Related papers: Does Dimensionality Reduction via Random Projectio…

Integrating hard constraints into deep learning is essential for safety-critical systems. Yet existing constructive layers that project predictions onto constraint boundaries face a fundamental bottleneck: gradient saturation. By collapsing…

Convolutional Neural Networks have been shown to be vulnerable to adversarial examples, which are known to locate in subspaces close to where normal data lies but are not naturally occurring and of low probability. In this work, we…

We address the challenge of correlated predictors in high-dimensional GLMs, where regression coefficients range from sparse to dense, by proposing a data-driven random projection method. This is particularly relevant for applications where…

The Expectation--Maximization (EM) algorithm is a simple meta-algorithm that has been used for many years as a methodology for statistical inference when there are missing measurements in the observed data or when the data is composed of…

Image restoration, which aims to recover high-quality images from their corrupted counterparts, often faces the challenge of being an ill-posed problem that allows multiple solutions for a single input. However, most deep learning based…

Electron tomography (ET) has become a standard technique for 3D characterization of materials at the nano-scale. Traditional reconstruction algorithms such as weighted back projection suffer from disruptive artifacts with insufficient…

Evolutionary algorithms (EA), a class of stochastic search methods based on the principles of natural evolution, have received widespread acclaim for their exceptional performance in various real-world optimization problems. While…

A major effort in modern high-dimensional statistics has been devoted to the analysis of linear predictors trained on nonlinear feature embeddings via empirical risk minimization (ERM). Gaussian equivalence theory (GET) has emerged as a…

State-of-the-art embedding models are increasingly derived from decoder-only Large Language Model (LLM) backbones adapted via contrastive learning. Given the emergence of reasoning models trained via Reinforcement Learning with Verifiable…

Fine-tuning large-scale pre-trained models is prohibitively expensive in terms of computation and memory costs. Low-Rank Adaptation (LoRA), a popular Parameter-Efficient Fine-Tuning (PEFT) method, offers an efficient solution by optimizing…

What does a world model learn from physical exploration, without any linguistic supervision? We argue the answer is organized by a single principle: the geometric structure of the physical world. Training a VAE-based world model on random…

Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to…

Dimensionality reduction is a common method for analyzing and visualizing high-dimensional data across domains. Dimensionality-reduction algorithms involve complex optimizations and the reduced dimensions computed by these algorithms…

Adversarial attacks can affect the object recognition capabilities of machines in wild. These can often result from spurious correlations between input and class labels, and are prone to memorization in large networks. While networks are…

During the last decades, we have witnessed a surge of interests of learning a low-dimensional space with discriminative information from one single view. Even though most of them can achieve satisfactory performance in some certain…

Embedding of large but redundant data, such as images or text, in a hierarchy of lower-dimensional spaces is one of the key features of representation learning approaches, which nowadays provide state-of-the-art solutions to problems once…

Deep learning approaches have provided state-of-the-art performance in many applications by relying on large and overparameterized neural networks. However, such networks have been shown to be very brittle and are difficult to deploy on…

Dimensionality reduction is a fundamental technique in machine learning and data analysis, enabling efficient representation and visualization of high-dimensional data. This paper explores five key methods: Principal Component Analysis…

High-dimensional sparse modeling via regularization provides a powerful tool for analyzing large-scale data sets and obtaining meaningful, interpretable models. The use of nonconvex penalty functions shows advantage in selecting important…

The development, integration, and maintenance of geospatial databases rely heavily on efficient and accurate matching procedures of Geospatial Entity Resolution (ER). While resolution of points-of-interest (POIs) has been widely addressed,…