Related papers: Learning Affine-Equivariant Proximal Operators
Proximal operators are ubiquitous in inverse problems, commonly appearing as part of algorithmic strategies to regularize problems that are otherwise ill-posed. Modern deep learning models have been brought to bear for these tasks too, as…
Seismic deconvolution is an essential step in seismic data processing that aims to extract layer information from noisy observed traces. In general, this is an ill-posed problem with non-unique solutions. Due to the sparse nature of the…
In this paper we propose integrating a priori knowledge into both design and training of convolutional neural networks (CNNs) to learn object representations that are invariant to affine transformations (i.e., translation, scale, rotation).…
Feed-forward, fully-connected Artificial Neural Networks (ANNs) or the so-called Multi-Layer Perceptrons (MLPs) are well-known universal approximators. However, their learning performance varies significantly depending on the function or…
The aim of this paper is twofold. First, we show that a certain concatenation of a proximity operator with an affine operator is again a proximity operator on a suitable Hilbert space. Second, we use our findings to establish so-called…
Underpinning the success of deep learning is effective regularizations that allow a variety of priors in data to be modeled. For example, robustness to adversarial perturbations, and correlations between multiple modalities. However, most…
In recent years the use of convolutional layers to encode an inductive bias (translational equivariance) in neural networks has proven to be a very fruitful idea. The successes of this approach have motivated a line of research into…
Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions. Such operators often arise from physical models expressed in terms of…
In the desire to quantify the success of neural networks in deep learning and other applications, there is a great interest in understanding which functions are efficiently approximated by the outputs of neural networks. By now, there…
Artificial Neuronal Networks are models widely used for many scientific tasks. One of the well-known field of application is the approximation of high-dimensional problems via Deep Learning. In the present paper we investigate the Deep…
We propose a new optimization method for training feed-forward neural networks. By rewriting the activation function as an equivalent proximal operator, we approximate a feed-forward neural network by adding the proximal operators to the…
Proximal operators are now ubiquitous in non-smooth optimization. Since their introduction in the seminal work of Moreau, many papers have shown their effectiveness on a wide variety of problems, culminating in their use to construct…
In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…
In this work, we describe a new approach that uses deep neural networks (DNN) to obtain regularization parameters for solving inverse problems. We consider a supervised learning approach, where a network is trained to approximate the…
In Reinforcement Learning (RL), Convolutional Neural Networks(CNNs) have been successfully applied as function approximators in Deep Q-Learning algorithms, which seek to learn action-value functions and policies in various environments.…
While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a single hidden layer can approximate accurately any nonlinear…
Equivariant neural networks have shown great success in reinforcement learning, improving sample efficiency and generalization when there is symmetry in the task. However, in many problems, only approximate symmetry is present, which makes…
We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems. Such invariant functions includes the much studied translation-invariant ones…
Recently, deep Convolutional Neural Networks (CNNs) have proven to be successful when employed in areas such as reduced order modeling of parametrized PDEs. Despite their accuracy and efficiency, the approaches available in the literature…
Neural networks have revolutionized the field of data science, yielding remarkable solutions in a data-driven manner. For instance, in the field of mathematical imaging, they have surpassed traditional methods based on convex…