Related papers: Banana: Banach Fixed-Point Network for Pointcloud …

We use a method similar to ultraproducts to study the common fixed point of a left reversible semitopological semigroup acting on a Banach space. As an application, we prove a Bruck-type theorem for nearly uniformly convex Banach spaces to…

Using deep neural networks that are either invariant or equivariant to permutations in order to learn functions on unordered sets has become prevalent. The most popular, basic models are DeepSets [Zaheer et al. 2017] and PointNet [Qi et al.…

In this paper, we study the connections between the normality, regularity, full regularity, and chain-complete property in partially ordered Banach spaces. Then, by applying these properties, we prove some fixed point theorems on partially…

This paper tackles the problem of parts-aware point cloud generation. Unlike existing works which require the point cloud to be segmented into parts a priori, our parts-aware editing and generation are performed in an unsupervised manner.…

Rotation equivariance is a desirable property in many practical applications such as motion forecasting and 3D perception, where it can offer benefits like sample efficiency, better generalization, and robustness to input perturbations.…

Large-scale point cloud semantic segmentation is an important task in 3D computer vision, which is widely applied in autonomous driving, robotics, and virtual reality. Current large-scale point cloud semantic segmentation methods usually…

Robust point cloud registration is a fundamental task in 3D computer vision and geometric deep learning, essential for applications such as large-scale 3D reconstruction, augmented reality, and scene understanding. However, the performance…

Batch normalization (BN) has become a critical component across diverse deep neural networks. The network with BN is invariant to positively linear re-scale transformation, which makes there exist infinite functionally equivalent networks…

Partial point cloud registration is a challenging problem in robotics, especially when the robot undergoes a large transformation, causing a significant initial pose error and a low overlap between measurements. This work proposes…

Despite the progress on 3D point cloud deep learning, most prior works focus on learning features that are invariant to translation and point permutation, and very limited efforts have been devoted for rotation invariant property. Several…

Previous studies have demonstrated the effectiveness of point-based neural models on the point cloud analysis task. However, there remains a crucial issue on producing the efficient input embedding for raw point coordinates. Moreover,…

The set of functions parameterized by a linear fully-connected neural network is a determinantal variety. We investigate the subvariety of functions that are equivariant or invariant under the action of a permutation group. Examples of such…

Given a pair of point clouds, the goal of assembly is to recover a rigid transformation that aligns one point cloud to the other. This task is challenging because the point clouds may be non-overlapped, and they may have arbitrary initial…

While widespread, Transformers lack inductive biases for geometric symmetries common in science and computer vision. Existing equivariant methods often sacrifice the efficiency and flexibility that make Transformers so effective through…

Operator learning has emerged as a promising tool for accelerating the solution of partial differential equations (PDEs). The Deep Operator Networks (DeepONets) represent a pioneering framework in this area: the "vanilla" DeepONet is valued…

Alternative iterative methods for a nonexpansive mapping in a Banach space are proposed and proved to be convergent to a common solution to a fixed point problem and a variational inequality. We give rates of asymptotic regularity for such…

Many learning tasks, including learning potential energy surfaces from ab initio calculations, involve global spatial symmetries and permutational symmetry between atoms or general particles. Equivariant graph neural networks are a standard…

Group Convolutional Neural Networks (G-CNNs) constrain learned features to respect the symmetries in the selected group, and lead to better generalization when these symmetries appear in the data. If this is not the case, however,…

In this paper, we study a new iterative method for finding the fixed point of a weak Bregman relatively nonexpansive mapping and the set of solutions of generalized mixed equilibrium problems in Banach spaces.

In this paper, we study a new iterative method for a common fixed point of a finite family of Bregman strongly nonexpansive mappings in the frame work of reflexive real Banach spaces. Moreover, we prove the strong convergence theorem for…