相关论文: Group Equivariant Stand-Alone Self-Attention For V…

Visual attention plays a critical role when our visual system executes active visual tasks by interacting with the physical scene. However, how to encode the visual object relationship in the psychological world of our brain deserves to be…

Learning and reasoning about 3D molecular structures with varying size is an emerging and important challenge in machine learning and especially in drug discovery. Equivariant Graph Neural Networks (GNNs) can simultaneously leverage the…

We introduce equivariant versions of uniform rationality: given an algebraic group G, a G-variety is called G-uniformly rational (resp. G-linearly uniformly rational) if every point has a G-invariant open neighborhood equivariantly…

Group invariant and equivariant Multilayer Perceptrons (MLP), also known as Equivariant Networks, have achieved remarkable success in learning on a variety of data structures, such as sequences, images, sets, and graphs. Using tools from…

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…

Training deep neural networks to estimate the viewpoint of objects requires large labeled training datasets. However, manually labeling viewpoints is notoriously hard, error-prone, and time-consuming. On the other hand, it is relatively…

A nonlinear observer on the Special Euclidean group $\mathrm{SE(3)}$ for full pose estimation, that takes the system outputs on the real projective space directly as inputs, is proposed. The observer derivation is based on a recent advanced…

In many machine learning tasks it is desirable that a model's prediction transforms in an equivariant way under transformations of its input. Convolutional neural networks (CNNs) implement translational equivariance by construction; for…

Equivariant network architectures are a well-established tool for predicting invariant or equivariant quantities. However, almost all learning problems considered in this context feature a global symmetry, i.e. each point of the underlying…

Correspondence matching is a fundamental problem in computer vision and robotics applications. Solving correspondence matching problems using neural networks has been on the rise recently. Rotation-equivariance and scale-equivariance are…

The translation equivariance of convolutional layers enables convolutional neural networks to generalize well on image problems. While translation equivariance provides a powerful inductive bias for images, we often additionally desire…

The study of $G$-equivariant operators is of great interest to explain and understand the architecture of neural networks. In this paper we show that each linear $G$-equivariant operator can be produced by a suitable permutant measure,…

By inferring latent groups in the training data, recent works introduce invariant learning to the case where environment annotations are unavailable. Typically, learning group invariance under a majority/minority split is empirically shown…

Transformers are increasingly dominating multi-modal reasoning tasks, such as visual question answering, achieving state-of-the-art results thanks to their ability to contextualize information using the self-attention and co-attention…

In this paper, we develop a manifestly geometric framework for equivariant manifold neural ordinary differential equations (NODEs) and use it to analyse their modelling capabilities for symmetric data. First, we consider the action of a Lie…

The upcoming large scale surveys like LSST are expected to find approximately $10^5$ strong gravitational lenses by analysing data of many orders of magnitude larger than those in contemporary astronomical surveys. In this case,…

Vision-language-action policies learn manipulation skills across tasks, environments and embodiments through large-scale pre-training. However, their ability to generalize to novel robot configurations remains limited. Most approaches…

Geometric quantum machine learning uses the symmetries inherent in data to design tailored machine learning tasks with reduced search space dimension. The field has been well-studied recently in an effort to avoid barren plateau issues…

In many applications, we desire neural networks to exhibit invariance or equivariance to certain groups due to symmetries inherent in the data. Recently, frame-averaging methods emerged to be a unified framework for attaining symmetries…

We present view-synthesis autoencoders (VSA) in this paper, which is a self-supervised learning framework designed for vision transformers. Different from traditional 2D pretraining methods, VSA can be pre-trained with multi-view data. In…