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The hyperbolic manifold is a smooth manifold of negative constant curvature. While the hyperbolic manifold is well-studied in the literature, it has gained interest in the machine learning and natural language processing communities lately…
Given a "data manifold" $M\subset \mathbb{R}^n$ and "latent space" $\mathbb{R}^\ell$, an autoencoder is a pair of continuous maps consisting of an "encoder" $E\colon \mathbb{R}^n\to \mathbb{R}^\ell$ and "decoder" $D\colon \mathbb{R}^\ell\to…
Multimodal Language Analysis is a demanding area of research, since it is associated with two requirements: combining different modalities and capturing temporal information. During the last years, several works have been proposed in the…
A big mystery in deep learning continues to be the ability of methods to generalize when the number of model parameters is larger than the number of training examples. In this work, we take a step towards a better understanding of the…
Learning useful representations with little or no supervision is a key challenge in artificial intelligence. We provide an in-depth review of recent advances in representation learning with a focus on autoencoder-based models. To organize…
Nonlinear dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. However, many popular methods can fail dramatically, even on simple two-dimensional manifolds, due to problems such as…
Auto-encoder models that preserve similarities in the data are a popular tool in representation learning. In this paper we introduce several auto-encoder models that preserve local distances when mapping from the data space to the latent…
Embedding graphs in continous spaces is a key factor in designing and developing algorithms for automatic information extraction to be applied in diverse tasks (e.g., learning, inferring, predicting). The reliability of graph embeddings…
Image synthesis is a core problem in modern deep learning, and many recent architectures such as autoencoders and Generative Adversarial networks produce spectacular results on highly complex data, such as images of faces or landscapes.…
Modern large language models (LLMs) excel at tasks that require storing and retrieving knowledge, such as factual recall and question answering. Transformers are central to this capability because they can encode information during training…
Learning mappings of data on manifolds is an important topic in contemporary machine learning, with applications in astrophysics, geophysics, statistical physics, medical diagnosis, biochemistry, 3D object analysis. This paper studies the…
Latent manifolds of autoencoders provide low-dimensional representations of data, which can be studied from a geometric perspective. We propose to describe these latent manifolds as implicit submanifolds of some ambient latent space. Based…
The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we…
A convolutional autoencoder is trained using a database of airfoil aerodynamic simulations and assessed in terms of overall accuracy and interpretability. The goal is to predict the stall and to investigate the ability of the autoencoder to…
The dynamics of a turbulent flow tend to occupy only a portion of the phase space at a statistically stationary regime. From a dynamical systems point of view, this portion is the attractor. The knowledge of the turbulent attractor is…
Autoencoders are unsupervised machine learning circuits whose learning goal is to minimize a distortion measure between inputs and outputs. Linear autoencoders can be defined over any field and only real-valued linear autoencoder have been…
A rapidly growing area of research is the use of machine learning approaches such as autoencoders for dimensionality reduction of data and models in scientific applications. We show that the canonical formulation of autoencoders suffers…
Masked Autoencoders is a simple yet powerful self-supervised learning method. However, it learns representations indirectly by reconstructing masked input patches. Several methods learn representations directly by predicting representations…
Network data are ubiquitous in modern machine learning, with tasks of interest including node classification, node clustering and link prediction. A frequent approach begins by learning an Euclidean embedding of the network, to which…
While many approaches exist in the literature to learn low-dimensional representations for data collections in multiple modalities, the generalizability of multi-modal nonlinear embeddings to previously unseen data is a rather overlooked…