Related papers: A Geometric Perspective on Autoencoders

Topology matters. Despite the recent success of point cloud processing with geometric deep learning, it remains arduous to capture the complex topologies of point cloud data with a learning model. Given a point cloud dataset containing…

In this work we introduce an Autoencoder for molecular conformations. Our proposed model converts the discrete spatial arrangements of atoms in a given molecular graph (conformation) into and from a continuous fixed-sized latent…

The autoencoder is an unsupervised learning paradigm that aims to create a compact latent representation of data by minimizing the reconstruction loss. However, it tends to overlook the fact that most data (images) are embedded in a…

Geometric trees are characterized by their tree-structured layout and spatially constrained nodes and edges, which significantly impacts their topological attributes. This inherent hierarchical structure plays a crucial role in domains such…

Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conventional methods in various fields and achieved great…

Deep generative models are tremendously successful in learning low-dimensional latent representations that well-describe the data. These representations, however, tend to much distort relationships between points, i.e. pairwise distances…

Learning neural operators on heterogeneous and irregular geometries remains a fundamental challenge, as existing approaches typically rely on structured discretisations or explicit mappings to a shared reference domain. We propose a unified…

Despite high-dimensionality of images, the sets of images of 3D objects have long been hypothesized to form low-dimensional manifolds. What is the nature of such manifolds? How do they differ across objects and object classes? Answering…

We propose a new geometric method for measuring the quality of representations obtained from deep learning. Our approach, called Random Polytope Descriptor, provides an efficient description of data points based on the construction of…

Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance,…

We propose a novel machine learning strategy for studying neuroanatomical shape variation. Our model works with volumetric binary segmentation images, and requires no pre-processing such as the extraction of surface points or a mesh. 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…

The shape of objects is an important source of visual information in a wide range of applications. One of the core challenges of shape quantification is to ensure that the extracted measurements remain invariant to transformations that…

In our previous work, we proposed that engrams in the brain could be biologically implemented as autoencoders over recurrent neural networks. These autoencoders would comprise basic excitatory/inhibitory motifs, with credit assignment…

Variational auto-encoders (VAEs) have proven to be a well suited tool for performing dimensionality reduction by extracting latent variables lying in a potentially much smaller dimensional space than the data. Their ability to capture…

In this paper, we focus on the problem of identifying semantic factors of variation in large image datasets. By training a convolutional Autoencoder on the image data, we create encodings, which describe each datapoint at a higher level of…

For multiple scientific endeavors it is common to measure a phenomenon of interest in more than one ways. We make observations of objects from several different perspectives in space, at different points in time; we may also measure…

Despite their great success in practical applications, there is still a lack of theoretical and systematic methods to analyze deep neural networks. In this paper, we illustrate an advanced information theoretic methodology to understand the…

The joint optimization of the reconstruction and classification error is a hard non convex problem, especially when a non linear mapping is utilized. In order to overcome this obstacle, a novel optimization strategy is proposed, in which a…

We introduce MGNet, a multi-task framework for monocular geometric scene understanding. We define monocular geometric scene understanding as the combination of two known tasks: Panoptic segmentation and self-supervised monocular depth…