Related papers: Equivariant neural networks for inverse problems
We consider the variational reconstruction framework for inverse problems and propose to learn a data-adaptive input-convex neural network (ICNN) as the regularization functional. The ICNN-based convex regularizer is trained adversarially…
Equivariant neural networks, whose hidden features transform according to representations of a group G acting on the data, exhibit training efficiency and an improved generalisation performance. In this work, we extend group invariant and…
Euclidean deep learning is often inadequate for addressing real-world signals where the representation space is irregular and curved with complex topologies. Interpreting the geometric properties of such feature spaces has become paramount…
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…
Incorporating group symmetry directly into the learning process has proved to be an effective guideline for model design. By producing features that are guaranteed to transform covariantly to the group actions on the inputs,…
We propose a framework for rotation and translation covariant deep learning using $SE(2)$ group convolutions. The group product of the special Euclidean motion group $SE(2)$ describes how a concatenation of two roto-translations results in…
Self-supervised image denoising methods have garnered significant research attention in recent years, for this kind of method reduces the requirement of large training datasets. Compared to supervised methods, self-supervised methods rely…
In this paper, we propose a novel deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems. Regularized iterative algorithms have emerged as the standard approach to ill-posed inverse problems in the…
This review provides an introduction to - and overview of - the current state of the art in neural-network based regularization methods for inverse problems in imaging. It aims to introduce readers with a solid knowledge in applied…
Regularization is critical for solving ill-posed geophysical inverse problems. Explicit regularization is often used, but there are opportunities to explore the implicit regularization effects that are inherent in a Neural Network…
Quantum neural network architectures that have little-to-no inductive biases are known to face trainability and generalization issues. Inspired by a similar problem, recent breakthroughs in machine learning address this challenge by…
Equivariance is a powerful inductive bias in neural networks, improving generalisation and physical consistency. Recently, however, non-equivariant models have regained attention, due to their better runtime performance and imperfect…
Group equivariant convolutional neural networks (G-CNNs) are generalizations of convolutional neural networks (CNNs) which excel in a wide range of technical applications by explicitly encoding symmetries, such as rotations and…
Incorporating group symmetries via equivariance into neural networks has emerged as a robust approach for overcoming the efficiency and data demands of modern deep learning. While most existing approaches, such as group convolutions and…
From early image processing to modern computational imaging, successful models and algorithms have relied on a fundamental property of natural signals: symmetry. Here symmetry refers to the invariance property of signal sets to…
Equivariances provide useful inductive biases in neural network modeling, with the translation equivariance of convolutional neural networks being a canonical example. Equivariances can be embedded in architectures through weight-sharing…
Invariance to spatial transformations such as translations and rotations is a desirable property and a basic design principle for classification neural networks. However, the commonly used convolutional neural networks (CNNs) are actually…
Equivariant neural networks incorporate symmetries through group actions, embedding them as an inductive bias to improve performance. Existing methods learn an equivariant action on the latent space, or design architectures that are…
Geophysical inversion attempts to estimate the distribution of physical properties in the Earth's interior from observations collected at or above the surface. Inverse problems are commonly posed as least-squares optimization problems in…
In many machine learning tasks it is desirable that a model's prediction transforms in an equivariant way under transformations of its input. Convolutional neural networks (CNNs) implement translational equivariance by construction; for…