Gaussian Process (GP) models are popular tools in uncertainty quantification (UQ) because they purport to furnish functional uncertainty estimates that can be used to represent model uncertainty . It is often difficult to state with precision what probabilistic interpretation attaches to such an uncertainty, and in what way is it calibrated. Without such a calibration statement, the value of such uncertainty estimates is quite limited and qualitative. We motivate the importance of proper probabilistic calibration of GP predictions by describing how GP predictive calibration failures can cause degraded convergence properties in a target optimization algorithm called T argeted Adaptive Design (T AD). We discuss the interpretation of GP-generated uncertainty intervals in UQ, and how one may learn to trust them, through a formal procedure for covariance kernel validation that exploits the multivariate normal nature of GP predictions. We give simple examples of GP regression misspecified 1-dimensional models, and discuss the situation with respect to higher-dimensional models.

We propose a Gaussian Process (GP)-based policy iteration framework for addressing both forward and inverse problems in Hamilton--Jacobi--Bellman (HJB) equations and mean field games (MFGs). Policy iteration is formulated as an alternating procedure between solving the value function under a fixed control policy and updating the policy based on the resulting value function. By exploiting the linear structure of GPs for function approximation, each policy evaluation step admits an explicit closed-form solution, eliminating the need for numerical optimization. To improve convergence, we incorporate the additive Schwarz acceleration as a preconditioning step following each policy update. Numerical experiments demonstrate the effectiveness of Schwarz acceleration in improving computational efficiency.

Characterizing conformational transitions in physical systems remains a fundamental challenge, as traditional sampling methods struggle with the high-dimensional nature of molecular systems and high-energy barriers between stable states. These rare events often represent the most biologically significant processes, yet may require months of continuous simulation to observe. One way to understand the function and mechanics of such systems is through the minimum energy path (MEP), which represents the most probable transition pathway between stable states in the high-friction, low-temperature limit. We present a method that reformulates MEP discovery as a fast and scalable neural optimization problem. By representing paths as implicit neural representations and training with differentiable molecular force fields, our method discovers transition pathways without expensive sampling. Our approach scales to large biomolecular systems through a simple loss function derived from the path's likelihood via the Onsager-Machlup action and a scalable new architecture, AdaPath. We demonstrate this approach on two proteins, including an explicitly hydrated BPTI system with more than 3,500 atoms. Our method identifies a MEP that captures the same conformational change observed in a millisecond-scale molecular dynamics (MD) simulation in just minutes on a standard GPU, rather than weeks on a specialized cluster.

The Otsu thresholding algorithm represents a fundamental technique in image segmentation, yet its computational efficiency is severely limited by exhaustive search requirements across all possible threshold values. This work presents an optimized implementation that leverages the bisection method to exploit the unimodal characteristics of the between-class variance function. Our approach reduces the computational complexity from O(L) to O(log L) evaluations while preserving segmentation accuracy. Experimental validation on 48 standard test images demonstrates a 91.63% reduction in variance computations and 97.21% reduction in algorithmic iterations compared to conventional exhaustive search. The bisection method achieves exact threshold matches in 66.67% of test cases, with 95.83% exhibiting deviations within 5 gray levels. The algorithm maintains universal convergence within theoretical logarithmic bounds while providing deterministic performance guarantees suitable for real-time applications. This optimization addresses critical computational bottlenecks in large-scale image processing systems without compromising the theoretical foundations or segmentation quality of the original Otsu method.

Autism Spectrum Disorder (ASD) lacks reliable biological markers, delaying early diagnosis. Using 159 salivary samples analyzed by ATR-FTIR spectroscopy, we developed GANet, a genetic algorithm-based network optimization framework leveraging PageRank and Degree for importance-based feature characterization. GANet systematically optimizes network structure to extract meaningful patterns from high-dimensional spectral data. It achieved superior performance compared to linear discriminant analysis, support vector machines, and deep learning models, reaching 0.78 accuracy, 0.61 sensitivity, 0.90 specificity, and a 0.74 harmonic mean. These results demonstrate GANet's potential as a robust, bio-inspired, non-invasive tool for precise ASD detection and broader spectral-based health applications.

Figure 1: Our Solo12 loco-manipulation policy is able to execute and smoothly transition between locomotion and manipulation to reach a specified target. Abstract-- Although humanoid and quadruped robots provide a wide range of capabilities, current control methods, such as Deep Reinforcement Learning, focus mainly on single skills. This approach is inefficient for solving more complicated tasks where high-level goals, physical robot limitations and desired motion style might all need to be taken into account. A more effective approach is to first train a multipurpose motion policy that acquires low-level skills through imitation, while providing latent space control over skill execution. Then, this policy can be used to efficiently solve downstream tasks. This method has already been successful for controlling characters in computer graphics. In this work, we apply the approach to humanoid and quadrupedal loco-manipulation by imitating either simple synthetic motions or kinematically retargeted dog motions. We extend the original formulation to handle constraints, ensuring deployment safety, and use a diffusion discriminator for better imitation quality.

