Related papers: Geometry-Preserving Neural Architectures on Manifo…

Manifold learning has been proven to be an effective method for capturing the implicitly intrinsic structure of non-Euclidean data, in which one of the primary challenges is how to maintain the distortion-free (isometry) of the data…

Graph neural networks (GNNs) are the dominant approach to solving machine learning problems defined over graphs. Despite much theoretical and empirical work in recent years, our understanding of finer-grained aspects of architectural design…

Bayesian learning with Gaussian processes demonstrates encouraging regression and classification performances in solving computer vision tasks. However, Bayesian methods on 3D manifold-valued vision data, such as meshes and point clouds,…

The ability to learn continually without forgetting the past tasks is a desired attribute for artificial learning systems. Existing approaches to enable such learning in artificial neural networks usually rely on network growth, importance…

Neural operators offer an effective framework for learning solutions of partial differential equations for many physical systems in a resolution-invariant and data-driven manner. Existing neural operators, however, often suffer from…

Graph Neural Networks (GNNs) have shown significant success for graph-based tasks. Motivated by the prevalence of large datasets in real-world applications, pooling layers are crucial components of GNNs. By reducing the size of input…

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…

Deep sequence models are said to store atomic facts predominantly in the form of associative memory: a brute-force lookup of co-occurring entities. We identify a dramatically different form of storage of atomic facts that we term as…

Node embedding is the task of extracting concise and informative representations of certain entities that are connected in a network. Various real-world networks include information about both node connectivity and certain node attributes,…

Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…

We present a lightweight network that infers grouping and boundaries, including curves, corners and junctions. It operates in a bottom-up fashion, analogous to classical methods for sub-pixel edge localization and edge-linking, but with a…

Though manifold-based clustering has become a popular research topic, we observe that one important factor has been omitted by these works, namely that the defined clustering loss may corrupt the local and global structure of the latent…

How to balance training accuracy and adversarial robustness has become a challenge since the birth of deep learning. Here, we introduce a geometry-aware deep learning framework that leverages layer-wise local training to sculpt the internal…

Modifications to a neural network's input and output layers are often required to accommodate the specificities of most practical learning tasks. However, the impact of such changes on architecture's approximation capabilities is largely…

3D generative modeling is accelerating as the technology allowing the capture of geometric data is developing. However, the acquired data is often inconsistent, resulting in unregistered meshes or point clouds. Many generative learning…

This paper introduces Neural Subdivision, a novel framework for data-driven coarse-to-fine geometry modeling. During inference, our method takes a coarse triangle mesh as input and recursively subdivides it to a finer geometry by applying…

Recent advances in 3D perception have shown impressive progress in understanding geometric structures of 3Dshapes and even scenes. Inspired by these advances in geometric understanding, we aim to imbue image-based perception with…

Data over non-Euclidean manifolds, often discretized as surface meshes, naturally arise in computer graphics and biological and physical systems. In particular, solutions to partial differential equations (PDEs) over manifolds depend…

Complex geometric tasks such as geometric modeling, physical simulation, and texture parametrization often involve the embedding of many complex sub-domains with potentially different dimensions. These tasks often require evolving the…

Neural ordinary differential equations (Neural ODEs) propose the idea that a sequence of layers in a neural network is just a discretisation of an ODE, and thus can instead be directly modelled by a parameterised ODE. This idea has had…