Related papers: Group Invariant Global Pooling
Credible forecasting and representation learning of dynamical systems are of ever-increasing importance for reliable decision-making. To that end, we propose a family of Gaussian processes (GP) for dynamical systems with linear…
In this paper, we propose a Graph Inception Diffusion Networks(GIDN) model. This model generalizes graph diffusion in different feature spaces, and uses the inception module to avoid the large amount of computations caused by complex…
In this paper, we introduce an inertial version of the Proximal Incremental Aggregated Gradient method (PIAG) for minimizing the sum of smooth convex component functions and a possibly nonsmooth convex regularization function.…
Graph neural networks (GNNs) have demonstrated a significant success in various graph learning tasks, from graph classification to anomaly detection. There recently has emerged a number of approaches adopting a graph pooling operation…
Group convolutional layers with respect to some group $G$ are modeled by convolutions or cross-correlations with a filter, and they provide the fundamental building block for group convolutional neural networks. For entirely unconstrained…
We sketch the construction of a gauge invariant Exact Renormalization Group (ERG). Starting from Polchinski's equation, the emphasis is on how a series of ideas have combined to yield the gauge invariant formalism. A novel symmetry of the…
In this work, we first tackle the problem of simultaneous pixel-level localization and image-level classification with only image-level labels for fully convolutional network training. We investigate the global pooling method which plays a…
Supervised learning with deep models has tremendous potential for applications in materials science. Recently, graph neural networks have been used in this context, drawing direct inspiration from models for molecules. However, materials…
This article focuses on automatically generating polynomial equations that are inductive loop invariants of computer programs. We propose a new algorithm for this task, which is based on polynomial interpolation. Though the proposed…
Handling geometric transformations, particularly rotations, remains a challenge in deep learning for computer vision. Standard neural networks lack inherent rotation invariance and typically rely on data augmentation or architectural…
Steerable convolutional neural networks (CNNs) provide a general framework for building neural networks equivariant to translations and transformations of an origin-preserving group $G$, such as reflections and rotations. They rely on…
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…
Graph neural networks have emerged as a powerful model for graph representation learning to undertake graph-level prediction tasks. Various graph pooling methods have been developed to coarsen an input graph into a succinct graph-level…
The explosion of massive urban data recently has provided us with a valuable opportunity to gain deeper insights into urban regions and the daily lives of residents. Urban region representation learning emerges as a crucial realm for…
Brain surface analysis is essential to neuroscience, however, the complex geometry of the brain cortex hinders computational methods for this task. The difficulty arises from a discrepancy between 3D imaging data, which is represented in…
Graph neural networks (GNNs) are a well-regarded tool for learned control of networked dynamical systems due to their ability to be deployed in a distributed manner. However, current distributed GNN architectures assume that all nodes in…
This is a brief overview of our work on the theory of group invariant solutions to differential equations. The motivations and applications of this work stem from problems in differential geometry and relativistic field theory. The key…
Graph prediction problems prevail in data analysis and machine learning. The inverse prediction problem, namely to infer input data from given output labels, is of emerging interest in various applications. In this work, we develop…
We describe a system to prove properties of programs. The key feature of this approach is a method to automatically synthesize inductive invariants of the loops contained in the program. The method is generic, i.e., it applies to a large…
Flows are exact-likelihood generative neural networks that transform samples from a simple prior distribution to the samples of the probability distribution of interest. Boltzmann Generators (BG) combine flows and statistical mechanics to…