Related papers: A Geometric Perspective on Autoencoders

When three-dimensional bodies contain thin features, non-trivial topology, or scan-derived surfaces, volumetric meshing can become the dominant bottleneck in simulation workflows. We replace this step with a learned geometric…

Visual data in autonomous driving perception, such as camera image and LiDAR point cloud, can be interpreted as a mixture of two aspects: semantic feature and geometric structure. Semantics come from the appearance and context of objects to…

Despite their empirical success, pushing Transformer architectures to extreme depth often leads to a paradoxical failure: representations become increasingly redundant, lose rank, and ultimately collapse. Existing explanations largely…

Graphs are ubiquitous data structures for representing interactions between entities. With an emphasis on the use of graphs to represent chemical molecules, we explore the task of learning to generate graphs that conform to a distribution…

In the real world, networks often contain multiple relationships among nodes, manifested as the heterogeneity of the edges in the networks. We convert the heterogeneous networks into multiple views by using each view to describe a specific…

Autonomous driving has received a lot of attention in the automotive industry and is often seen as the future of transportation. Passenger vehicles equipped with a wide array of sensors (e.g., cameras, front-facing radars, LiDARs, and IMUs)…

In this paper, we propose a method to learn a minimizing geodesic within a data manifold. Along the learned geodesic, our method can generate high-quality interpolations between two given data samples. Specifically, we use an autoencoder…

This paper presents KeypointNet, an end-to-end geometric reasoning framework to learn an optimal set of category-specific 3D keypoints, along with their detectors. Given a single image, KeypointNet extracts 3D keypoints that are optimized…

Graph auto-encoders are widely used to construct graph representations in Euclidean vector spaces. However, it has already been pointed out empirically that linear models on many tasks can outperform graph auto-encoders. In our work, we…

Recent advancements in the discipline of quantum algorithms have displayed the importance of the geometry of quantum operators. Given this thrust, this paper develops a rigorous geometric framework to analyze how the Riemannian structure of…

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…

World models compress rich sensory streams into compact latent codes that anticipate future observations. We let separate agents acquire such models from distinct viewpoints of the same environment without any parameter sharing or…

We examine two fundamental tasks associated with graph representation learning: link prediction and semi-supervised node classification. We present a novel autoencoder architecture capable of learning a joint representation of both local…

Generative self-supervised learning on graphs, particularly graph masked autoencoders, has emerged as a popular learning paradigm and demonstrated its efficacy in handling non-Euclidean data. However, several remaining issues limit the…

We study a simple unsupervised regularization scheme for autoencoders called Manifold-Matching (MMAE): we align the pairwise distances in the latent space to those of the input data space by minimizing mean squared error. Because alignment…

We develop data-driven methods incorporating geometric and topological information to learn parsimonious representations of nonlinear dynamics from observations. The approaches learn nonlinear state-space models of the dynamics for general…

Representing graph data in a low-dimensional space for subsequent tasks is the purpose of attributed graph embedding. Most existing neural network approaches learn latent representations by minimizing reconstruction errors. Rare work…

Autoencoders are a deep learning model for representation learning. When trained to minimize the distance between the data and its reconstruction, linear autoencoders (LAEs) learn the subspace spanned by the top principal directions but…

Enhanced modeling of microlensing variations in light curves of strongly lensed quasars improves measurements of cosmological time delays, the Hubble Constant, and quasar structure. Traditional methods for modeling extra-galactic…

The length of the geodesic between two data points along a Riemannian manifold, induced by a deep generative model, yields a principled measure of similarity. Current approaches are limited to low-dimensional latent spaces, due to the…