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

We prove strong convergence theorems of some iterative algorithms in a real uniformly smooth Banach space. The results presented extend, generalize and improve the corresponding results recently announced by many authors.

Incomplete point clouds captured by 3D sensors often result in the loss of both geometric and semantic information. Most existing point cloud completion methods are built on rotation-variant frameworks trained with data in canonical poses,…

Generative Adversarial Networks (GAN) can achieve promising performance on learning complex data distributions on different types of data. In this paper, we first show a straightforward extension of existing GAN algorithm is not applicable…

Convolutional neural networks (CNNs) have demonstrated gratifying results at learning discriminative features. However, when applied to unseen domains, state-of-the-art models are usually prone to errors due to domain shift. After…

Unsupervised domain adaptation for object detection is a challenging problem with many real-world applications. Unfortunately, it has received much less attention than supervised object detection. Models that try to address this task tend…

Point cloud is an important type of geometric data structure. Due to its irregular format, most researchers transform such data to regular 3D voxel grids or collections of images. This, however, renders data unnecessarily voluminous and…

We develop a theory of category-equivariant neural networks (CENNs) that unifies group/groupoid-equivariant networks, poset/lattice-equivariant networks, graph and sheaf neural networks. Equivariance is formulated as naturality in a…

We consider nonlinear inverse problems described by operator equations in Banach spaces. Assuming conditional stability of the inverse problem, that is, assuming that stability holds on a closed, convex subset of the domain of the operator,…

Rotation equivariance constitutes one of the most general and crucial structural priors for visual data, yet it remains notably absent from current Mamba-based vision architectures. Despite the success of Mamba in natural language…

In this paper, we introduce a novel two-point gradient method for solving the ill-posed problems in Banach spaces and study its convergence analysis. The method is based on the well known iteratively regularized Landweber iteration method…

Efficient transfer learning algorithms are key to the success of foundation models on diverse downstream tasks even with limited data. Recent works of Basu et al. (2023) and Kaba et al. (2022) propose group averaging (equitune) and…

Translating or rotating an input image should not affect the results of many computer vision tasks. Convolutional neural networks (CNNs) are already translation equivariant: input image translations produce proportionate feature map…

Part-level point cloud segmentation has recently attracted significant attention in 3D computer vision. Nevertheless, existing research is constrained by two major challenges: native 3D models lack generalization due to data scarcity, while…

Convolutions encode equivariance symmetries into neural networks leading to better generalisation performance. However, symmetries provide fixed hard constraints on the functions a network can represent, need to be specified in advance, and…

A machine learning model is traditionally considered robust if its prediction remains (almost) constant under input perturbations with small norm. However, real-world tasks like molecular property prediction or point cloud segmentation have…

Continual Learning aims to learn multiple incoming new tasks continually, and to keep the performance of learned tasks at a consistent level. However, existing research on continual learning assumes the pose of the object is pre-defined and…

Convolutional Neural Networks(CNN) are inherently equivariant under translations, however, they do not have an equivalent embedded mechanism to handle other transformations such as rotations and change in scale. Several approaches exist…

We explain equivariant neural networks, a notion underlying breakthroughs in machine learning from deep convolutional neural networks for computer vision to AlphaFold 2 for protein structure prediction, without assuming knowledge of…

We investigate the relation between end-to-end equivariance and layerwise equivariance in deep neural networks. We prove the following: For a network whose end-to-end function is equivariant with respect to group actions on the input and…

Shift equivariance is a fundamental principle that governs how we perceive the world - our recognition of an object remains invariant with respect to shifts. Transformers have gained immense popularity due to their effectiveness in both…