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Understanding the latent space geometry of large language models (LLMs) is key to interpreting their behavior and improving alignment. Yet it remains unclear to what extent LLMs linearly organize representations related to semantic…

In this era of big data, data analytics and machine learning, it is imperative to find ways to compress large data sets such that intrinsic features necessary for subsequent analysis are not lost. The traditional workhorse for data…

Multi-label learning problems have manifested themselves in various machine learning applications. The key to successful multi-label learning algorithms lies in the exploration of inter-label correlations, which usually incur great…

The robustness of machine learning algorithms to distributions shift is primarily discussed in the context of supervised learning (SL). As such, there is a lack of insight on the robustness of the representations learned from unsupervised…

Deep learning's success has led to larger and larger models to handle more and more complex tasks; trained models can contain millions of parameters. These large models are compute- and memory-intensive, which makes it a challenge to deploy…

Building on the abstract Generalized Singular Value Decomposition (GSVD) theory of Brown et al. [2025], we prove that most modern neural architectures admit a generalized SVD representation in which they are left-invertible before a final…

Recently there has been increased interest in semi-supervised classification in the presence of graphical information. A new class of learning models has emerged that relies, at its most basic level, on classifying the data after first…

Understanding generalization in modern machine learning settings has been one of the major challenges in statistical learning theory. In this context, recent years have witnessed the development of various generalization bounds suggesting…

Building on the remarkable achievements in generative sampling of natural images, we propose an innovative challenge, potentially overly ambitious, which involves generating samples of entire multivariate time series that resemble images.…

Variable selection for high-dimensional, highly correlated data has long been a challenging problem, often yielding unstable and unreliable models. We propose a resample-aggregate framework that exploits diffusion models' ability to…

Self-supervised learning (SSL) has empirically shown its data representation learnability in many downstream tasks. There are only a few theoretical works on data representation learnability, and many of those focus on final data…

Given a hypergraph $H$, the Planar Support problem asks whether there is a planar graph $G$ on the same vertex set as $H$ such that each hyperedge induces a connected subgraph of $G$. Planar Support is motivated by applications in graph…

Deep neural networks typically outperform more traditional machine learning models in their ability to classify complex data, and yet is not clear how the individual hidden layers of a deep network contribute to the overall classification…

This paper presents a kernel-based discriminative learning framework on probability measures. Rather than relying on large collections of vectorial training examples, our framework learns using a collection of probability distributions that…

Learning well-separated features in high-dimensional spaces, such as text or image embeddings, is crucial for many machine learning applications. Achieving such separation can be effectively accomplished through the dispersion of…

Modeling uncertainty in deep neural networks, despite recent important advances, is still an open problem. Bayesian neural networks are a powerful solution, where the prior over network weights is a design choice, often a normal…

Efficient lossless compression is essential for minimizing storage costs and transmission overhead while preserving data integrity. Traditional compression techniques, such as dictionary-based and statistical methods, often struggle to…

The task of steel surface defect recognition is an industrial problem with great industry values. The data insufficiency is the major challenge in training a robust defect recognition network. Existing methods have investigated to enlarge…

We study the typical learning properties of the recently proposed Support Vectors Machines. The generalization error on linearly separable tasks, the capacity, the typical number of Support Vectors, the margin, and the robustness or noise…

Synthetic dataset generation in Computer Vision, particularly for industrial applications, is still underexplored. Industrial defect segmentation, for instance, requires highly accurate labels, yet acquiring such data is costly and…