Related papers: Equivariant Deep Dynamical Model for Motion Predic…
Generative models of 3D human motion are often restricted to a small number of activities and can therefore not generalize well to novel movements or applications. In this work we propose a deep learning framework for human motion capture…
Neural networks that incorporate geometric relationships respecting SE(3) group transformations (e.g. rotations and translations) are increasingly important in molecular applications, such as molecular property prediction, protein structure…
Representation learning has become increasingly important, especially as powerful models have shifted towards learning latent representations before fine-tuning for downstream tasks. This approach is particularly valuable in leveraging the…
Forecasting vehicular motions in autonomous driving requires a deep understanding of agent interactions and the preservation of motion equivariance under Euclidean geometric transformations. Traditional models often lack the sophistication…
Molecular 3D conformations play a key role in determining how molecules interact with other molecules or protein surfaces. Recent deep learning advancements have improved conformation prediction, but slow training speeds and difficulties in…
We propose a novel Transformer-based architecture for the task of generative modelling of 3D human motion. Previous work commonly relies on RNN-based models considering shorter forecast horizons reaching a stationary and often implausible…
Incorporating inductive bias by embedding geometric entities (such as rays) as input has proven successful in multi-view learning. However, the methods adopting this technique typically lack equivariance, which is crucial for effective 3D…
Mental rotation -- the ability to compare objects seen from different viewpoints -- is a fundamental example of mental simulation and spatial world modeling in humans. Here we propose a mechanistic model of human mental rotation, leveraging…
Modeling the complex three-dimensional (3D) dynamics of relational systems is an important problem in the natural sciences, with applications ranging from molecular simulations to particle mechanics. Machine learning methods have achieved…
We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…
In recent years, deep learning techniques have shown great success in various tasks related to inverse problems, where a target quantity of interest can only be observed through indirect measurements by a forward operator. Common approaches…
We introduce a general method for learning representations that are equivariant to symmetries of data. Our central idea is to decompose the latent space into an invariant factor and the symmetry group itself. The components semantically…
Invariance (defined in a general sense) has been one of the most effective priors for representation learning. Direct factorization of parametric models is feasible only for a small range of invariances, while regularization approaches,…
Learning and inference movement is a very challenging problem due to its high dimensionality and dependency to varied environments or tasks. In this paper, we propose an effective probabilistic method for learning and inference of basic…
Learning or identifying dynamics from a sequence of high-dimensional observations is a difficult challenge in many domains, including reinforcement learning and control. The problem has recently been studied from a generative perspective…
While data augmentation is widely used to train symmetry-agnostic models, it remains unclear how quickly and effectively they learn to respect symmetries. We investigate this by deriving a principled measure of equivariance error that, for…
Equivariant neural networks enforce symmetry within the structure of their convolutional layers, resulting in a substantial improvement in sample efficiency when learning an equivariant or invariant function. Such models are applicable to…
From early image processing to modern computational imaging, successful models and algorithms have relied on a fundamental property of natural signals: symmetry. Here symmetry refers to the invariance property of signal sets to…
This work introduces E3x, a software package for building neural networks that are equivariant with respect to the Euclidean group $\mathrm{E}(3)$, consisting of translations, rotations, and reflections of three-dimensional space. Compared…
Convolutional networks are successful, but they have recently been outperformed by new neural networks that are equivariant under rotations and translations. These new networks work better because they do not struggle with learning each…