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Heterogeneous Bayesian decentralized data fusion captures the set of problems in which two robots must combine two probability density functions over non-equal, but overlapping sets of random variables. In the context of multi-robot dynamic systems, this enables robots to take a "divide and conquer" approach to reason and share data over complementary tasks instead of over the full joint state space. For example, in a target tracking application, this allows robots to track different subsets of targets and share data on only common targets. This paper presents a framework by which robots can each use a local factor graph to represent relevant partitions of a complex global joint probability distribution, thus allowing them to avoid reasoning over the entirety of a more complex model and saving communication as well as computation costs. From a theoretical point of view, this paper makes contributions by casting the heterogeneous decentralized fusion problem in terms of a factor graph, analyzing the challenges that arise due to dynamic filtering, and then developing a new conservative filtering algorithm that ensures statistical correctness. From a practical point of view, we show how this framework can be used to represent different multi-robot applications and then test it with simulations and hardware experiments to validate and demonstrate its statistical conservativeness, applicability, and robustness to real-world challenges.

We propose a trust-region stochastic sequential quadratic programming algorithm (TR-StoSQP) to solve nonlinear optimization problems with stochastic objectives and deterministic equality constraints. We consider a fully stochastic setting, where at each step a single sample is generated to estimate the objective gradient. The algorithm adaptively selects the trust-region radius and, compared to the existing line-search StoSQP schemes, allows us to utilize indefinite Hessian matrices (i.e., Hessians without modification) in SQP subproblems. As a trust-region method for constrained optimization, our algorithm must address an infeasibility issue -- the linearized equality constraints and trust-region constraints may lead to infeasible SQP subproblems. In this regard, we propose an adaptive relaxation technique to compute the trial step, consisting of a normal step and a tangential step. To control the lengths of these two steps while ensuring a scale-invariant property, we adaptively decompose the trust-region radius into two segments, based on the proportions of the rescaled feasibility and optimality residuals to the rescaled full KKT residual. The normal step has a closed form, while the tangential step is obtained by solving a trust-region subproblem, to which a solution ensuring the Cauchy reduction is sufficient for our study. We establish a global almost sure convergence guarantee for TR-StoSQP, and illustrate its empirical performance on both a subset of problems in the CUTEst test set and constrained logistic regression problems using data from the LIBSVM collection.

The paper studies the problem of constructing nonparametric simultaneous confidence bands with nonasymptotic and distribition-free guarantees. The target function is assumed to be band-limited and the approach is based on the theory of Paley-Wiener reproducing kernel Hilbert spaces. The starting point of the paper is a recently developed algorithm to which we propose three types of improvements. First, we relax the assumptions on the noises by replacing the symmetricity assumption with a weaker distributional invariance principle. Then, we propose a more efficient way to estimate the norm of the target function, and finally we enhance the construction of the confidence bands by tightening the constraints of the underlying convex optimization problems. The refinements are also illustrated through numerical experiments.

Many scientific and technological problems are related to optimization. Among them, black-box optimization in high-dimensional space is particularly challenging. Recent neural network-based black-box optimization studies have shown noteworthy achievements. However, their capability in high-dimensional search space is still limited. This study proposes a black-box optimization method based on the evolution strategy (ES) and the generative neural network (GNN) model. We designed the algorithm so that the ES and the GNN model work cooperatively. This hybrid model enables reliable training of surrogate networks; it optimizes multi-objective, high-dimensional, and stochastic black-box functions. Our method outperforms baseline optimization methods in this experiment, including ES, and Bayesian optimization.

We explore a novel methodology for constructing confidence regions for parameters of linear models, using predictions from any arbitrary predictor. Our framework requires minimal assumptions on the noise and can be extended to functions deviating from strict linearity up to some adjustable threshold, thereby accommodating a comprehensive and pragmatically relevant set of functions. The derived confidence regions can be cast as constraints within a Mixed Integer Linear Programming framework, enabling optimisation of linear objectives. This representation enables robust optimization and the extraction of confidence intervals for specific parameter coordinates. Unlike previous methods, the confidence region can be empty, which can be used for hypothesis testing. Finally, we validate the empirical applicability of our method on synthetic data.

