Related papers: Group Invariant Global Pooling
Graph Pooling technology plays an important role in graph node classification tasks. Sorting pooling technologies maintain large-value units for pooling graphs of varying sizes. However, by analyzing the statistical characteristic of…
Recent advances in image clustering typically focus on learning better deep representations. In contrast, we present an orthogonal approach that does not rely on abstract features but instead learns to predict image transformations and…
The goal of this paper is to present a modified version (GML) of ML invariant which should take into account rulings over a projective base and allow further stratification of smooth affine rational surfaces. We provide a non-trivial…
Multi-Label Image Recognition (MLIR) is a challenging task that aims to predict multiple object labels in a single image while modeling the complex relationships between labels and image regions. Although convolutional neural networks and…
Quantum Graph Neural Networks (QGNNs) offer a promising approach to combining quantum computing with graph-structured data processing. While classical Graph Neural Networks (GNNs) are scalable and robust, existing QGNNs often lack…
We introduce geometric invariants for $p$-groups of class $2$ and exponent $p$. We report on their effectiveness in distinguishing among 5-generator $p$-groups of this type.
Convolutional graph networks are used in particle physics for effective event reconstructions and classifications. However, their performances can be limited by the considerable amount of sensors used in modern particle detectors if applied…
Learning representation on graph plays a crucial role in numerous tasks of pattern recognition. Different from grid-shaped images/videos, on which local convolution kernels can be lattices, however, graphs are fully coordinate-free on…
Simulation-based inference with conditional neural density estimators is a powerful approach to solving inverse problems in science. However, these methods typically treat the underlying forward model as a black box, with no way to exploit…
Graph neural networks (GNN) has been demonstrated to be effective in classifying graph structures. To further improve the graph representation learning ability, hierarchical GNN has been explored. It leverages the differentiable pooling to…
This work generalizes graph neural networks (GNNs) beyond those based on the Weisfeiler-Lehman (WL) algorithm, graph Laplacians, and diffusions. Our approach, denoted Relational Pooling (RP), draws from the theory of finite partial…
We propose a class of intrinsic Gaussian processes (in-GPs) for interpolation, regression and classification on manifolds with a primary focus on complex constrained domains or irregular shaped spaces arising as subsets or submanifolds of…
Graph Neural Networks (GNN) come in many flavors, but should always be either invariant (permutation of the nodes of the input graph does not affect the output) or equivariant (permutation of the input permutes the output). In this paper,…
Data of general object images have two most common structures: (1) each object of a given shape can be rendered in multiple different views, and (2) shapes of objects can be categorized in such a way that the diversity of shapes is much…
This paper is a continuation of [2], where we complete our partial proof of the Deser-Schwimmer conjecture on the structure of ``global conformal invariants''. Our theorem deals with such invariants P(g^n) that locally depend only on the…
With the development of graph convolutional networks (GCN), deep learning methods have started to be used on graph data. In additional to convolutional layers, pooling layers are another important components of deep learning. However, no…
We propose PiNet, a generalised differentiable attention-based pooling mechanism for utilising graph convolution operations for graph level classification. We demonstrate high sample efficiency and superior performance over other graph…
Equivariance has emerged as a desirable property of representations of objects subject to identity-preserving transformations that constitute a group, such as translations and rotations. However, the expressivity of a representation…
Effectively predicting molecular interactions has the potential to accelerate molecular dynamics by multiple orders of magnitude and thus revolutionize chemical simulations. Graph neural networks (GNNs) have recently shown great successes…
We prove finite generation of the algebras of invariants for a class of linear actions of suitable non-reductive groups on projective and affine varieties, and give a geometric construction for their GIT quotients.