Related papers: $SE(3)$ Equivariant Ray Embeddings for Implicit Mu…

Incorporating equivariance as an inductive bias into deep learning architectures to take advantage of the data symmetry has been successful in multiple applications, such as chemistry and dynamical systems. In particular, roto-translations…

A wide range of techniques have been proposed in recent years for designing neural networks for 3D data that are equivariant under rotation and translation of the input. Most approaches for equivariance under the Euclidean group…

We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds $\mathcal{M}$ using…

Recent advancements in self-supervised audio-visual representation learning have demonstrated its potential to capture rich and comprehensive representations. However, despite the advantages of data augmentation verified in many learning…

Robotic surgery has become a powerful tool for performing minimally invasive procedures, providing advantages in dexterity, precision, and 3D vision, over traditional surgery. One popular robotic system is the da Vinci surgical platform,…

Latent representations are used extensively for downstream tasks, such as visualization, interpolation or feature extraction of deep learning models. Invariant and equivariant neural networks are powerful and well-established models for…

When manipulating three-dimensional data, it is possible to ensure that rotational and translational symmetries are respected by applying so-called SE(3)-equivariant models. Protein structure prediction is a prominent example of a task…

At the core of self-supervised learning for vision is the idea of learning invariant or equivariant representations with respect to a set of data transformations. This approach, however, introduces strong inductive biases, which can render…

This paper analyzes the robustness of recent 3D shape descriptors to SO(3) rotations, something that is fundamental to shape modeling. Specifically, we formulate the task of rotated 3D object instance detection. To do so, we consider a…

In this paper, we investigate a new optimization framework for multi-view 3D shape reconstructions. Recent differentiable rendering approaches have provided breakthrough performances with implicit shape representations though they can still…

Equivariances provide useful inductive biases in neural network modeling, with the translation equivariance of convolutional neural networks being a canonical example. Equivariances can be embedded in architectures through weight-sharing…

Recent advances in imitation learning have shown significant promise for robotic control and embodied intelligence. However, achieving robust generalization across diverse mounted camera observations remains a critical challenge. In this…

In this work we investigate how to achieve equivariance to input transformations in deep networks, purely from data, without being given a model of those transformations. Convolutional Neural Networks (CNNs), for example, are equivariant to…

This work is about understanding the impact of invariance and equivariance on generalisation in supervised learning. We use the perspective afforded by an averaging operator to show that for any predictor that is not equivariant, there is…

Depth data has a widespread use since the popularity of high-resolution 3D sensors. In multi-view sequences, depth information is used to supplement the color data of each view. This article proposes a joint encoding of multiple depth maps…

Recent work has shown deep learning can accelerate the prediction of physical dynamics relative to numerical solvers. However, limited physical accuracy and an inability to generalize under distributional shift limit its applicability to…

Determining the 3D orientations of an object in an image, known as single-image pose estimation, is a crucial task in 3D vision applications. Existing methods typically learn 3D rotations parametrized in the spatial domain using Euler…

We introduce a convolutional neural network model for unsupervised learning of depth and ego-motion from cylindrical panoramic video. Panoramic depth estimation is an important technology for applications such as virtual reality, 3D…

This work investigates the geometric foundations of modern stereo vision systems, with a focus on how 3D structure and human-inspired perception contribute to accurate depth reconstruction. We revisit the Cyclopean Eye model and propose…

In this paper, we propose a simple yet effective method to endow deep 3D models with rotation invariance by expressing the coordinates in an intrinsic frame determined by the object shape itself. Key to our approach is to find such an…