Isocontouring is one of the most widely used visualization techniques. However, many popular contouring algorithms were created prior to the advent of ubiquitous parallel approaches, such as multi-core, shared memory computing systems. With increasing data sizes and computational loads, it is essential to reimagine such algorithms to leverage the increased computing capabilities available today. To this end we have redesigned the SurfaceNets algorithm, a powerful technique which is often employed to isocontour non-continuous, discrete, volumetric scalar fields such as segmentation label maps. Label maps are ubiquitous to medical computing and biological analysis, used in applications ranging from anatomical atlas creation to brain connectomics. This novel Parallel SurfaceNets algorithm has been redesigned using concepts from the high-performance Flying Edges continuous isocontouring algorrithm. It consists of two basic steps, surface extraction followed by constrained smoothing, parallelized over volume edges and employing a double-buffering smoothing approach to guarantee determinism. The algorithm can extract and smooth multiple segmented objects in a single execution, producing a polygonal (triangular/quadrilateral) mesh with points and polygons fully shared between neighboring objects. Performance is typically one to two orders of magnitude faster than the current sequential algorithms for discrete isosurface extraction on small core-count commodity CPU hardware. We demonstrate the effectiveness of the algorithm on five different datasets including human torso and brain atlases, mouse brain segmentation, and electron microscopy connectomics. The software is currently available under a permissive, open source license in the VTK visualization system.

In recent years, large-scale pre-trained multimodal models (LMM) generally emerge to integrate the vision and language modalities, achieving considerable success in various natural language processing and computer vision tasks. The growing size of LMMs, however, results in a significant computational cost for fine-tuning these models for downstream tasks. Hence, prompt-based interaction strategy is studied to align modalities more efficiently. In this contex, we propose a novel prompt-based multimodal interaction strategy inspired by human memory strategy, namely Memory-Inspired Temporal Prompt Interaction (MITP). Our proposed method involves in two stages as in human memory strategy: the acquiring stage, and the consolidation and activation stage. We utilize temporal prompts on intermediate layers to imitate the acquiring stage, leverage similarity-based prompt interaction to imitate memory consolidation, and employ prompt generation strategy to imitate memory activation. The main strength of our paper is that we interact the prompt vectors on intermediate layers to leverage sufficient information exchange between modalities, with compressed trainable parameters and memory usage. We achieve competitive results on several datasets with relatively small memory usage and 2.0M of trainable parameters (about 1% of the pre-trained foundation model).

The recent introduction of the Least-Squares Support Vector Regression (LS-SVR) algorithm for solving differential and integral equations has sparked interest. In this study, we expand the application of this algorithm to address systems of differential-algebraic equations (DAEs). Our work presents a novel approach to solving general DAEs in an operator format by establishing connections between the LS-SVR machine learning model, weighted residual methods, and Legendre orthogonal polynomials. To assess the effectiveness of our proposed method, we conduct simulations involving various DAE scenarios, such as nonlinear systems, fractional-order derivatives, integro-differential, and partial DAEs. Finally, we carry out comparisons between our proposed method and currently established state-of-the-art approaches, demonstrating its reliability and effectiveness.

We design a distributed coordinated guiding vector field (CGVF) for a group of robots to achieve ordering-flexible motion coordination while maneuvering on a desired two-dimensional (2D) surface. The CGVF is characterized by three terms, i.e., a convergence term to drive the robots to converge to the desired surface, a propagation term to provide a traversing direction for maneuvering on the desired surface, and a coordinated term to achieve the surface motion coordination with an arbitrary ordering of the robotic group. By setting the surface parameters as additional virtual coordinates, the proposed approach eliminates the potential singularity of the CGVF and enables both the global convergence to the desired surface and the maneuvering on the surface from all possible initial conditions. The ordering-flexible surface motion coordination is realized by each robot to share with its neighbors only two virtual coordinates, i.e. that of a given target and that of its own, which reduces the communication and computation cost in multi-robot surface navigation. Finally, the effectiveness of the CGVF is substantiated by extensive numerical simulations.

Large language models (LLMs) often generate convincing, fluent explanations. However, different from humans, they often generate inconsistent explanations on different inputs. For example, an LLM may generate the explanation "all birds can fly" when answering the question "Can sparrows fly?" but meanwhile answer "no" to the related question "Can penguins fly?". Explanations should be consistent across related examples so that they allow a human to simulate the LLM's decision process on multiple examples. We propose explanation-consistency finetuning (EC-finetuning), a method that adapts LLMs to generate more consistent natural-language explanations on related examples. EC-finetuning involves finetuning LLMs on synthetic data that is carefully constructed to contain consistent explanations. Across a variety of question-answering datasets in various domains, EC-finetuning yields a 10.0% relative explanation consistency improvement on four finetuning datasets, and generalizes to seven out-of-distribution datasets not seen during finetuning (+4.5% relative). Code is available at //github.com/yandachen/explanation-consistency-finetuning .