Related papers: Intrinsic dimension estimation for discrete metric…

Utilizing recently developed abstract notions of sectional curvature, we introduce a method for constructing a curvature-based geometric profile of discrete metric spaces. The curvature concept that we use here captures the metric relations…

Dimension Estimation (DE) and Dimension Reduction (DR) are two closely related topics, but with quite different goals. In DE, one attempts to estimate the intrinsic dimensionality or number of latent variables in a set of measurements of a…

As network data has become ubiquitous in the sciences, there has been growing interest in network models whose structure is driven by latent node-level variables in a (typically low-dimensional) latent geometric space. These "latent…

Sharing images online poses security threats to a wide range of users due to the unawareness of privacy information. Deep features have been demonstrated to be a powerful representation for images. However, deep features usually suffer from…

Out-of-distribution (OOD) detection is a critical issue for the stable and reliable operation of systems using a deep neural network (DNN). Although many OOD detection methods have been proposed, it remains unclear how the differences…

Private data analysis suffers a costly curse of dimensionality. However, the data often has an underlying low-dimensional structure. For example, when optimizing via gradient descent, the gradients often lie in or near a low-dimensional…

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…

Dimension reduction is a common strategy to study non-linear dynamical systems composed by a large number of variables. The goal is to find a smaller version of the system whose time evolution is easier to predict while preserving some of…

The Manifold Hypothesis is a widely accepted tenet of Machine Learning which asserts that nominally high-dimensional data are in fact concentrated near a low-dimensional manifold, embedded in high-dimensional space. This phenomenon is…

Gradients have been used to quantify feature importance in machine learning models. Unfortunately, in nonlinear deep networks, not only individual neurons but also the whole network can saturate, and as a result an important input feature…

Many recently trained neural networks employ large numbers of parameters to achieve good performance. One may intuitively use the number of parameters required as a rough gauge of the difficulty of a problem. But how accurate are such…

Intrusion detection has attracted a considerable interest from researchers and industries. The community, after many years of research, still faces the problem of building reliable and efficient IDS that are capable of handling large…

Many algorithms in machine learning and computational geometry require, as input, the intrinsic dimension of the manifold that supports the probability distribution of the data. This parameter is rarely known and therefore has to be…

Differential privacy (DP) is an essential technique for privacy-preserving. It was found that a large model trained for privacy preserving performs worse than a smaller model (e.g. ResNet50 performs worse than ResNet18). To better…

Image generation models trained on large datasets can synthesize high-quality images but often produce spatially inconsistent and distorted images due to limited information about the underlying structures and spatial layouts. In this work,…

The machine learning community has recently put effort into quantized or low-precision arithmetics to scale large models. This paper proposes performing probabilistic inference in the quantized, discrete parameter space created by these…

Prompting has become an important mechanism by which users can more effectively interact with many flavors of foundation model. Indeed, the last several years have shown that well-honed prompts can sometimes unlock emergent capabilities…

While nowadays visual anomaly detection algorithms use deep neural networks to extract salient features from images, the high dimensionality of extracted features makes it difficult to apply those algorithms to large data with 1000s of…

Based on our observation that there exists a dramatic drop for the singular values of the fully connected layers or a single feature map of the convolutional layer, and that the dimension of the concatenated feature vector almost equals the…

We propose a multifidelity dimension reduction method to identify a low-dimensional structure present in many engineering models. The structure of interest arises when functions vary primarily on a low-dimensional subspace of the…