Related papers: Permutation Equivariant Neural Functionals
Deep learning models have achieved state-of-the-art performance in many classification tasks. However, most of them cannot provide an interpretation for their classification results. Machine learning models that are interpretable are…
Equivariant neural networks provide a principled framework for incorporating symmetry into learning architectures and have been extensively analyzed through the lens of their separation power, that is, the ability to distinguish inputs…
Incorporating symmetry as an inductive bias into neural network architecture has led to improvements in generalization, data efficiency, and physical consistency in dynamics modeling. Methods such as CNNs or equivariant neural networks use…
Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually…
Equivariant neural networks have proven to be effective for tasks with known underlying symmetries. However, optimizing equivariant networks can be tricky and best training practices are less established than for standard networks. In…
Gradients of neural networks encode valuable information for optimization, editing, and analysis of models. Therefore, practitioners often treat gradients as inputs to task-specific algorithms, e.g. for pruning or optimization. Recent works…
There exist many problem domains where the interpretability of neural network models is essential for deployment. Here we introduce a recurrent architecture composed of input-switched affine transformations - in other words an RNN without…
This paper presents a novel framework for non-linear equivariant neural network layers on homogeneous spaces. The seminal work of Cohen et al. on equivariant $G$-CNNs on homogeneous spaces characterized the representation theory of such…
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…
Solving the intricate quantum behavior of interacting particles is key to unlocking the mysteries of condensed matter, but capturing their complex correlations across different scales remains a monumental challenge. We introduce a neural…
Group equivariance has emerged as a valuable inductive bias in deep learning, enhancing generalization, data efficiency, and robustness. Classically, group equivariant methods require the groups of interest to be known beforehand, which may…
Equivariance of neural networks to transformations helps to improve their performance and reduce generalization error in computer vision tasks, as they apply to datasets presenting symmetries (e.g. scalings, rotations, translations). The…
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 devise a new type of feedforward neural network. It is equivariant with respect to the unitary group $U(n)$. The input and output can be vectors in $\mathbb{C}^n$ with arbitrary dimension $n$. No convolution layer is required in our…
In recent years, there has been a surge in applying deep learning to various challenging design problems in communication networks. The early attempts adopt neural architectures inherited from applications such as computer vision, which…
Convolutional neural networks revolutionized computer vision and natrual language processing. Their efficiency, as compared to fully connected neural networks, has its origin in the architecture, where convolutions reflect the translation…
Graph neural networks (GNNs) have been shown promising in improving the efficiency of learning communication policies by leveraging their permutation properties. Nonetheless, existing works design GNNs only for specific wireless policies,…
We introduce a new class of non-linear models for functional data based on neural networks. Deep learning has been very successful in non-linear modeling, but there has been little work done in the functional data setting. We propose two…
Graph Neural Networks (GNNs) have paved the way for being a cornerstone in graph-related learning tasks. Yet, the ability of GNNs to capture structural interactions within graphs remains under-explored. In this work, we address this gap by…
Different neural networks trained on the same dataset often learn similar input-output mappings with very different weights. Is there some correspondence between these neural network solutions? For linear networks, it has been shown that…