Related papers: Hypoelliptic Diffusion Maps I: Tangent Bundles

We propose a new fast method of measuring distances between large numbers of related high dimensional datasets called the Diffusion Earth Mover's Distance (EMD). We model the datasets as distributions supported on common data graph that is…

We present a new nonlinear dimensionality reduction method, MAPLE, that enhances UMAP by improving manifold modeling. MAPLE employs a self-supervised learning approach to more efficiently encode low-dimensional manifold geometry. Central to…

This paper introduces MDP homomorphic networks for deep reinforcement learning. MDP homomorphic networks are neural networks that are equivariant under symmetries in the joint state-action space of an MDP. Current approaches to deep…

Image segmentation is crucial in many computational pathology pipelines, including accurate disease diagnosis, subtyping, outcome, and survivability prediction. The common approach for training a segmentation model relies on a pre-trained…

High Definition (HD) maps play an important role in modern traffic scenes. However, the development of HD maps coverage grows slowly because of the cost limitation. To efficiently model HD maps, we proposed a convolutional neural network…

Simulation of conditioned diffusion processes is an essential tool in inference for stochastic processes, data imputation, generative modelling, and geometric statistics. Whilst simulating diffusion bridge processes is already difficult on…

Drawing motivation from the manifold hypothesis, which posits that most high-dimensional data lies on or near low-dimensional manifolds, we apply manifold learning to the space of neural networks. We learn manifolds where datapoints are…

The dominant paradigm for learning on graph-structured data is message passing. Despite being a strong inductive bias, the local message passing mechanism suffers from pathological issues such as over-smoothing, over-squashing, and limited…

The idea of renormalization and scale invariance is pervasive across disciplines. It has not only drawn numerous surprising connections between physical systems under the guise of holographic duality, but has also inspired the development…

High-dimensional data are often assumed to lie on lower-dimensional manifolds. We study how to construct diffusion processes on this data manifold using only point cloud samples and without access to charts, projections, or other geometric…

Heterogeneous Graph Neural Networks (HGNNs) have achieved promising results in various heterogeneous graph learning tasks, owing to their superiority in capturing the intricate relationships and diverse relational semantics inherent in…

Constructing HD semantic maps is a central component of autonomous driving. However, traditional pipelines require a vast amount of human efforts and resources in annotating and maintaining the semantics in the map, which limits its…

Diffusion models are powerful deep generative models, but unlike classical models, they lack an explicit low-dimensional latent space that parameterizes the data manifold. This absence makes it difficult to perform manifold-aware…

Denoising Diffusion Probabilistic Models (DDPM) are powerful state-of-the-art methods used to generate synthetic data from high-dimensional data distributions and are widely used for image, audio, and video generation as well as many more…

High-order Graph Neural Networks (HO-GNNs) have been developed to infer consistent latent spaces in the heterophilic regime, where the label distribution is not correlated with the graph structure. However, most of the existing HO-GNNs are…

Up-to-date High-Definition (HD) maps are essential for self-driving cars. To achieve constantly updated HD maps, we present a deep neural network (DNN), Diff-Net, to detect changes in them. Compared to traditional methods based on object…

End-to-end planning has emerged as a dominant paradigm for autonomous driving, where recent models often adopt a scoring-selection framework to choose trajectories from a large set of candidates, with diffusion-based decoding showing strong…

Diffusion models (DMs) have recently been introduced in image deblurring and exhibited promising performance, particularly in terms of details reconstruction. However, the diffusion model requires a large number of inference iterations to…

In a previous work, the authors introduced the notion of `coherent tangent bundle', which is useful for giving a treatment of singularities of smooth maps without ambient spaces. Two different types of Gauss-Bonnet formulas on coherent…

Histological artifacts pose challenges for both pathologists and Computer-Aided Diagnosis (CAD) systems, leading to errors in analysis. Current approaches for histological artifact restoration, based on Generative Adversarial Networks…