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Deep learning has emerged as a powerful framework for analyzing biomolecular dynamics trajectories, enabling efficient representations that capture essential system dynamics and facilitate mechanistic studies. We propose a neural network…

We study the approximation by tensor networks (TNs) of functions from classical smoothness classes. The considered approximation tool combines a tensorization of functions in $L^p([0,1))$, which allows to identify a univariate function with…

In machine learning, a loss function measures the difference between model predictions and ground-truth (or target) values. For neural network models, visualizing how this loss changes as model parameters are varied can provide insights…

Spectral-based subspace clustering methods have proved successful in many challenging applications such as gene sequencing, image recognition, and motion segmentation. In this work, we first propose a novel spectral-based subspace…

With the development of computational power and techniques for data collection, deep learning demonstrates a superior performance over most existing algorithms on visual benchmark data sets. Many efforts have been devoted to studying the…

In this paper we present a comprehensive treatment of function spaces with logarithmic smoothness (Besov, Sobolev, Triebel-Lizorkin). We establish the following results: Sharp embeddings between the Besov spaces defined by differences and…

Clustering is central to many data-driven application domains and has been studied extensively in terms of distance functions and grouping algorithms. Relatively little work has focused on learning representations for clustering. In this…

Deep clustering algorithms combine representation learning and clustering by jointly optimizing a clustering loss and a non-clustering loss. In such methods, a deep neural network is used for representation learning together with a…

Social network analysis is an important problem in data mining. A fundamental step for analyzing social networks is to encode network data into low-dimensional representations, i.e., network embeddings, so that the network topology…

Unsupervised learning has gained prominence in the big data era, offering a means to extract valuable insights from unlabeled datasets. Deep clustering has emerged as an important unsupervised category, aiming to exploit the non-linear…

Deep-embedding methods aim to discover representations of a domain that make explicit the domain's class structure and thereby support few-shot learning. Disentangling methods aim to make explicit compositional or factorial structure. We…

Deep clustering - joint representation learning and latent space clustering - is a well studied problem especially in computer vision and text processing under the deep learning framework. While the representation learning is generally…

Deep neural networks can be effective means to automatically classify aerial images but is easy to overfit to the training data. It is critical for trained neural networks to be robust to variations that exist between training and test…

We propose a novel shape representation useful for analyzing and processing shape collections, as well for a variety of learning and inference tasks. Unlike most approaches that capture variability in a collection by using a template model…

Deep Learning methods have significantly advanced various data-driven tasks such as regression, classification, and forecasting. However, much of this progress has been predicated on the strong but often unrealistic assumption that training…

We consider the problem of learning low-dimensional representations for large-scale Markov chains. We formulate the task of representation learning as that of mapping the state space of the model to a low-dimensional state space, called the…

Deep learning research aims at discovering learning algorithms that discover multiple levels of distributed representations, with higher levels representing more abstract concepts. Although the study of deep learning has already led to…

Constructing good representations is critical for learning complex tasks in a sample efficient manner. In the context of meta-learning, representations can be constructed from common patterns of previously seen tasks so that a future task…

Deep metric learning algorithms have been utilized to learn discriminative and generalizable models which are effective for classifying unseen classes. In this paper, a novel noise tolerant deep metric learning algorithm is proposed. The…

We introduce implicit Bayesian neural networks, a simple and scalable approach for uncertainty representation in deep learning. Standard Bayesian approach to deep learning requires the impractical inference of the posterior distribution…