Related papers: Embed Me If You Can: A Geometric Perceptron

The creation of a volumetric mesh representing the interior of an input polygonal mesh is a common requirement in graphics and computational mechanics applications. Most mesh creation techniques assume that the input surface is not…

Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian through a pull-back metric,…

We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…

Modern deep learning architectures are ordinarily performed on high-performance computing facilities due to the large size of the input features and complexity of its model. This paper proposes traditional multilayer perceptrons (MLP) with…

Firms earning prediction plays a vital role in investment decisions, dividends expectation, and share price. It often involves multiple tensor-compatible datasets with non-linear multi-way relationships, spatiotemporal structures, and…

We present TetGAN, a convolutional neural network designed to generate tetrahedral meshes. We represent shapes using an irregular tetrahedral grid which encodes an occupancy and displacement field. Our formulation enables defining…

We present a novel global representation of 3D shapes, suitable for the application of 2D CNNs. We represent 3D shapes as multi-layered height-maps (MLH) where at each grid location, we store multiple instances of height maps, thereby…

Graph transformers typically embed every node in a single Euclidean space, blurring heterogeneous topologies. We prepend a lightweight Riemannian mixture-of-experts layer that routes each node to various kinds of manifold, mixture of…

Deep learning-based bilateral grid processing has emerged as a promising solution for image enhancement, inherently encoding spatial and intensity information while enabling efficient full-resolution processing through slicing operations.…

The recent surge of utilizing deep neural networks for geometric processing and shape modeling has opened up exciting avenues. However, there is a conspicuous lack of research efforts on using powerful neural representations to extend the…

Geometric embedding methods have shown to be useful for multi-hop reasoning on knowledge graphs by mapping entities and logical operations to geometric regions and geometric transformations, respectively. Geometric embeddings provide direct…

We present a geometric formulation of the Multiple Kernel Learning (MKL) problem. To do so, we reinterpret the problem of learning kernel weights as searching for a kernel that maximizes the minimum (kernel) distance between two convex…

Multilayer perceptron is the most common used class of feed-forward artificial neural network. It contains many applications in diverse fields such as speech recognition, image recognition, and machine translation software. To cater for the…

Multimodal Large Language Models (MLLMs) have achieved remarkable progress in 2D visual tasks but still exhibit limited physical spatial awareness when processing real-world visual streams. Recently, feed-forward geometric foundation…

Many complex systems involve interactions between more than two agents. Hypergraphs capture these higher-order interactions through hyperedges that may link more than two nodes. We consider the problem of embedding a hypergraph into…

Implicit neural representations are powerful for geometric modeling, but their practical use is often limited by the high computational cost of network evaluations. We observe that implicit representations require progressively lower…

We propose a deep learning strategy to estimate the mean curvature of two-dimensional implicit interfaces in the level-set method. Our approach is based on fitting feed-forward neural networks to synthetic data sets constructed from…

Consider a set of $n$ data points in the Euclidean space $\mathbb{R}^d$. This set is called dataset in machine learning and data science. Manifold hypothesis states that the dataset lies on a low-dimensional submanifold with high…

The purpose of this paper is to outline a generalised model for representing hybrids of relational-categorical, symbolic, perceptual-sensory and perceptual-latent data, so as to embody, in the same architectural data layer, representations…

We propose a novel neural network architecture, the normalized Transformer (nGPT) with representation learning on the hypersphere. In nGPT, all vectors forming the embeddings, MLP, attention matrices and hidden states are unit norm…