Space-air-ground integrated multi-access edge computing (SAGIN-MEC) provides a promising solution for the rapidly developing low-altitude economy (LAE) to deliver flexible and wide-area computing services. However, fully realizing the potential of SAGIN-MEC in the LAE presents significant challenges, including coordinating decisions across heterogeneous nodes with different roles, modeling complex factors such as mobility and network variability, and handling real-time decision-making under partially observable environment with hybrid variables. To address these challenges, we first present a hierarchical SAGIN-MEC architecture that enables the coordination between user devices (UDs), uncrewed aerial vehicles (UAVs), and satellites. Then, we formulate a UD cost minimization optimization problem (UCMOP) to minimize the UD cost by jointly optimizing the task offloading ratio, UAV trajectory planning, computing resource allocation, and UD association. We show that the UCMOP is an NP-hard problem. To overcome this challenge, we propose a multi-agent deep deterministic policy gradient (MADDPG)-convex optimization and coalitional game (MADDPG-COCG) algorithm. Specifically, we employ the MADDPG algorithm to optimize the continuous temporal decisions for heterogeneous nodes in the partially observable SAGIN-MEC system. Moreover, we propose a convex optimization and coalitional game (COCG) method to enhance the conventional MADDPG by deterministically handling the hybrid and varying-dimensional decisions. Simulation results demonstrate that the proposed MADDPG-COCG algorithm significantly enhances the user-centric performances in terms of the aggregated UD cost, task completion delay, and UD energy consumption, with a slight increase in UAV energy consumption, compared to the benchmark algorithms. Moreover, the MADDPG-COCG algorithm shows superior convergence stability and scalability.

Reliably characterizing the full conditional distribution of a multivariate response variable given a set of covariates is crucial for trustworthy decision-making. However, misspecified or miscalibrated multivariate models may yield a poor approximation of the joint distribution of the response variables, leading to unreliable predictions and suboptimal decisions. Furthermore, standard recalibration methods are primarily limited to univariate settings, while conformal prediction techniques, despite generating multivariate prediction regions with coverage guarantees, do not provide a full probability density function. We address this gap by first introducing a novel notion of latent calibration, which assesses probabilistic calibration in the latent space of a conditional normalizing flow. Second, we propose latent recalibration (LR), a novel post-hoc model recalibration method that learns a transformation of the latent space with finite-sample bounds on latent calibration. Unlike existing methods, LR produces a recalibrated distribution with an explicit multivariate density function while remaining computationally efficient. Extensive experiments on both tabular and image datasets show that LR consistently improves latent calibration error and the negative log-likelihood of the recalibrated models.

Accelerating inverse design of crystalline materials with generative models has significant implications for a range of technologies. Unlike other atomic systems, 3D crystals are invariant to discrete groups of isometries called the space groups. Crucially, these space group symmetries are known to heavily influence materials properties. We propose SGEquiDiff, a crystal generative model which naturally handles space group constraints with space group invariant likelihoods. SGEquiD-iff consists of an SE(3)-invariant, telescoping discrete sampler of crystal lattices; permutation-invariant, transformer-based autoregressive sampling of Wyckoff positions, elements, and numbers of symmetrically unique atoms; and space group equivariant diffusion of atomic coordinates. We show that space group equivariant vector fields automatically live in the tangent spaces of the Wyckoff positions. SGEquiDiff achieves state-of-the-art performance on standard benchmark datasets as assessed by quantitative proxy metrics and quantum mechanical calculations. Our code is available at https://github.com/rees-c/sgequidiff.

