Over the past decades, Linear Programming (LP) has been widely used in different areas and considered as one of the mature technologies in numerical optimization. However, the complexity offered by state-of-the-art algorithms (i.e.

Wind farm placement arranges the size and the location of multiple wind farms within a given region. The power output is highly related to the wind speed on spatial and temporal levels, which can be modeled by advanced data-driven approaches. To this end, we use a probabilistic neural network as a surrogate that accounts for the spatiotemporal correlations of wind speed. This neural network uses ReLU activation functions so that it can be reformulated as mixed-integer linear set of constraints (constraint learning). We embed these constraints into the placement decision problem, formulated as a two-stage stochastic optimization problem. Specifically, conditional quantiles of the total electricity production are regarded as recursive decisions in the second stage. We use real high-resolution regional data from a northern region in Spain. We validate that the constraint learning approach outperforms the classical bilinear interpolation method. Numerical experiments are implemented on risk-averse investors. The results indicate that risk-averse investors concentrate on dominant sites with strong wind, while exhibiting spatial diversification and sensitive capacity spread in non-dominant sites. Furthermore, we show that if we introduce transmission line costs in the problem, risk-averse investors favor locations closer to the substations. On the contrary, risk-neutral investors are willing to move to further locations to achieve higher expected profits. Our results conclude that the proposed novel approach is able to tackle a portfolio of regional wind farm placements and further provide guidance for risk-averse investors.

The recently proposed Broximal Point Method (BPM) [Gruntkowska et al., 2025] offers an idealized optimization framework based on iteratively minimizing the objective function over norm balls centered at the current iterate. It enjoys striking global convergence guarantees, converging linearly and in a finite number of steps for proper, closed and convex functions. However, its theoretical analysis has so far been confined to the Euclidean geometry. At the same time, emerging trends in deep learning optimization, exemplified by algorithms such as Muon [Jordan et al., 2024] and Scion [Pethick et al., 2025], demonstrate the practical advantages of minimizing over balls defined via non-Euclidean norms which better align with the underlying geometry of the associated loss landscapes. In this note, we ask whether the convergence theory of BPM can be extended to this more general, non-Euclidean setting. We give a positive answer, showing that most of the elegant guarantees of the original method carry over to arbitrary norm geometries. Along the way, we clarify which properties are preserved and which necessarily break down when leaving the Euclidean realm. Our analysis positions Non-Euclidean BPM as a conceptual blueprint for understanding a broad class of geometry-aware optimization algorithms, shedding light on the principles behind their practical effectiveness.

Recovering a low-CP-rank tensor from noisy linear measurements is a central challenge in high-dimensional data analysis, with applications spanning tensor PCA, tensor regression, and beyond. We exploit the intrinsic geometry of rank-one tensors by casting the recovery task as an optimization problem over the Segre manifold, the smooth Riemannian manifold of rank-one tensors. This geometric viewpoint yields two powerful algorithms: Riemannian Gradient Descent (RGD) and Riemannian Gauss-Newton (RGN), each of which preserves feasibility at every iteration. Under mild noise assumptions, we prove that RGD converges at a local linear rate, while RGN exhibits an initial local quadratic convergence phase that transitions to a linear rate as the iterates approach the statistical noise floor. Extensive synthetic experiments validate these convergence guarantees and demonstrate the practical effectiveness of our methods.

An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the constraints are defined by an expectation or an average over a large (finite) number of terms. The main idea of the algorithm is to solve a sequence of equality-constrained problems, each involving a finite sample of constraint-function terms, over which the sample set grows progressively. Under assumptions about the constraint functions and their first- and second-order derivatives that are reasonable in some real-world settings of interest, it is shown that -- with a sufficiently large initial sample -- solving a sequence of problems defined through progressive sampling yields a better worst-case sample complexity bound compared to solving a single problem with a full set of samples. The results of numerical experiments with a set of test problems demonstrate that the proposed approach can be effective in practice.

