Related papers: Joint Group Invariant Functions on Data-Parameter …

In this study, we introduce a method for learning group (known or unknown) equivariant functions by learning the associated quadratic form $x^T A x$ corresponding to the group from the data. Certain groups, known as orthogonal groups,…

We explore the universality of neural encodings in convolutional neural networks trained on image classification tasks. We develop a procedure to directly compare the learned weights rather than their representations. It is based on a…

Recently, deep learning approaches with various network architectures have achieved significant performance improvement over existing iterative reconstruction methods in various imaging problems. However, it is still unclear why these deep…

Flow control is key to maximize energy efficiency in a wide range of applications. However, traditional flow-control methods face significant challenges in addressing non-linear systems and high-dimensional data, limiting their application…

Universality results for equivariant neural networks remain rare. Those that do exist typically hold only in restrictive settings: either they rely on regular or higher-order tensor representations, leading to impractically high-dimensional…

Deep Neural Networks (DNNs) suffer from domain shift when the test dataset follows a distribution different from the training dataset. Domain generalization aims to tackle this issue by learning a model that can generalize to unseen…

Manifold learning-based encoders have been playing important roles in nonlinear dimensionality reduction (NLDR) for data exploration. However, existing methods can often fail to preserve geometric, topological and/or distributional…

Domain generalization refers to the problem where we aim to train a model on data from a set of source domains so that the model can generalize to unseen target domains. Naively training a model on the aggregate set of data (pooled from all…

Recent years have witnessed a hot wave of deep neural networks in various domains; however, it is not yet well understood theoretically. A theoretical characterization of deep neural networks should point out their approximation ability and…

Convolutional neural networks have been extremely successful in the image recognition domain because they ensure equivariance to translations. There have been many recent attempts to generalize this framework to other domains, including…

We propose the Interferometric Graph Transform (IGT), which is a new class of deep unsupervised graph convolutional neural network for building graph representations. Our first contribution is to propose a generic, complex-valued spectral…

Regularization plays a pivotal role in integrating prior information into inverse problems. While many deep learning methods have been proposed to solve inverse problems, determining where to apply regularization remains a crucial…

The universal approximation theorem establishes that neural networks can approximate any continuous function on a compact set. Later works in approximation theory provide quantitative approximation rates for ReLU networks on the class of…

We employ deep neural networks to represent the field derivative of the scale-dependent effective potential in the functional renormalization group (fRG) framework for nonperturbative quantum field theory. By embedding the fRG flow…

Graph and hypergraph representation learning has attracted increasing attention from various research fields. Despite the decent performance and fruitful applications of Graph Neural Networks (GNNs), Hypergraph Neural Networks (HGNNs), and…

We consider applications of neural networks in nonlinear system identification and formulate a hypothesis that adjusting general network structure by incorporating frequency information or other known orthogonal transform, should result in…

In this study, a novel feature coding method that exploits invariance for transformations represented by a finite group of orthogonal matrices is proposed. We prove that the group-invariant feature vector contains sufficient discriminative…

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…

Reconstructing training data from trained neural networks is an active area of research with significant implications for privacy and explainability. Recent advances have demonstrated the feasibility of this process for several data types.…

Artificial and biological agents cannon learn given completely random and unstructured data. The structure of data is encoded in the metric relationships between data points. In the context of neural networks, neuronal activity within a…