Related papers: Softmax parameterization of the occupation numbers…

In the present work, we investigate the computational efficiency afforded by higher-order finite-element discretization of the saddle-point formulation of orbital-free density functional theory. We first investigate the robustness of viable…

This paper presents a novel approach to construct regularizing operators for severely ill-posed Fredholm integral equations of the first kind by introducing parametrized discretization. The optimal values of discretization and…

The softmax function is a fundamental building block of deep neural networks, commonly used to define output distributions in classification tasks or attention weights in transformer architectures. Despite its widespread use and proven…

Many electronic structure methods rely on the minimization of the energy of the system with respect to the one-body reduced density matrix (1-RDM). To formulate a minimization algorithm, the 1-RDM is often expressed in terms of its…

The exchange-correlation energy in Kohn-Sham density functional theory is expressed as a functional of the electronic density and the Kohn-Sham orbitals. An alternative to Kohn-Sham theory is to express the energy as a functional of the…

Dimension reduction is often necessary in functional data analysis, with functional principal component analysis being one of the most widely used techniques. A key challenge in applying these methods is determining the number of…

The possibility to use functionals of occupation numbers and natural orbitals for interacting fermions is discussed as an alternative to multi-reference energy density functional method. An illustration based on the two-level Lipkin model…

Favorably scaling numerical time-dependent many-electron techniques such as time-dependent density functional theory (TDDFT) with adiabatic exchange-correlation potentials typically fail in capturing highly correlated electron dynamics. We…

Particle-based shape modeling (PSM) is a popular approach to automatically quantify shape variability in populations of anatomies. The PSM family of methods employs optimization to automatically populate a dense set of corresponding…

Normalization methods improve both optimization and generalization of ConvNets. To further boost performance, the recently-proposed switchable normalization (SN) provides a new perspective for deep learning: it learns to select different…

In many of the approximate functionals in one-body reduced density matrix (1RDM) functional theory, the approximate two-body reduced density matrix (2RDM) in the natural orbital representation only depends on the natural occupation numbers.…

Softmax is widely used in deep learning to map some representation to a probability distribution. As it is based on exp/log functions that are relatively expensive in multi-party computation, Mohassel and Zhang (2017) proposed a simpler…

Incorporating a non-Euclidean variable metric to first-order algorithms is known to bring enhancement. However, due to the lack of an optimal choice, such an enhancement appears significantly underestimated. In this work, we establish a…

One of the major computational bottlenecks in one-body reduced density matrix (1RDM) functional theory is the evaluation of approximate 1RDM functionals and their derivatives. The reason is that more advanced approximate functionals are…

The Softmax function is ubiquitous in machine learning, multiple previous works suggested faster alternatives for it. In this paper we propose a way to compute classical Softmax with fewer memory accesses and hypothesize that this reduction…

Deep Metric Learning (DML) loss functions traditionally aim to control the forces of separability and compactness within an embedding space so that the same class data points are pulled together and different class ones are pushed apart.…

We introduce the concept of natural super-orbitals for many-body operators, defined as the eigenvectors of the one-body super-density matrix associated with a vectorized operator. We relate these objects to measures of non-Gaussianity of…

In the recent work of S. Sharma \emph{et al.}, (arxiv.org: arxiv:0912.1118), a single-electron spectrum associated with the natural orbitals was defined as the derivative of the total energy with respect to the occupation numbers at half…

In recent years, the softmax model and its fast approximations have become the de-facto loss functions for deep neural networks when dealing with multi-class prediction. This loss has been extended to language modeling and recommendation,…

The impact of softmax on the value function itself in reinforcement learning (RL) is often viewed as problematic because it leads to sub-optimal value (or Q) functions and interferes with the contraction properties of the Bellman operator.…