Active learning sequentially selects the best instance for labeling by optimizing an acquisition function to enhance data/label efficiency. The selection can be either from a discrete instance set (pool-based scenario) or a continuous instance space (query synthesis scenario). In this work, we study both active learning scenarios for Gaussian Process Classification (GPC). The existing active learning strategies that maximize the Estimated Error Reduction (EER) aim at reducing the classification error after training with the new acquired instance in a one-step-look-ahead manner. The computation of EER-based acquisition functions is typically prohibitive as it requires retraining the GPC with every new query.

In this paper, we suggest a novel data-driven approach to active learning (AL).

Partial differential equations (PDEs) form the mathematical foundation for modeling physical systems in science and engineering, where numerical solutions demand rigorous accuracy-efficiency tradeoffs. Mesh movement techniques address this challenge by dynamically relocating mesh nodes to rapidly-varying regions, enhancing both simulation accuracy and computational efficiency. However, traditional approaches suffer from high computational complexity and geometric inflexibility, limiting their applicability, and existing supervised learning-based approaches face challenges in zero-shot generalization across diverse PDEs and mesh topologies.In this paper, we present an Unsupervised and Generalizable Mesh Movement Network (UGM2N). We first introduce unsupervised mesh adaptation through localized geometric feature learning, eliminating the dependency on pre-adapted meshes. We then develop a physics-constrained loss function, M-Uniform loss, that enforces mesh equidistribution at the nodal level.Experimental results demonstrate that the proposed network exhibits equation-agnostic generalization and geometric independence in efficient mesh adaptation. It demonstrates consistent superiority over existing methods, including robust performance across diverse PDEs and mesh geometries, scalability to multi-scale resolutions and guaranteed error reduction without mesh tangling.

The example in the introduction section of the main text is a synthetic binary phase diagram.

Practitioners of Bayesian statistics have long depended on Markov chain Monte Carlo (MCMC) to obtain samples from intractable posterior distributions. Unfortunately, MCMC algorithms are typically serial, and do not scale to the large datasets typical of modern machine learning. The recently proposed consensus Monte Carlo algorithm removes this limitation by partitioning the data and drawing samples conditional on each partition in parallel (Scott et al, 2013). A fixed aggregation function then combines these samples, yielding approximate posterior samples. We introduce variational consensus Monte Carlo (VCMC), a variational Bayes algorithm that optimizes over aggregation functions to obtain samples from a distribution that better approximates the target. The resulting objective contains an intractable entropy term; we therefore derive a relaxation of the objective and show that the relaxed problem is blockwise concave under mild conditions. We illustrate the advantages of our algorithm on three inference tasks from the literature, demonstrating both the superior quality of the posterior approximation and the moderate overhead of the optimization step. Our algorithm achieves a relative error reduction (measured against serial MCMC) of up to 39% compared to consensus Monte Carlo on the task of estimating 300-dimensional probit regression parameter expectations; similarly, it achieves an error reduction of 92% on the task of estimating cluster comembership probabilities in a Gaussian mixture model with 8 components in 8 dimensions. Furthermore, these gains come at moderate cost compared to the runtime of serial MCMC, achieving near-ideal speedup in some instances.

Partial Differential Equations (PDEs) describe phenomena ranging from turbulence and epidemics to quantum mechanics and financial markets. Despite recent advances in computational science, solving such PDEs for real-world applications remains prohibitively expensive because of the necessity of resolving a broad range of spatiotemporal scales. In turn, practitioners often rely on coarse-grained approximations of the original PDEs, trading off accuracy for reduced computational resources. To mitigate the loss of detail inherent in such approximations, closure models are employed to represent unresolved spatiotemporal interactions. We present a framework for developing closure models for PDEs using synthetic data acquired through the method of manufactured solutions. These data are used in conjunction with reinforcement learning to provide closures for coarse-grained PDEs. We illustrate the efficacy of our method using the one-dimensional and two-dimensional Burgers' equations and the two-dimensional advection equation. Moreover, we demonstrate that closure models trained for inhomogeneous PDEs can be effectively generalized to homogeneous PDEs. The results demonstrate the potential for developing accurate and computationally efficient closure models for systems with scarce data.

--Autonomy in Minimally Invasive Robotic Surgery (MIRS) has the potential to reduce surgeon cognitive and task load, thereby increasing procedural efficiency. However, implementing accurate autonomous control can be difficult due to poor end-effector proprioception, a limitation of their cable-driven mechanisms. Although the robot may have joint encoders for the end-effector pose calculation, various non-idealities make the entire kinematics chain inaccurate. Modern vision-based pose estimation methods lack real-time capability or can be hard to train and generalize. In this work, we demonstrate a real-time capable, vision transformer-based pose estimation approach that is trained using end-to-end differentiable kinematics and rendering in simulation. We demonstrate the potential of this method to correct for noisy pose estimates in simulation, with the longer term goal of verifying the sim-to-real transferability of our approach. The da Vinci Surgical System has been widely applied into different kinds of MIRS procedures in specializations such as, urologic [1], gynecologic [2], and cardiothoracic [3] surgery.

Large language models have been developed with ongoing efforts to improve their functionality, comprehend their internal workings, and guarantee their ethical and safe application. New developments in the field have led to the concept of'activation engineering'[13], which posits that activation vectors can mediate particular behaviors within LLMs. This development has made it possible to adjust and regulate the output of these models in new ways. This paper is motivated by the potential to extend this line of inquiry into the domain of personality traits in LLMs. The ability to dynamically adjust the personality of a language model without extensive retraining could mark a significant advancement in the field, offering improved flexibility in AI applications. This approach could potentially revolutionize how we interact with and deploy AI systems, allowing for more personalized and context-appropriate responses.