Related papers: HodgeFormer: Transformers for Learnable Operators …
We introduce Hodge Diffusion Maps, a novel manifold learning algorithm designed to analyze and extract topological information from high-dimensional data-sets. This method approximates the exterior derivative acting on differential forms,…
Data-driven learning of partial differential equations' solution operators has recently emerged as a promising paradigm for approximating the underlying solutions. The solution operators are usually parameterized by deep learning models…
Constrained by the limitations of learning toolkits engineered for other applications, such as those in image processing, many mesh-based learning algorithms employ data flows that would be atypical from the perspective of conventional…
Mesh denoising, aimed at removing noise from input meshes while preserving their feature structures, is a practical yet challenging task. Despite the remarkable progress in learning-based mesh denoising methodologies in recent years, their…
In this paper, we study solution operators of physical field equations on geometric meshes from a function-space perspective. We reveal that Hodge orthogonality fundamentally resolves spectral interference by isolating unlearnable…
Neural operators have emerged as promising frameworks for learning mappings governed by partial differential equations (PDEs), serving as data-driven alternatives to traditional numerical methods. While methods such as the Fourier neural…
Operator learning enables data-driven modeling of partial differential equations (PDEs) by learning mappings between function spaces. However, scaling transformer-based operator models to high-resolution, multiscale domains remains a…
Spatially localized deformation components are very useful for shape analysis and synthesis in 3D geometry processing. Several methods have recently been developed, with an aim to extract intuitive and interpretable deformation components.…
Transformers have become one of the dominant architectures in deep learning, particularly as a powerful alternative to convolutional neural networks (CNNs) in computer vision. However, Transformer training and inference in previous works…
This article introduces a new and general construction of discrete Hodge operator in the context of Discrete Exterior Calculus (DEC). This discrete Hodge operator enables to circumvent the well-centeredness limitation on the mesh with the…
Recently, self-supervised pre-training has advanced Vision Transformers on various tasks w.r.t. different data modalities, e.g., image and 3D point cloud data. In this paper, we explore this learning paradigm for 3D mesh data analysis based…
Transformers have recently gained attention in the computer vision domain due to their ability to model long-range dependencies. However, the self-attention mechanism, which is the core part of the Transformer model, usually suffers from…
Transformers are built upon multi-head scaled dot-product attention and positional encoding, which aim to learn the feature representations and token dependencies. In this work, we focus on enhancing the distinctive representation by…
While convolutional neural networks have shown a tremendous impact on various computer vision tasks, they generally demonstrate limitations in explicitly modeling long-range dependencies due to the intrinsic locality of the convolution…
The Transformer architecture has inarguably revolutionized deep learning, overtaking classical architectures like multi-layer perceptrons (MLPs) and convolutional neural networks (CNNs). At its core, the attention block differs in form and…
Graph Transformers typically rely on explicit positional or structural encodings and dense global attention to incorporate graph topology. In this work, we show that neither is essential. We introduce HopFormer, a graph Transformer that…
Vision Transformer (ViT) models have demonstrated a breakthrough in a wide range of computer vision tasks. However, compared to the Convolutional Neural Network (CNN) models, it has been observed that the ViT models struggle to capture…
Transformers are effective and efficient at modeling complex relationships and learning patterns from structured data in many applications. The main aim of this paper is to propose and design NLAFormer, which is a transformer-based…
This paper presents a novel attention-based neural network for structured reconstruction, which takes a 2D raster image as an input and reconstructs a planar graph depicting an underlying geometric structure. The approach detects corners…
In this work, we present Eformer - Edge enhancement based transformer, a novel architecture that builds an encoder-decoder network using transformer blocks for medical image denoising. Non-overlapping window-based self-attention is used in…