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A hybrid framework integrating the Virtual Element Method (VEM) with deep learning is presented as an initial step toward developing efficient and flexible numerical models for one-dimensional Euler-Bernoulli beams. The primary aim is to…

(Visual) Simultaneous Localization and Mapping (SLAM) remains a fundamental challenge in enabling autonomous systems to navigate and understand large-scale environments. Traditional SLAM approaches struggle to balance efficiency and…

Recent years have witnessed remarkable progress in developing Vision-Language Models (VLMs) capable of processing both textual and visual inputs. These models have demonstrated impressive performance, leading to their widespread adoption in…

We introduce a new technique for solving uni-parametric versions of linear programs, convex quadratic programs, and linear complementarity problems in which a single parameter is permitted to be present in any of the input data. We…

We provide a unified framework that applies to a general family of convex losses across binary and multiclass settings in the overparameterized regime to approximately characterize the implicit bias of gradient descent in closed form.…

Information Retrieval (IR) methods aim to identify documents relevant to a query, which have been widely applied in various natural language tasks. However, existing approaches typically consider only the textual content within documents,…

Vision-Language Models (VLMs) are increasingly used in safety-critical applications because of their broad reasoning capabilities and ability to generalize with minimal task-specific engineering. Despite these advantages, they can exhibit…

This paper presents a novel framework for processing volumetric medical information using Visual Transformers (ViTs). First, We extend the state-of-the-art Swin Transformer model to the 3D medical domain. Second, we propose a new approach…

In this paper, we propose a single UniFied transfOrmer (UFO), which is capable of processing either unimodal inputs (e.g., image or language) or multimodal inputs (e.g., the concatenation of the image and the question), for vision-language…

In our prior work [arXiv:2109.09316], neural network methods with inputs based on domain of dependence and a converging sequence were introduced for solving one dimensional conservation laws, in particular the Euler systems. To predict a…

In the Large Language Model(LLM) reasoning scenario, people often estimate state value via Monte Carlo sampling. Though Monte Carlo estimation is an elegant method with less inductive bias, noise and errors are inevitably introduced due to…

Variational inference (VI) has become the method of choice for fitting many modern probabilistic models. However, practitioners are faced with a fragmented literature that offers a bewildering array of algorithmic options. First, the…

We consider the optimal value of information (VoI) problem, where the goal is to sequentially select a set of tests with a minimal cost, so that one can efficiently make the best decision based on the observed outcomes. Existing algorithms…

The Large Vision Language Model (VLM) has recently addressed remarkable progress in bridging two fundamental modalities. VLM, trained by a sufficiently large dataset, exhibits a comprehensive understanding of both visual and linguistic to…

In data analysis, there continues to be a need for interpretable dimensionality reduction methods whereby instrinic meaning associated with the data is retained in the reduced space. Standard approaches such as Principal Component Analysis…

Most of the existing methods for estimating the local intrinsic dimension of a data distribution do not scale well to high-dimensional data. Many of them rely on a non-parametric nearest neighbors approach which suffers from the curse of…

We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical…

This work presents UNO, a unified monocular visual odometry framework that enables robust and adaptable pose estimation across diverse environments, platforms, and motion patterns. Unlike traditional methods that rely on deployment-specific…

Large Language Models (LLMs) can memorize sensitive information, raising concerns about potential misuse. LLM Unlearning, a post-hoc approach to remove this information from trained LLMs, offers a promising solution to mitigate these risks.…

Mutual information (MI) is a fundamental measure of statistical dependence between two variables, yet accurate estimation from finite data remains notoriously difficult. No estimator is universally reliable, and common approaches fail in…