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Learned denoisers play a fundamental role in various signal generation (e.g., diffusion models) and reconstruction (e.g., compressed sensing) architectures, whose success derives from their ability to leverage low-dimensional structure in…

Unsupervised learning is of growing interest because it unlocks the potential held in vast amounts of unlabelled data to learn useful representations for inference. Autoencoders, a form of generative model, may be trained by learning to…

Autoencoders learn data representations (codes) in such a way that the input is reproduced at the output of the network. However, it is not always clear what kind of properties of the input data need to be captured by the codes. Kernel…

Autoencoders are certainly among the most studied and used Deep Learning models: the idea behind them is to train a model in order to reconstruct the same input data. The peculiarity of these models is to compress the information through a…

High dimensional data is often assumed to be concentrated on or near a low-dimensional manifold. Autoencoders (AE) is a popular technique to learn representations of such data by pushing it through a neural network with a low dimension…

Deep neural network autoencoders are routinely used computationally for model reduction. They allow recognizing the intrinsic dimension of data that lie in a $k$-dimensional subset $K$ of an input Euclidean space $\mathbb{R}^n$. The…

One aim of dimensionality reduction is to discover the main factors that explain the data, and as such is paramount to many applications. When working with high dimensional data, autoencoders offer a simple yet effective approach to learn…

Depth perception is considered an invaluable source of information for various vision tasks. However, depth maps acquired using consumer-level sensors still suffer from non-negligible noise. This fact has recently motivated researchers to…

With the rapid growth of graph-structured data in critical domains, unsupervised graph-level anomaly detection (UGAD) has become a pivotal task. UGAD seeks to identify entire graphs that deviate from normal behavioral patterns. However,…

A fundamental task in data exploration is to extract simplified low dimensional representations that capture intrinsic geometry in data, especially for faithfully visualizing data in two or three dimensions. Common approaches to this task…

Conformal Autoencoders are a neural network architecture that imposes orthogonality conditions between the gradients of latent variables to obtain disentangled representations of data. In this work we show that orthogonality relations…

We propose a kernel-spectral embedding algorithm for learning low-dimensional nonlinear structures from high-dimensional and noisy observations, where the datasets are assumed to be sampled from an intrinsically low-dimensional manifold and…

We present a representation learning method that learns features at multiple different levels of scale. Working within the unsupervised framework of denoising autoencoders, we observe that when the input is heavily corrupted during…

In spectroscopic experiments, data acquisition in multi-dimensional phase space may require long acquisition time, owing to the large phase space volume to be covered. In such case, the limited time available for data acquisition can be a…

An autoencoder is a neural network which data projects to and from a lower dimensional latent space, where this data is easier to understand and model. The autoencoder consists of two sub-networks, the encoder and the decoder, which carry…

We present an application of autoencoders to the problem of noise reduction in single-shot astronomical images and explore its suitability for upcoming large-scale surveys. Autoencoders are a machine learning model that summarises an input…

Data living on manifolds commonly appear in many applications. Often this results from an inherently latent low-dimensional system being observed through higher dimensional measurements. We show that under certain conditions, it is possible…

While deep neural networks have been shown to perform remarkably well in many machine learning tasks, labeling a large amount of ground truth data for supervised training is usually very costly to scale. Therefore, learning robust…

Electrocardiogram (ECG) signals are often degraded by various noise sources such as baseline wander, motion artifacts, and electromyographic interference, posing a major challenge in clinical settings. This paper presents a lightweight deep…

We propose a deep autoencoder with graph topology inference and filtering to achieve compact representations of unorganized 3D point clouds in an unsupervised manner. Many previous works discretize 3D points to voxels and then use…