Motivated by the need to efficiently identify multiple candidates in high trial-and-error cost tasks such as drug discovery, we propose a near-optimal algorithm to identify all ε-best arms (i.e., those at most ε worse than the optimum). Specifically, we introduce LinFACT, an algorithm designed to optimize the identification of all ε-best arms in linear bandits. We establish a novel information-theoretic lower bound on the sample complexity of this problem and demonstrate that LinFACT achieves instance optimality by matching this lower bound up to a logarithmic factor. A key ingredient of our proof is to integrate the lower bound directly into the scaling process for upper bound derivation, determining the termination round and thus the sample complexity. We also extend our analysis to settings with model misspecification and generalized linear models. Numerical experiments, including synthetic and real drug discovery data, demonstrate that LinFACT identifies more promising candidates with reduced sample complexity, offering significant computational efficiency and accelerating early-stage exploratory experiments.

Open-World Object Detection (OWOD) enriches traditional object detectors by enabling continual discovery and integration of unknown objects via human guidance. However, existing OWOD approaches frequently suffer from semantic confusion between known and unknown classes, alongside catastrophic forgetting, leading to diminished unknown recall and degraded known-class accuracy. To overcome these challenges, we propose Combinatorial Open-World Detection (CROWD), a unified framework reformulating unknown object discovery and adaptation as an interwoven combinatorial (set-based) data-discovery (CROWD-Discover) and representation learning (CROWD-Learn) task. CROWD-Discover strategically mines unknown instances by maximizing Submodular Conditional Gain (SCG) functions, selecting representative examples distinctly dissimilar from known objects. Subsequently, CROWD-Learn employs novel combinatorial objectives that jointly disentangle known and unknown representations while maintaining discriminative coherence among known classes, thus mitigating confusion and forgetting. Extensive evaluations on OWOD benchmarks illustrate that CROWD achieves improvements of 2.83% and 2.05% in known-class accuracy on M-OWODB and S-OWODB, respectively, and nearly 2.4x unknown recall compared to leading baselines.

The proliferation of transformer-based language models has revolutionized NLP domain while simultaneously introduced significant challenges regarding model transparency and trustworthiness. The complexity of achieving explainable systems in this domain is evidenced by the extensive array of explanation methods and evaluation metrics developed by researchers. To address the challenge of selecting optimal explainability approaches, we present \textbf{\texttt{o-mega}}, a hyperparameter optimization tool designed to automatically identify the most effective explainable AI methods and their configurations within the semantic matching domain. We evaluate o-mega on a post-claim matching pipeline using a curated dataset of social media posts paired with refuting claims. Our tool systematically explores different explainable methods and their hyperparameters, demonstrating improved transparency in automated fact-checking systems. As a result, such automated optimization of explanation methods can significantly enhance the interpretability of claim-matching models in critical applications such as misinformation detection, contributing to more trustworthy and transparent AI systems.

Data-driven approaches have revolutionized the design and optimization of photonic metadevices by harnessing advanced artificial intelligence methodologies. This review takes a model-centric perspective that synthesizes emerging design strategies and delineates how traditional trial-and-error and computationally intensive electromagnetic simulations are being supplanted by deep learning frameworks that efficiently navigate expansive design spaces. We discuss artificial intelligence implementation in several metamaterial design aspects from high-degree-of-freedom design to large language model-assisted design. By addressing challenges such as transformer model implementation, fabrication limitations, and intricate mutual coupling effects, these AI-enabled strategies not only streamline the forward modeling process but also offer robust pathways for the realization of multifunctional and fabrication-friendly nanophotonic devices. This review further highlights emerging opportunities and persistent challenges, setting the stage for next-generation strategies in nanophotonic engineering.

Embodied Artificial Intelligence (AI) promises to handle edge cases in robotic vehicle systems where data is scarce by using common-sense reasoning grounded in perception and action to generalize beyond training distributions and adapt to novel real-world situations. These capabilities, however, also create new security risks. In this paper, we introduce CHAI (Command Hijacking against embodied AI), a new class of prompt-based attacks that exploit the multimodal language interpretation abilities of Large Visual-Language Models (LVLMs). CHAI embeds deceptive natural language instructions, such as misleading signs, in visual input, systematically searches the token space, builds a dictionary of prompts, and guides an attacker model to generate Visual Attack Prompts. We evaluate CHAI on four LVLM agents; drone emergency landing, autonomous driving, and aerial object tracking, and on a real robotic vehicle. Our experiments show that CHAI consistently outperforms state-of-the-art attacks. By exploiting the semantic and multimodal reasoning strengths of next-generation embodied AI systems, CHAI underscores the urgent need for defenses that extend beyond traditional adversarial robustness.