相关论文: A Discussion On the Validity of Manifold Learning

Simultaneously addressing multiple objectives is becoming increasingly important in modern machine learning. At the same time, data is often high-dimensional and costly to label. For a single objective such as prediction risk, conventional…

In a world where Machine Learning (ML) is increasingly deployed to support decision-making in critical domains, providing decision-makers with explainable, stable, and relevant inputs becomes fundamental. Understanding how machine learning…

Comprehensive evaluation of Large Language Models (LLMs) is an open research problem. Existing evaluations rely on deterministic point estimates generated via greedy decoding. However, we find that deterministic evaluations fail to capture…

Deep reinforcement learning (DRL) demonstrates great potential in mapless navigation domain. However, such a navigation model is normally restricted to a fixed configuration of the range sensor because its input format is fixed. In this…

Statistical heterogeneity severely limits the performance of federated learning (FL), motivating several explorations e.g., FedProx, MOON and FedDyn, to alleviate this problem. Despite effectiveness, their considered scenario generally…

Understanding how Large Language Models (LLMs) perform complex reasoning and their failure mechanisms is a challenge in interpretability research. To provide a measurable geometric analysis perspective, we define the concept of the…

Based on the numerical manifold method principle, we developed a mathematical framework of a neural network manifold: Deep Manifold and discovered that neural networks: 1) is numerical computation combining forward and inverse; 2) have near…

Recently, there has been much interest in spectral approaches to learning manifolds---so-called kernel eigenmap methods. These methods have had some successes, but their applicability is limited because they are not robust to noise. To…

Many machine learning problems involve regressing variables on a non-Euclidean manifold -- e.g. a discrete probability distribution, or the 6D pose of an object. One way to tackle these problems through gradient-based learning is to use a…

Deep Metric Learning (DML) models often require strong local and global representations, however, effective integration of local and global features in DML model training is a challenge. DML models are often trained with specific loss…

Deep metric learning (DML) has received much attention in deep learning due to its wide applications in computer vision. Previous studies have focused on designing complicated losses and hard example mining methods, which are mostly…

Neural operators offer an effective framework for learning solutions of partial differential equations for many physical systems in a resolution-invariant and data-driven manner. Existing neural operators, however, often suffer from…

With the rapid expansion of applied 3D computational vision, shape descriptors have become increasingly important for a wide variety of applications and objects from molecules to planets. Appropriate shape descriptors are critical for…

The imperative to eliminate undesirable data memorization underscores the significance of machine unlearning for large language models (LLMs). Recent research has introduced a series of promising unlearning methods, notably boosting the…

Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of…

This paper studies double/debiased machine learning (DML) methods applied to weakly dependent data. We allow observations to be situated in a general metric space that accommodates spatial and network data. Existing work implements…

Deep Learning (DL) algorithms have become the de facto Machine Learning (ML) algorithm for large scale data analysis. DL algorithms are computationally expensive - even distributed DL implementations which use MPI require days of training…

Nonlinear dimensionality reduction (NLDR) algorithms such as Isomap, LLE and Laplacian Eigenmaps address the problem of representing high-dimensional nonlinear data in terms of low-dimensional coordinates which represent the intrinsic…

Numerous problems in machine learning are formulated as optimization with manifold constraints. In this paper, we propose the Manifold alternating directions method of multipliers (MADMM), an extension of the classical ADMM scheme for…

We study multigrade deep learning (MGDL) as a principled framework for structured error refinement in deep neural networks. While the approximation power of neural networks is now relatively well understood, training very deep architectures…