Abstract--Generative artificial intelligence (AI) models in smart grids have advanced significantly in recent years due to their ability to generate large amounts of synthetic data, which would otherwise be difficult to obtain in the real world due to confidentiality constraints. A key challenge in utilizing such synthetic data is how to assess the data quality produced from such generative models. Traditional metrics such as sample-wise Euclidean distance and distributional distances applied directly to raw generated data inadequately reflect higher-order temporal dependencies and cross-temporal relationships between real and synthetic series, and thus struggle to discriminate generative quality. In this work, we propose a novel metric based on the Fr echet Distance (FD) estimated between two datasets in a learned feature space. The proposed method assesses synthetic data quality via distributional comparisons in a feature space derived from a model tailored to the smart grid domain. Empirical results demonstrate the superiority of the proposed metric across downstream tasks and generative models, enhancing the reliability of data-driven decision-making in smart grid operations. ENERA TIVE models in the electric energy sector have been an active field of research in the past few years, thanks to their potential to create realistic and diverse scenarios for system planning, reliability assessment, and renewable energy integration--ultimately enhancing grid resilience and operational efficiency. These models, such as Generative Adversarial Networks (GANs), allow researchers to access much larger sets of synthetic data across multiple time scales that would otherwise be unavailable due to confidentiality constraints [1]. In contrast to traditional methods that involve creating synthetic power networks and subsequently using commercial-grade simulation software to generate electrical measurement variables [2], these generative approaches leverage a data-driven methodology.

In this paper we show that visual diffusion models can serve as effective geometric solvers: they can directly reason about geometric problems by working in pixel space. We first demonstrate this on the Inscribed Square Problem, a long-standing problem in geometry that asks whether every Jordan curve contains four points forming a square. We then extend the approach to two other well-known hard geometric problems: the Steiner Tree Problem and the Simple Polygon Problem. Our method treats each problem instance as an image and trains a standard visual diffusion model that transforms Gaussian noise into an image representing a valid approximate solution that closely matches the exact one. The model learns to transform noisy geometric structures into correct configurations, effectively recasting geometric reasoning as image generation. Unlike prior work that necessitates specialized architectures and domain-specific adaptations when applying diffusion to parametric geometric representations, we employ a standard visual diffusion model that operates on the visual representation of the problem. This simplicity highlights a surprising bridge between generative modeling and geometric problem solving. Beyond the specific problems studied here, our results point toward a broader paradigm: operating in image space provides a general and practical framework for approximating notoriously hard problems, and opens the door to tackling a far wider class of challenging geometric tasks.

AI agents hold the potential to revolutionize scientific productivity by automating literature reviews, replicating experiments, analyzing data, and even proposing new directions of inquiry; indeed, there are now many such agents, ranging from general-purpose "deep research" systems to specialized science-specific agents, such as AI Scientist and AIGS. Rigorous evaluation of these agents is critical for progress. Yet existing benchmarks fall short on several fronts: they (1) fail to provide holistic, product-informed measures of real-world use cases such as science research; (2) lack reproducible agent tools necessary for a controlled comparison of core agentic capabilities; (3) do not account for confounding variables such as model cost and tool access; (4) do not provide standardized interfaces for quick agent prototyping and evaluation; and (5) lack comprehensive baseline agents necessary to identify true advances. In response, we define principles and tooling for more rigorously benchmarking agents. Using these, we present AstaBench, a suite that provides the first holistic measure of agentic ability to perform scientific research, comprising 2400+ problems spanning the entire scientific discovery process and multiple scientific domains, and including many problems inspired by actual user requests to deployed Asta agents. Our suite comes with the first scientific research environment with production-grade search tools that enable controlled, reproducible evaluation, better accounting for confounders. Alongside, we provide a comprehensive suite of nine science-optimized classes of Asta agents and numerous baselines. Our extensive evaluation of 57 agents across 22 agent classes reveals several interesting findings, most importantly that despite meaningful progress on certain individual aspects, AI remains far from solving the challenge of science research assistance.

