Related papers: Regularizing Towards Soft Equivariance Under Mixed…

Regularization plays a pivotal role when facing the challenge of solving ill-posed inverse problems, where the number of observations is smaller than the ambient dimension of the object to be estimated. A line of recent work has studied…

How to extract more and useful information for single image super resolution is an imperative and difficult problem. Learning-based method is a representative method for such task. However, the results are not so stable as there may exist…

Deep networks are an integral part of the current machine learning paradigm. Their inherent ability to learn complex functional mappings between data and various target variables, while discovering hidden, task-driven features, makes them a…

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…

Regularization is a powerful technique for extracting useful information from noisy data. Typically, it is implemented by adding some sort of norm constraint to an objective function and then exactly optimizing the modified objective…

In many applications where collecting data is expensive, for example neuroscience or medical imaging, the sample size is typically small compared to the feature dimension. It is challenging in this setting to train expressive, non-linear…

Sparse models for high-dimensional linear regression and machine learning have received substantial attention over the past two decades. Model selection, or determining which features or covariates are the best explanatory variables, is…

For regularized optimization that minimizes the sum of a smooth term and a regularizer that promotes structured solutions, inexact proximal-Newton-type methods, or successive quadratic approximation (SQA) methods, are widely used for their…

Many machine learning tasks in the natural sciences are precisely equivariant to particular symmetries. Nonetheless, equivariant methods are often not employed, perhaps because training is perceived to be challenging, or the symmetry is…

When working with textual data, a natural application of disentangled representations is fair classification where the goal is to make predictions without being biased (or influenced) by sensitive attributes that may be present in the data…

The solution of inverse problems is of fundamental interest in medical and astronomical imaging, geophysics as well as engineering and life sciences. Recent advances were made by using methods from machine learning, in particular deep…

Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…

The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite…

There are various inverse problems -- including reconstruction problems arising in medical imaging -- where one is often aware of the forward operator that maps variables of interest to the observations. It is therefore natural to ask…

B-spline models are a powerful way to represent scientific data sets with a functional approximation. However, these models can suffer from spurious oscillations when the data to be approximated are not uniformly distributed. Model…

State-of-the-art neural networks can be trained to become remarkable solutions to many problems. But while these architectures can express symbolic, perfect solutions, trained models often arrive at approximations instead. We show that the…

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…

The progress in the last decade has enabled machine learning models to achieve impressive performance across a wide range of tasks in Computer Vision. However, a plethora of works have demonstrated the susceptibility of these models to…

In many applications, SMT solvers are utilized to solve similar or identical tasks over time. Significant variations in performance due to small changes in the input are not uncommon and lead to frustration for users. This sort of stability…

Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an…