相关论文: Active Manifolds: A non-linear analogue to Active …

In this article we study high-dimensional approximation capacities of shallow and deep artificial neural networks (ANNs) with the rectified linear unit (ReLU) activation. In particular, it is a key contribution of this work to reveal that…

In much of the literature on function approximation by deep networks, the function is assumed to be defined on some known domain, such as a cube or a sphere. In practice, the data might not be dense on these domains, and therefore, the…

The Active Contour Model (ACM) is a standard image analysis technique whose numerous variants have attracted an enormous amount of research attention across multiple fields. Incorrectly, however, the ACM's differential-equation-based…

This paper develops the concept of the Adjacent Deviation Subspace (ADS), a novel framework for reducing infinite-dimensional functional data into finite-dimensional vector or scalar representations while preserving critical information of…

A statistical emulator can be used as a surrogate of complex physics-based calculations to drastically reduce the computational cost. Its successful implementation hinges on an accurate representation of the nonlinear response surface with…

Approximate subgraph matching (ASM) is a task that determines the approximate presence of a given query graph in a large target graph. Being an NP-hard problem, ASM is critical in graph analysis with a myriad of applications ranging from…

Deep-learning architectures for classification problems involve the cross-entropy loss sometimes assisted with auxiliary loss functions like center loss, contrastive loss and triplet loss. These auxiliary loss functions facilitate better…

Active subspace is a model reduction method widely used in the uncertainty quantification community. In this paper, we propose analyzing the internal structure and vulnerability and deep neural networks using active subspace. Firstly, we…

The minimum action method (MAM) is to calculate the most probable transition path in randomly perturbed stochastic dynamics, based on the idea of action minimization in the path space. The accuracy of the numerical path between different…

Active learning (AL) has interesting features for parameter scans of new models. We show on a variety of models that AL scans bring large efficiency gains to the traditionally tedious work of finding boundaries for BSM models. In the MSSM,…

Many recent loss functions in deep metric learning are expressed with logarithmic and exponential forms, and they involve margin and scale as essential hyper-parameters. Since each data class has an intrinsic characteristic, several…

Background: Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, with the goal to gain a better understanding of the system. The…

Agentic artificial intelligence (AI) -- multi-agent systems that combine large language models with external tools and autonomous planning -- are rapidly transitioning from research laboratories into high-stakes domains. Our earlier "Basic"…

We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation matrices that are drawn from an invariant random matrix…

We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…

Neural ordinary differential equations (NODE) have garnered significant attention for their design of continuous-depth neural networks and the ability to learn data/feature dynamics. However, for high-dimensional systems, estimating…

Identifying the optimal diagnostic test and hardware system instance to infer reliability characteristics using field data is challenging, especially when constrained by fixed budgets and minimal maintenance cycles. Active Learning (AL) has…

We introduce a proximal subdifferential and develop a calculus for nonsmooth functions defined on any Riemannian manifold $M$. We give several applications of this theory, concerning: 1) differentiability and geometrical properties of the…

An efficient procedure using a novel semi-analytical forward solver for identifying heterogeneous and anisotropic elastic parameters from only one full-field measurement is proposed and explored. We formulate the inverse problem as an…

We develop an approach for active semantic perception which refers to using the semantics of the scene for tasks such as exploration. We build a compact, hierarchical multi-layer scene graph that can represent large, complex indoor…