Related papers: Hardware-Friendly Input Expansion for Accelerating…

We present Advancing Front Mapping (AFM), a provably robust algorithm for the computation of surface mappings to simple base domains. Given an input mesh and a convex or star-shaped target domain, AFM installs a (possibly refined) version…

The trade-off between clean accuracy and adversarial robustness is a pervasive phenomenon in deep learning, yet its geometric origin remains elusive. In this work, we utilize Symmetry-Breaking Dimensional Expansion (SBDE) as a controlled…

In this work, we present a study combining two approaches in the context of solving PDEs: the continuous finite element method (FEM) and more recent techniques based on neural networks. In recent years, physics-informed neural networks…

The $hp$-adaptive finite element method (FEM) - where one independently chooses the mesh size ($h$) and polynomial degree ($p$) to be used on each cell - has long been known to have better theoretical convergence properties than either $h$-…

Recent hardware acceleration advances have enabled powerful specialized accelerators for finite element computations, spiking neural network inference, and sparse tensor operations. However, existing approaches face fundamental limitations:…

We consider the problem of subset selection for $\ell_{p}$ subspace approximation, that is, to efficiently find a \emph{small} subset of data points such that solving the problem optimally for this subset gives a good approximation to…

Simplifying complex 3D meshes is a crucial step in robotics applications to enable efficient motion planning and physics simulation. Common methods, such as approximate convex decomposition, represent a mesh as a collection of simple parts,…

Recent advances in the field of artificial intelligence have been made possible by deep neural networks. In applications where data are scarce, transfer learning and data augmentation techniques are commonly used to improve the…

Deep neural networks have proven to be particularly effective in visual and audio recognition tasks. Existing models tend to be computationally expensive and memory intensive, however, and so methods for hardware-oriented approximation have…

For a large class of orthogonal basis functions, there has been a recent identification of expansion methods for computing accurate, stable approximations of a quantity of interest. This paper presents, within the context of uncertainty…

In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…

Chaotic free surface flows are challenging problems to simulate numerically, mainly due to the significant changes in geometry and frequent topological changes. Methods that track the evolution of the fluid in a Lagrangian formulation are a…

The use of integral equation methods for the efficient numerical solution of PDE boundary value problems requires two main tools: quadrature rules for the evaluation of layer potential integral operators with singular kernels, and fast…

Learning distance functions between complex objects, such as the Wasserstein distance to compare point sets, is a common goal in machine learning applications. However, functions on such complex objects (e.g., point sets and graphs) are…

Ensembles of deep neural networks demonstrate improved performance over single models. For enhancing the diversity of ensemble members while keeping their performance, particle-based inference methods offer a promising approach from a…

In this paper, we propose new learning algorithms for approximating high-dimensional functions using tree tensor networks in a least-squares setting. Given a dimension tree or architecture of the tensor network, we provide an algorithm that…

One of the arguments to explain the success of deep learning is the powerful approximation capacity of deep neural networks. Such capacity is generally accompanied by the explosive growth of the number of parameters, which, in turn, leads…

Approximate nearest neighbor search (ANN) data structures have widespread applications in machine learning, computational biology, and text processing. The goal of ANN is to preprocess a set S so that, given a query q, we can find a point y…

Emergent misalignment, where fine-tuning on narrow, non-harmful tasks induces harmful behaviors, poses a key challenge for AI safety in LLMs. Despite growing empirical evidence, its underlying mechanism remains unclear. To uncover the…

Adapting pre-trained foundation models for various downstream tasks has been prevalent in artificial intelligence. Due to the vast number of tasks and high costs, adjusting all parameters becomes unfeasible. To mitigate this, several…