相关论文: Hierarchical Learning in Euclidean Neural Networks

3D Euclidean symmetry equivariant neural networks have demonstrated notable success in modeling complex physical systems. We introduce a framework for relaxed $E(3)$ graph equivariant neural networks that can learn and represent symmetry…

Many classes of images exhibit rotational symmetry. Convolutional neural networks are sometimes trained using data augmentation to exploit this, but they are still required to learn the rotation equivariance properties from the data.…

This paper pertains to an emerging machine learning paradigm: learning higher-order functions, i.e. functions whose inputs are functions themselves, $\textit{particularly when these inputs are Neural Networks (NNs)}$. With the growing…

Equivariant machine learning is an approach for designing deep learning models that respect the symmetries of the problem, with the aim of reducing model complexity and improving generalization. In this paper, we focus on an extension of…

The success of deep learning has revolutionized many fields of research including areas of computer vision, text and speech processing. Enormous research efforts have led to numerous methods that are capable of efficiently analyzing data,…

Unsupervised machine learning methods can be of great help in many traditional engineering disciplines, where huge amount of labeled data is not readily available or is extremely difficult or costly to generate. Two specific examples…

In recent years, tasks of machine learning ranging from image processing & audio/video analysis to natural language understanding have been transformed by deep learning. The data content in all these scenarios are expressed via Euclidean…

The effectiveness of Convolutional Neural Networks (CNNs) has been substantially attributed to their built-in property of translation equivariance. However, CNNs do not have embedded mechanisms to handle other types of transformations. In…

3D data is a valuable asset the computer vision filed as it provides rich information about the full geometry of sensed objects and scenes. Recently, with the availability of both large 3D datasets and computational power, it is today…

Geometric deep learning enables the encoding of physical symmetries in modeling 3D objects. Despite rapid progress in encoding 3D symmetries into Graph Neural Networks (GNNs), a comprehensive evaluation of the expressiveness of these…

Designing machine learning architectures for processing neural networks in their raw weight matrix form is a newly introduced research direction. Unfortunately, the unique symmetry structure of deep weight spaces makes this design very…

Neural network force fields have significantly advanced ab initio atomistic simulations across diverse fields. However, their application in the realm of magnetic materials is still in its early stage due to challenges posed by the subtle…

Augmentation-based self-supervised learning methods have shown remarkable success in self-supervised visual representation learning, excelling in learning invariant features but often neglecting equivariant ones. This limitation reduces the…

A number of machine learning tasks entail a high degree of invariance: the data distribution does not change if we act on the data with a certain group of transformations. For instance, labels of images are invariant under translations of…

The accuracy of density functional theory hinges on the approximation of non-local contributions to the exchange-correlation (XC) functional. To date, machine-learned and human-designed approximations suffer from insufficient accuracy,…

Advancements in modern science have led to the increasing availability of non-Euclidean data in metric spaces. This paper addresses the challenge of modeling relationships between non-Euclidean responses and multivariate Euclidean…

Equivariance is a nice property to have as it produces much more parameter efficient neural architectures and preserves the structure of the input through the feature mapping. Even though some combinations of transformations might never…

One of the central questions in the theory of deep learning is to understand how neural networks learn hierarchical features. The ability of deep networks to extract salient features is crucial to both their outstanding generalization…

Conventional application of convolutional neural networks (CNNs) for image classification and recognition is based on the assumption that all target classes are equal(i.e., no hierarchy) and exclusive of one another (i.e., no overlap).…

We propose a metric learning framework for the construction of invariant geometric functions of planar curves for the Eucledian and Similarity group of transformations. We leverage on the representational power of convolutional neural…