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Autoencoders are a type of unsupervised neural networks, which can be used to solve various tasks, e.g., dimensionality reduction, image compression, and image denoising. An AE has two goals: (i) compress the original input to a…
Image and video restoration has achieved a remarkable leap with the advent of deep learning. The success of deep learning paradigm lies in three key components: data, model, and loss. Currently, many efforts have been devoted to the first…
Deep learning based image compression has recently witnessed exciting progress and in some cases even managed to surpass transform coding based approaches that have been established and refined over many decades. However, state-of-the-art…
Manifold learning is a hot research topic in the field of computer science and has many applications in the real world. A main drawback of manifold learning methods is, however, that there is no explicit mappings from the input data…
Inspired by the success of deep learning techniques in the physical and chemical sciences, we apply a modification of an autoencoder type deep neural network to the task of dimension reduction of molecular dynamics data. We can show that…
This paper describes one objective function for learning semantically coherent feature embeddings in multi-output classification problems, i.e., when the response variables have dimension higher than one. In particular, we consider the…
Manifold learning techniques have become increasingly valuable as data continues to grow in size. By discovering a lower-dimensional representation (embedding) of the structure of a dataset, manifold learning algorithms can substantially…
This work describes a novel data-driven latent space inference framework built on paired autoencoders to handle observational inconsistencies when solving inverse problems. Our approach uses two autoencoders, one for the parameter space and…
Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. This thesis presents a mathematical…
There has been a growing interest in statistical inference from data satisfying the so-called manifold hypothesis, assuming data points in the high-dimensional ambient space to lie in close vicinity of a submanifold of much lower dimension.…
Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian through a pull-back metric,…
High-resolution medical images are beneficial for analysis but their acquisition may not always be feasible. Alternatively, high-resolution images can be created from low-resolution acquisitions using conventional upsampling methods, but…
The problem of learning a manifold structure on a dataset is framed in terms of a generative model, to which we use ideas behind autoencoders (namely adversarial/Wasserstein autoencoders) to fit deep neural networks. From a machine learning…
Autoencoders are the simplest neural network for unsupervised learning, and thus an ideal framework for studying feature learning. While a detailed understanding of the dynamics of linear autoencoders has recently been obtained, the study…
Neural networks transform high-dimensional data into compact, structured representations, often modeled as elements of a lower dimensional latent space. In this paper, we present an alternative interpretation of neural models as dynamical…
Datasets such as images, text, or movies are embedded in high-dimensional spaces. However, in important cases such as images of objects, the statistical structure in the data constrains samples to a manifold of dramatically lower…
Weakly-supervised anomaly detection aims at learning an anomaly detector from a limited amount of labeled data and abundant unlabeled data. Recent works build deep neural networks for anomaly detection by discriminatively mapping the normal…
Physics-constrained data-driven computing is an emerging computational paradigm that allows simulation of complex materials directly based on material database and bypass the classical constitutive model construction. However, it remains…
Manifold learning offers nonlinear dimensionality reduction of high-dimensional datasets. In this paper, we bring geometry processing to bear on manifold learning by introducing a new approach based on metric connection for generating a…
By replacing the lens with a thin optical element, lensless imaging enables new applications and solutions beyond those supported by traditional camera design and post-processing, e.g. compact and lightweight form factors and visual…