相关论文: Equivariant Networks for Pixelized Spheres

Deep learning has achieved a remarkable performance breakthrough in several fields, most notably in speech recognition, natural language processing, and computer vision. In particular, convolutional neural network (CNN) architectures…

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging,…

This paper considers Platonic solids/polytopes in the real Euclidean space R^n of dimension 3 <= n < infinity. The Platonic solids/polytopes are described together with their faces of dimensions 0 <= d <= n-1. Dual pairs of Platonic…

Graph Convolutional Networks (GCNs) have been widely demonstrated their powerful ability in graph data representation and learning. Existing graph convolution layers are mainly designed based on graph signal processing and transform aspect…

The conventional CNN, widely used for two-dimensional images, however, is not directly applicable to non-regular geometric surface, such as a cortical thickness. We propose Geometric CNN (gCNN) that deals with data representation over a…

Since the seminal work of [9] and their Physics-Informed neural networks (PINNs), many efforts have been conducted towards solving partial differential equations (PDEs) with Deep Learning models. However, some challenges remain, for…

Alignment, the tendency of adjacent weight matrices in deep networks to develop compatible subspace orientations, underlies gradient flow, Neural Collapse, and representation similarity across architectures. Despite extensive empirical…

Retaining spatial characteristics of panchromatic image and spectral information of multispectral bands is a critical issue in pansharpening. This paper proposes a pyramid based deep fusion framework that preserves spectral and spatial…

Neural networks that are equivariant to rotations, translations, reflections, and permutations on n-dimensional geometric space have shown promise in physical modeling for tasks such as accurately but inexpensively modeling complex…

In this draft paper, we introduce a novel architecture for graph networks which is equivariant to the Euclidean group in $n$-dimensions. The model is designed to work with graph networks in their general form and can be shown to include…

Neural networks efficiently encode learned information within their parameters. Consequently, many tasks can be unified by treating neural networks themselves as input data. When doing so, recent studies demonstrated the importance of…

Although numerical models provide accurate solutions for ice sheet dynamics based on physics laws, they accompany intensified computational demands to solve partial differential equations. In recent years, convolutional neural networks…

The inclusion of symmetries as an inductive bias, known as equivariance, often improves generalization on geometric data (e.g. grids, sets, and graphs). However, equivariant architectures are usually highly constrained, designed for…

Physics-informed neural networks (PINNs) have been demonstrated to be efficient in solving partial differential equations (PDEs) from a variety of experimental perspectives. Some recent studies have also proposed PINN algorithms for PDEs on…

We explore architectures for general pixel-level prediction problems, from low-level edge detection to mid-level surface normal estimation to high-level semantic segmentation. Convolutional predictors, such as the fully-convolutional…

How can we design neural networks that allow for stable universal approximation of maps between topologically interesting manifolds? The answer is with a coordinate projection. Neural networks based on topological data analysis (TDA) use…

Defining and reliably finding a canonical orientation for 3D surfaces is key to many Computer Vision and Robotics applications. This task is commonly addressed by handcrafted algorithms exploiting geometric cues deemed as distinctive and…

Canonicalization is a widely used strategy in equivariant machine learning, enforcing symmetry in neural networks by mapping each input to a standard form. Yet, it often introduces discontinuities that can affect stability during training,…

In computer vision, convolutional neural networks (CNNs) have recently achieved new levels of performance for several inverse problems where RGB pixel appearance is mapped to attributes such as positions, normals or reflectance. In computer…

We present a general framework for symmetrizing an arbitrary neural-network architecture and making it equivariant with respect to a given group. We build upon the proposals of Kim et al. (2023); Kaba et al. (2023) for symmetrization, and…