Obstacle avoidance is central to safe navigation, especially for robots with arbitrary and nonconvex geometries operating in cluttered environments. Existing Control Barrier Function (CBF) approaches often rely on analytic clearance computations, which are infeasible for complex geometries, or on polytopic approximations, which become intractable when robot configurations are unknown. To address these limitations, this paper trains a residual neural network on a large dataset of robot-obstacle configurations to enable fast and tractable clearance prediction, even at unseen configurations. The predicted clearance defines the radius of a Local Safety Ball (LSB), which ensures continuous-time collision-free navigation. The LSB boundary is encoded as a Discrete-Time High-Order CBF (DHOCBF), whose constraints are incorporated into a nonlinear optimization framework. To improve feasibility, a novel relaxation technique is applied. The resulting framework ensure that the robot's rigid-body motion between consecutive time steps remains collision-free, effectively bridging discrete-time control and continuous-time safety. We show that the proposed method handles arbitrary, including nonconvex, robot geometries and generates collision-free, dynamically feasible trajectories in cluttered environments. Experiments demonstrate millisecond-level solve times and high prediction accuracy, highlighting both safety and efficiency beyond existing CBF-based methods.

This paper investigates artificial intelligence (AI) methodologies for the synthesis and transpilation of permutation circuits across generic topologies. Our approach uses Reinforcement Learning (RL) techniques to achieve near-optimal synthesis of permutation circuits up to 25 qubits. Rather than developing specialized models for individual topologies, we train a foundational model on a generic rectangular lattice, and employ masking mechanisms to dynamically select subsets of topologies during the synthesis. This enables the synthesis of permutation circuits on any topology that can be embedded within the rectangular lattice, without the need to re-train the model. In this paper we show results for 5x5 lattice and compare them to previous AI topology-oriented models and classical methods, showing that they outperform classical heuristics, and match previous specialized AI models, and performs synthesis even for topologies that were not seen during training. We further show that the model can be fine tuned to strengthen the performance for selected topologies of interest. This methodology allows a single trained model to efficiently synthesize circuits across diverse topologies, allowing its practical integration into transpilation workflows.

Multi-vehicle trajectory planning is a non-convex problem that becomes increasingly difficult in dense environments due to the rapid growth of collision constraints. Efficient exploration of feasible behaviors and resolution of tight interactions are essential for real-time, large-scale coordination. This paper introduces SMART, Scalable Multi-Agent Reasoning and Trajectory Planning, a hierarchical framework that combines priority-based search with distributed optimization to achieve efficient and feasible multi-vehicle planning. The upper layer explores diverse interaction modes using reinforcement learning-based priority estimation and large-step hybrid A* search, while the lower layer refines solutions via parallelizable convex optimization. By partitioning space among neighboring vehicles and constructing robust feasible corridors, the method decouples the joint non-convex problem into convex subproblems solved efficiently in parallel. This design alleviates the step-size trade-off while ensuring kinematic feasibility and collision avoidance. Experiments show that SMART consistently outperforms baselines. On 50 m x 50 m maps, it sustains over 90% success within 1 s up to 25 vehicles, while baselines often drop below 50%. On 100 m x 100 m maps, SMART achieves above 95% success up to 50 vehicles and remains feasible up to 90 vehicles, with runtimes more than an order of magnitude faster than optimization-only approaches. Built on vehicle-to-everything communication, SMART incorporates vehicle-infrastructure cooperation through roadside sensing and agent coordination, improving scalability and safety. Real-world experiments further validate this design, achieving planning times as low as 0.014 s while preserving cooperative behaviors.

Large language models (LLMs) have become integral to a wide range of applications worldwide, driving an unprecedented global demand for effective multilingual capabilities. Central to achieving robust multilingual performance is the strategic allocation of language proportions within training corpora. However, determining optimal language ratios is highly challenging due to intricate cross-lingual interactions and sensitivity to dataset scale. This paper introduces Climb (Cross-Lingual Interaction-aware Multilingual Balancing), a novel framework designed to systematically optimize multilingual data allocation. At its core, Climb introduces a cross-lingual interaction-aware language ratio, explicitly quantifying each language's effective allocation by capturing inter-language dependencies. Leveraging this ratio, Climb proposes a principled two-step optimization procedure--first equalizing marginal benefits across languages, then maximizing the magnitude of the resulting language allocation vectors--significantly simplifying the inherently complex multilingual optimization problem. Extensive experiments confirm that Climb can accurately measure cross-lingual interactions across various multilingual settings. LLMs trained with Climb-derived proportions consistently achieve state-of-the-art multilingual performance, even achieving competitive performance with open-sourced LLMs trained with more tokens.