Related papers: Group Invariant Global Pooling
Generative modeling seeks to uncover the underlying factors that give rise to observed data that can often be modeled as the natural symmetries that manifest themselves through invariances and equivariances to certain transformation laws.…
We introduce Group equivariant Convolutional Neural Networks (G-CNNs), a natural generalization of convolutional neural networks that reduces sample complexity by exploiting symmetries. G-CNNs use G-convolutions, a new type of layer that…
State-of-the-art patch-based image representations involve a pooling operation that aggregates statistics computed from local descriptors. Standard pooling operations include sum- and max-pooling. Sum-pooling lacks discriminability because…
Finding local correspondences between images with different viewpoints requires local descriptors that are robust against geometric transformations. An approach for transformation invariance is to integrate out the transformations by…
Given a real inner product space $V$ and a group $G$ of linear isometries, we construct a family of $G$-invariant real-valued functions on $V$ that we call max filters. In the case where $V=\mathbb{R}^d$ and $G$ is finite, a suitable max…
Bilinear pooling has been recently proposed as a feature encoding layer, which can be used after the convolutional layers of a deep network, to improve performance in multiple vision tasks. Different from conventional global average pooling…
Graph Neural Networks (GNNs) have shown significant success for graph-based tasks. Motivated by the prevalence of large datasets in real-world applications, pooling layers are crucial components of GNNs. By reducing the size of input…
Learning transformation invariant representations of visual data is an important problem in computer vision. Deep convolutional networks have demonstrated remarkable results for image and video classification tasks. However, they have…
A common architectural choice for deep metric learning is a convolutional neural network followed by global average pooling (GAP). Albeit simple, GAP is a highly effective way to aggregate information. One possible explanation for the…
Many machine learning tasks are invariant under the action of a group $G$ of transformations: signal classification can be invariant under translations, image classification under 2D rotations, and spherical-image classification under 3D…
Graph pooling is a crucial operation for encoding hierarchical structures within graphs. Most existing graph pooling approaches formulate the problem as a node clustering task which effectively captures the graph topology. Conventional…
We present group equivariant capsule networks, a framework to introduce guaranteed equivariance and invariance properties to the capsule network idea. Our work can be divided into two contributions. First, we present a generic routing by…
Several popular approaches to 3D vision tasks process multiple views of the input independently with deep neural networks pre-trained on natural images, achieving view permutation invariance through a single round of pooling over all views.…
Many rotational invariants for crystal structure representations have been used to describe the structure-property relationship by machine learning. The machine learning interatomic potential (MLIP) is one of the applications of rotational…
Graph neural networks (GNNs) have achieved remarkable success in molecular property prediction. However, traditional graph representations struggle to effectively encode the inherent 3D spatial structures of molecules, as molecular…
In Graph Neural Networks (GNNs), hierarchical pooling operators generate local summaries of the data by coarsening the graph structure and the vertex features. While considerable attention has been devoted to analyzing the expressive power…
Invariance to nuisance transformations is one of the desirable properties of effective representations. We consider transformations that form a \emph{group} and propose an approach based on kernel methods to derive local group invariant…
Despite the success of deep learning in domains such as image, voice, and graphs, there has been little progress in deep representation learning for domains without a known structure between features. For instance, a tabular dataset of…
We introduce a method to design a computationally efficient $G$-invariant neural network that approximates functions invariant to the action of a given permutation subgroup $G \leq S_n$ of the symmetric group on input data. The key element…
Graph pooling is a central component of a myriad of graph neural network (GNN) architectures. As an inheritance from traditional CNNs, most approaches formulate graph pooling as a cluster assignment problem, extending the idea of local…