Related papers: Monomial Matrix Group Equivariant Neural Functiona…

Convolutions encode equivariance symmetries into neural networks leading to better generalisation performance. However, symmetries provide fixed hard constraints on the functions a network can represent, need to be specified in advance, and…

Exploiting symmetries and invariance in data is a powerful, yet not fully exploited, way to achieve better generalisation with more efficiency. In this paper, we introduce two graph network architectures that are equivariant to several…

The automated segmentation of cortical areas has been a long-standing challenge in medical image analysis. The complex geometry of the cortex is commonly represented as a polygon mesh, whose segmentation can be addressed by graph-based…

Convolutional neural network (CNN) has achieved impressive success in computer vision during the past few decades. The image convolution operation helps CNNs to get good performance on image-related tasks. However, it also has high…

Rank minimization methods have attracted considerable interest in various areas, such as computer vision and machine learning. The most representative work is nuclear norm minimization (NNM), which can recover the matrix rank exactly under…

In this paper we propose a generalization of deep neural networks called deep function machines (DFMs). DFMs act on vector spaces of arbitrary (possibly infinite) dimension and we show that a family of DFMs are invariant to the dimension of…

The introduction of convolutional layers greatly advanced the performance of neural networks on image tasks due to innately capturing a way of encoding and learning translation-invariant operations, matching one of the underlying symmetries…

Equivariance of linear neural network layers is well studied. In this work, we relax the equivariance condition to only be true in a projective sense. We propose a way to construct a projectively equivariant neural network through building…

This paper introduces a new model to learn graph neural networks equivariant to rotations, translations, reflections and permutations called E(n)-Equivariant Graph Neural Networks (EGNNs). In contrast with existing methods, our work does…

The ability to generalize compositionally is key to understanding the potentially infinite number of sentences that can be constructed in a human language from only a finite number of words. Investigating whether NLP models possess this…

Symmetric nonnegative matrix factorization (NMF), a special but important class of the general NMF, is demonstrated to be useful for data analysis and in particular for various clustering tasks. Unfortunately, designing fast algorithms for…

Neural networks (NNs) have been successfully deployed in various fields. In NNs, a large number of multiplyaccumulate (MAC) operations need to be performed. Most existing digital hardware platforms rely on parallel MAC units to accelerate…

Graph representation learning has been widely studied and demonstrated effectiveness in various graph tasks. Most existing works embed graph data in the Euclidean space, while recent works extend the embedding models to hyperbolic or…

Fast feedforward networks (FFFs) are a class of neural networks that exploit the observation that different regions of the input space activate distinct subsets of neurons in wide networks. FFFs partition the input space into separate…

Convolutional neural networks (CNN) are widely used in computer vision, especially in image classification. However, the way in which information and invariance properties are encoded through in deep CNN architectures is still an open…

We develop a theory of category-equivariant neural networks (CENNs) that unifies group/groupoid-equivariant networks, poset/lattice-equivariant networks, graph and sheaf neural networks. Equivariance is formulated as naturality in a…

Many learning problems involve symmetries, and while invariance can be built into neural architectures, it can also emerge implicitly when training on group-structured data. We study this phenomenon in classical Hopfield networks and show…

Background: Deep neural networks have proven to be powerful computational tools for modeling, prediction, and generation. However, the workings of these models have generally been opaque. Recent work has shown that the performance of some…

In this paper, we study complex-valued neural network (CVNNs) with tensor-valued hidden-to-output weights within the framework of neural-network quantum field theory (NN-QFT). For standard CVNNs with scalar weights, we derive the generating…

We study the problem of optimal power allocation in a single-hop ad hoc wireless network. In solving this problem, we depart from classical purely model-based approaches and propose a hybrid method that retains key modeling elements in…