Related papers: Softmax parameterization of the occupation numbers…

Functionals that explicitly depend on occupied, unoccupied, or fractionally-occupied orbitals are rigorously formalized using Clifford algebras, and a variational principle is established that facilitates orbital (and occupation)…

In reinforcement learning, the softmax parametrization is the standard approach for policies over discrete action spaces. However, it fails to capture the order relationship between actions. Motivated by a real-world industrial problem, we…

Occupation numbers of natural orbitals capture the physics of strong electron correlations in momentum space. A Natural Orbital Density Functional Theory based on the antisymmetrized geminal product provides these occupation numbers and the…

The softmax function is a widely used activation function in the output layers of neural networks, responsible for converting raw scores into class probabilities while introducing essential non-linearity. Implementing Softmax efficiently…

It is the intention of this paper to rigorously clarify the role of the occupation numbers in the current practical applications of the density functional formalism. In these calculations one has to decide how to distribute a given, fixed…

We present a novel approach to address the challenges of variable occupation numbers in direct optimization of density functional theory (DFT). By parameterizing both the eigenfunctions and the occupation matrix, our method minimizes the…

Natural orbital functional (NOF) theory offers a promising approach for studying strongly correlated systems at an affordable computational cost, with an accuracy comparable to highly demanding wavefunction-based methods. However, its…

The softmax function is widely used in artificial neural networks for the multiclass classification problems, where the softmax transformation enforces the output to be positive and sum to one, and the corresponding loss function allows to…

We report equations of motion for the occupation numbers of natural spin orbitals and show that adiabatic extensions of common functionals employed in ground-state reduced-density-matrix-functional theory have the shortcoming of leading…

This paper addresses the distributed stochastic minimax optimization problem subject to stochastic constraints. We propose a novel first-order Softmax-Weighted Switching Gradient method tailored for federated learning. Under full client…

The one-particle reduced density-matrix (1-RDM) functional theory is a promising alternative to density-functional theory (DFT) that uses the 1-RDM rather than the electronic density as a basic variable. However, long-standing challenges…

This chapter provides a comprehensive review of fundamental concepts related to approximate natural orbital functionals (NOFs), emphasizing their significance in quantum chemistry and physics. Focusing on fermions, the discussion excludes…

Softmax is popular normalization method used in machine learning. Deep learning solutions like Transformer or BERT use the softmax function intensively, so it is worthwhile to optimize its performance. This article presents our methodology…

Softmax function is widely used in artificial neural networks for multiclass classification, multilabel classification, attention mechanisms, etc. However, its efficacy is often questioned in literature. The log-softmax loss has been shown…

Nowadays artificial neural network models achieve remarkable results in many disciplines. Functions mapping the representation provided by the model to the probability distribution are the inseparable aspect of deep learning solutions.…

Reduced density matrix functional theory (RDMFT) calculations are usually implemented in a decoupled manner, where the orbital and occupation optimizations are repeated alternately. Typically, orbital updates are performed using the unitary…

In the past decade, natural orbital functional (NOF) approximations have emerged as prominent tools for characterizing electron correlation. Despite their effectiveness, these approaches, which rely on natural orbitals and their associated…

Spectral decomposition of linear operators plays a central role in many areas of machine learning and scientific computing. Recent work has explored training neural networks to approximate eigenfunctions of such operators, enabling scalable…

The nuclear many-body problem for medium-mass systems is commonly addressed using wave-function expansion methods that build upon a second-quantized representation of many-body operators with respect to a chosen computational basis. While…

Transformers have transformed the field of natural language processing. This performance is largely attributed to the use of stacked self-attention layers, each of which consists of matrix multiplies as well as softmax operations. As a…