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The ever-increasing number of parameters in deep neural networks poses challenges for memory-limited applications. Regularize-and-prune methods aim at meeting these challenges by sparsifying the network weights. In this context we quantify…

Hard X-ray spectra in solar flares provide knowledge of the electron spectrum that results from acceleration and propagation in the solar atmosphere. However, the inference of the electron spectra from solar X-ray spectra is an ill-posed…

Neural networks have emerged as effective tools for solving ill-posed inverse problems. In many scientific applications, however, observational training data are insufficient, and learned inverse operators must instead be trained on…

The reconstruction of images from their corresponding noisy Radon transform is a typical example of an ill-posed linear inverse problem as arising in the application of computerized tomography (CT). As the (naive) solution does not depend…

We consider the tuning parameter selection rules for nuclear norm regularized multivariate linear regression (NMLR) in high-dimensional setting. High-dimensional multivariate linear regression is widely used in statistics and machine…

The solution of linear inverse problems arising, for example, in signal and image processing is a challenging problem since the ill-conditioning amplifies, in the solution, the noise present in the data. Recently introduced algorithms based…

Neutrino cross-section measurements are often presented as unfolded binned distributions in "true" variables. The ill-posedness of the unfolding problem can lead to results with strong anti-correlations and fluctuations between bins, which…

In this paper, we introduce a physics-driven regularization method for training of deep neural networks (DNNs) for use in engineering design and analysis problems. In particular, we focus on prediction of a physical system, for which in…

Probabilistic models must be well calibrated to support reliable decision-making. While calibration in single-output regression is well studied, defining and achieving multivariate calibration in multi-output regression remains considerably…

Inverse problems arise in a number of domains such as medical imaging, remote sensing, and many more, relying on the use of advanced signal and image processing approaches -- such as sparsity-driven techniques -- to determine their…

In the current quantum computing paradigm, significant focus is placed on the reduction or mitigation of quantum decoherence. When designing new quantum processing units, the general objective is to reduce the amount of noise qubits are…

The data consistency for the physical forward model is crucial in inverse problems, especially in MR imaging reconstruction. The standard way is to unroll an iterative algorithm into a neural network with a forward model embedded. The…

Over-parameterized deep neural networks trained by simple first-order methods are known to be able to fit any labeling of data. Such over-fitting ability hinders generalization when mislabeled training examples are present. On the other…

Regularization techniques such as L2 regularization (Weight Decay) and Dropout are fundamental to training deep neural networks, yet their underlying physical mechanisms regarding feature frequency selection remain poorly understood. In…

Machine learning techniques work best when the data used for training resembles the data used for evaluation. This holds true for learned single-image denoising algorithms, which are applied to real raw camera sensor readings but, due to…

Learning approaches have recently become very popular in the field of inverse problems. A large variety of methods has been established in recent years, ranging from bi-level learning to high-dimensional machine learning techniques. Most…

A widely believed explanation for the remarkable generalization capacities of overparameterized neural networks is that the optimization algorithms used for training induce an implicit bias towards benign solutions. To grasp this…

Generalization is one of the fundamental issues in machine learning. However, traditional techniques like uniform convergence may be unable to explain generalization under overparameterization. As alternative approaches, techniques based on…

Due to the over-parameterization nature, neural networks are a powerful tool for nonlinear function approximation. In order to achieve good generalization on unseen data, a suitable inductive bias is of great importance for neural networks.…

Generative diffusion models can provide powerful prior probability models for inverse problems in imaging, but existing implementations suffer from two key limitations: $(i)$ the prior density is represented implicitly, and $(ii)$ they rely…