Designing incentives for a multi-agent system to induce a desirable Nash equilibrium is both a crucial and challenging problem appearing in many decision-making domains, especially for a large number of agents $N$. Under the exchangeability assumption, we formalize this incentive design (ID) problem as a parameterized mean-field game (PMFG), aiming to reduce complexity via an infinite-population limit. We first show that when dynamics and rewards are Lipschitz, the finite-$N$ ID objective is approximated by the PMFG at rate $\mathscr{O}(\frac{1}{\sqrt{N}})$. Moreover, beyond the Lipschitz-continuous setting, we prove the same $\mathscr{O}(\frac{1}{\sqrt{N}})$ decay for the important special case of sequential auctions, despite discontinuities in dynamics, through a tailored auction-specific analysis. Built on our novel approximation results, we further introduce our Adjoint Mean-Field Incentive Design (AMID) algorithm, which uses explicit differentiation of iterated equilibrium operators to compute gradients efficiently. By uniting approximation bounds with optimization guarantees, AMID delivers a powerful, scalable algorithmic tool for many-agent (large $N$) ID. Across diverse auction settings, the proposed AMID method substantially increases revenue over first-price formats and outperforms existing benchmark methods.

Facial Landmark Detection (FLD) in thermal imagery is critical for applications in challenging lighting conditions, but it is hampered by the lack of rich visual cues. Conventional cross-modal solutions, like feature fusion or image translation from RGB data, are often computationally expensive or introduce structural artifacts, limiting their practical deployment. To address this, we propose Multi-Level Cross-Modal Knowledge Distillation (MLCM-KD), a novel framework that decouples high-fidelity RGB-to-thermal knowledge transfer from model compression to create both accurate and efficient thermal FLD models. A central challenge during knowledge transfer is the profound modality gap between RGB and thermal data, where traditional unidirectional distillation fails to enforce semantic consistency across disparate feature spaces. To overcome this, we introduce Dual-Injected Knowledge Distillation (DIKD), a bidirectional mechanism designed specifically for this task. DIKD establishes a connection between modalities: it not only guides the thermal student with rich RGB features but also validates the student's learned representations by feeding them back into the frozen teacher's prediction head. This closed-loop supervision forces the student to learn modality-invariant features that are semantically aligned with the teacher, ensuring a robust and profound knowledge transfer. Experiments show that our approach sets a new state-of-the-art on public thermal FLD benchmarks, notably outperforming previous methods while drastically reducing computational overhead.

Abstract-- T o address the need for high-precision localization of climbing robots in complex high-altitude environments, this paper proposes a multi-sensor fusion system that overcomes the limitations of single-sensor approaches. Firstly, the localization scenarios and the problem model are analyzed. An integrated architecture of Attention Mechanism-based Fusion Algorithm (AMF A) incorporating planar array Ultra-Wideband (UWB), GPS, Inertial Measurement Unit (IMU), and barometer is designed to handle challenges such as GPS occlusion and UWB Non-Line-of-Sight (NLOS) problem. Then, End-to-end neural network inference models for UWB and barometer are developed, along with a multimodal attention mechanism for adaptive data fusion. An Unscented Kalman Filter (UKF) is applied to refine the trajectory, improving accuracy and robustness. Finally, real-world experiments show that the method achieves 0.48 m localization accuracy and lower MAX error of 1.50 m, outperforming baseline algorithms such as GPS/INS-EKF and demonstrating stronger robustness.

Efficiently solving constrained optimization problems is crucial for numerous real-world applications, yet traditional solvers are often computationally prohibitive for real-time use. Machine learning-based approaches have emerged as a promising alternative to provide approximate solutions at faster speeds, but they struggle to strictly enforce constraints, leading to infeasible solutions in practice. To address this, we propose the Feasibility-Seeking Neural Network (FSNet), which integrates a feasibility-seeking step directly into its solution procedure to ensure constraint satisfaction. This feasibility-seeking step solves an unconstrained optimization problem that minimizes constraint violations in a differentiable manner, enabling end-to-end training and providing guarantees on feasibility and convergence. Our experiments across a range of different optimization problems, including both smooth/nonsmooth and convex/nonconvex problems, demonstrate that FSNet can provide feasible solutions with solution quality comparable to (or in some cases better than) traditional solvers, at significantly faster speeds.