements compared to existing methods.

In recent times, reinforcement learning (RL) with physical robots has attracted the attention of a wide range of researchers. However, state-of-the-art RL algorithms do not consider that physical environments do not wait for the RL agent to make decisions or updates. RL agents learn by periodically conducting computationally expensive gradient updates. When decision-making and gradient update tasks are carried out sequentially by the RL agent in a physical robot, it significantly increases the agent's response time. In a rapidly changing environment, this increased response time may be detrimental to the performance of the learning agent. Asynchronous RL methods, which separate the computation of decision-making and gradient updates, are a potential solution to this problem. However, only a few comparisons between asynchronous and synchronous RL have been made with physical robots. For this reason, the exact performance benefits of using asynchronous RL methods over synchronous RL methods are still unclear. In this study, we provide a performance comparison between asynchronous and synchronous RL using a physical robotic arm called Franka Emika Panda. Our experiments show that the agents learn faster and attain significantly more returns using asynchronous RL. Our experiments also demonstrate that the learning agent with a faster response time performs better than the agent with a slower response time, even if the agent with a slower response time performs a higher number of gradient updates.

We introduce and study the spherical dimension, a natural topological relaxation of the VC dimension that unifies several results in learning theory where topology plays a key role in the proofs. The spherical dimension is defined by extending the set of realizable datasets (used to define the VC dimension) to the continuous space of realizable distributions. In this space, a shattered set of size d (in the VC sense) is completed into a continuous object, specifically a d-dimensional sphere of realizable distributions. The spherical dimension is then defined as the dimension of the largest sphere in this space. Thus, the spherical dimension is at least the VC dimension. The spherical dimension serves as a common foundation for leveraging the Borsuk-Ulam theorem and related topological tools. We demonstrate the utility of the spherical dimension in diverse applications, including disambiguations of partial concept classes, reductions from classification to stochastic convex optimization, stability and replicability, and sample compression schemes. Perhaps surprisingly, we show that the open question posed by Alon, Hanneke, Holzman, and Moran (FOCS 2021) of whether there exist non-trivial disambiguations for halfspaces with margin is equivalent to the basic open question of whether the VC and spherical dimensions are finite together.