Related papers: Breaking the curse of dimensionality with Isolatio…

We consider neural networks with a single hidden layer and non-decreasing homogeneous activa-tion functions like the rectified linear units. By letting the number of hidden units grow unbounded and using classical non-Euclidean…

This paper demonstrates that when a shallow neural network with a Lipschitz continuous activation function is trained using either empirical or population risk to approximate a target function that is $r$ times continuously differentiable…

In this paper we prove that rectified deep neural networks do not suffer from the curse of dimensionality when approximating McKean--Vlasov SDEs in the sense that the number of parameters in the deep neural networks only grows polynomially…

This work investigates the optimization instability of deep neural networks from a less-explored yet insightful perspective: the emergence and amplification of singularities in the parametric space. Our analysis reveals that parametric…

Today's best language models still struggle with hallucinations: factually incorrect generations, which impede their ability to reliably retrieve information seen during training. The reversal curse, where models cannot recall information…

Single Image Super-Resolution (SISR) aims to improve resolution of small-size low-quality image from a single one. With popularity of consumer electronics in our daily life, this topic has become more and more attractive. In this paper, we…

We introduce a priori Sobolev-space error estimates for the solution of nonlinear, and possibly parametric, PDEs using Gaussian process and kernel based methods. The primary assumptions are: (1) a continuous embedding of the reproducing…

The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…

Agglomerative hierarchical clustering (AHC) is one of the popular clustering approaches. Existing AHC methods, which are based on a distance measure, have one key issue: it has difficulty in identifying adjacent clusters with varied…

Support Vector Machines (SVMs) are powerful learners that have led to state-of-the-art results in various computer vision problems. SVMs suffer from various drawbacks in terms of selecting the right kernel, which depends on the image…

The aim of this paper is to propose a geometric framework for modelling similarity search in large and multidimensional data spaces of general nature, which seems to be flexible enough to address such issues as analysis of complexity,…

Why do even the most powerful 7B-parameter embedding models struggle with simple retrieval tasks that the decades old BM25 handles with ease? Recent theory suggests that this happens because of a dimensionality bottleneck. This occurs when…

Over the last years, security kernels have played a promising role in reshaping the landscape of platform security on today's ubiquitous embedded devices. Security kernels, such as separation kernels, enable constructing high-assurance…

Symmetry is an important composition feature by investigating similar sides inside an image plane. It has a crucial effect to recognize man-made or nature objects within the universe. Recent symmetry detection approaches used a smoothing…

Spacetime singularities in numerical relativity can be avoided by excising a region of the computational domain from inside the apparent horizon. We report on results of such a scheme that is based on using ({\it i}) a horizon locking…

We explain how to use Kolmogorov Superposition Theorem (KST) to break the curse of dimensionality when approximating a dense class of multivariate continuous functions. We first show that there is a class of functions called…

Quantum machine learning, which involves running machine learning algorithms on quantum devices, may be one of the most significant flagship applications for these devices. Unlike its classical counterparts, the role of data in quantum…

To adapt kernel two-sample and independence testing to complex structured data, aggregation of multiple kernels is frequently employed to boost testing power compared to single-kernel tests. However, we observe a phenomenon that directly…

We present a sequential version of the kernelized Stein discrepancy goodness-of-fit test, which allows for conducting goodness-of-fit tests for unnormalized densities that are continuously monitored and adaptively stopped. That is, the…

Trajectory clustering enables the discovery of common patterns in trajectory data. Current methods of trajectory clustering rely on a distance measure between two points in order to measure the dissimilarity between two trajectories. The…