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Binary Neural Networks (BNNs) are an extremely promising method to reduce deep neural networks' complexity and power consumption massively. Binarization techniques, however, suffer from ineligible performance degradation compared to their…

Neural network potentials are a powerful tool for atomistic simulations, allowing to accurately reproduce \textit{ab initio} potential energy surfaces with computational performance approaching classical force fields. A central component of…

The prediction of the atomistic structure and properties of crystals including defects based on ab-initio accurate simulations is essential for unraveling the nano-scale mechanisms that control the micromechanical and macroscopic behaviour…

The development of modern technology has enabled data collection of unprecedented size, which poses new challenges to many statistical estimation and inference problems. This paper studies the maximum score estimator of a semi-parametric…

Despite classical statistical theory predicting severe overfitting, modern massively overparameterized neural networks still generalize well. This unexpected property is attributed to the network's so-called implicit bias, which describes…

Improved performance in higher-order spectral density estimation is achieved using a general class of infinite-order kernels. These estimates are asymptotically less biased but with the same order of variance as compared to the classical…

Deep neural networks can be trained in reciprocal space, by acting on the eigenvalues and eigenvectors of suitable transfer operators in direct space. Adjusting the eigenvalues, while freezing the eigenvectors, yields a substantial…

Machine learning, and representation learning in particular, has the potential to facilitate drug discovery by screening a large chemical space in silico. A successful approach for representing molecules is to treat them as a graph and…

Representation learning algorithms offer the opportunity to learn invariant representations of the input data with regard to nuisance factors. Many authors have leveraged such strategies to learn fair representations, i.e., vectors where…

We present a model for spectral theory of families of selfadjoint operators, and their corresponding unitary one-parameter groups (acting in Hilbert space.) The models allow for a scale of complexity, indexed by the natural numbers…

A neural network is used to train, predict, and evaluate a model to calculate the energies of 3-dimensional systems composed of Ti and O atoms. Python classes are implemented to quantify atomic interactions through symmetry functions and to…

The most critical limitation to the wide-scale use of classical molecular dynamics for alloy design is the availability of suitable interatomic potentials. In this work, we demonstrate a simple procedure to generate a library of accurate…

We consider the problem of estimating the directions of arrival (DOAs) of multiple sources from a single snapshot of an antenna array, a task with many practical applications. In such settings, the classical Bartlett beamformer is commonly…

The development of next-generation molecular simulation models requires moving beyond pre-defined functional forms toward machine learning (ML) techniques that directly capture multiscale physics. Here, we demonstrate such an approach using…

Neural operators have emerged as a powerful tool for learning the mapping between infinite-dimensional parameter and solution spaces of partial differential equations (PDEs). In this work, we focus on multiscale PDEs that have important…

We present the proper orthogonal descriptors for efficient and accuracy representation of the potential energy surface. The potential energy surface is represented as a many-body expansion of parametrized potentials in which the potentials…

A deep neural network (DNN) model consisting of two hidden layers was proposed for predicting the immediate environments of specific atoms based on X-ray absorption near-edge spectra (XANES). The output layer of the DNN can be adjusted to…

While model selection is a well-studied topic in parametric and nonparametric regression or density estimation, selection of possibly high-dimensional nuisance parameters in semiparametric problems is far less developed. In this paper, we…

Using a reference molecular atlas to ensure self-consistency of wavelength calibration is widespread practice. Boesch \& Reiners (Astronomy \& Astrophysics 582 A43 (2015)) reported a line list from a discharge of molecular nitrogen from…

We develop fast spectral algorithms for tensor decomposition that match the robustness guarantees of the best known polynomial-time algorithms for this problem based on the sum-of-squares (SOS) semidefinite programming hierarchy. Our…