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Mechanistic models in biology often involve numerous parameters about which we do not have direct experimental information. The traditional approach is to fit these parameters using extensive numerical simulations (e.g. by the Monte-Carlo…

Order parameters based on spherical harmonics and Fourier coefficients already play a significant role in condensed matter research in the context of systems of spherical or point particles. Here, we extend these types of order parameter to…

Multi-task learning has gained popularity due to the advantages it provides with respect to resource usage and performance. Nonetheless, the joint optimization of parameters with respect to multiple tasks remains an active research topic.…

Computations for the softmax function are significantly expensive when the number of output classes is large. In this paper, we present a novel softmax inference speedup method, Doubly Sparse Softmax (DS-Softmax), that leverages sparse…

This article is devoted to one particular case of using universal accelerated proximal envelopes to obtain computationally efficient accelerated versions of methods used to solve various optimization problem setups. In this paper, we…

Learning distributed representations, or embeddings, that encode the relational similarity patterns among objects is a relevant task in machine learning. A popular method to learn the embedding matrices $X, Y$ is optimizing a loss function…

Large language models (LLMs) have brought about significant transformations in human society. Among the crucial computations in LLMs, the softmax unit holds great importance. Its helps the model generating a probability distribution on…

The maximization of submodular functions have found widespread application in areas such as machine learning, combinatorial optimization, and economics, where practitioners often wish to enforce various constraints; the matroid constraint…

The correct description of nondynamic correlation by electronic structure methods not belonging to the multireference family is a challenging issue. The transition of $D_{2h}$ to $D_{4h}$ symmetry in H$_4$ molecule is among the most simple…

Converting an n-dimensional vector to a probability distribution over n objects is a commonly used component in many machine learning tasks like multiclass classification, multilabel classification, attention mechanisms etc. For this,…

We introduce a hybrid quantum-classical algorithm to compute the Green function for strongly correlated electrons on noisy intermediate-scale quantum (NISQ) devices. The technique consists in the construction of a non-orthogonal excitation…

Ab initio pseudopotentials are a linchpin of modern molecular and condensed matter electronic structure calculations. In this work, we employ multi-objective optimization to maximize pseudopotential softness while maintaining high accuracy…

Density functional theory (DFT) embedding provides a formally exact framework for interfacing correlated wave-function theory (WFT) methods with lower-level descriptions of electronic structure. Here, we report techniques to improve the…

These notes focus on the minimization of convex functionals using first-order optimization methods, which are fundamental in many areas of applied mathematics and engineering. The primary goal of this document is to introduce and analyze…

In order to investigate correspondences between 3D shapes, many methods rely on a feature descriptor which is invariant under almost isometric transformations. An interesting class of models for such descriptors relies on partial…

The synthesis of classical Computational Complexity Theory with Recursive Analysis provides a quantitative foundation to reliable numerics. Here the operators of maximization, integration, and solving ordinary differential equations are…

The exact formulation of multi-configuration density-functional theory (DFT) is discussed in this work. As an alternative to range-separated methods, where electron correlation effects are split in the coordinate space, the combination of…

As a new approach to efficiently describe correlation effects in the relativistic quantum world we propose to consider reduced density matrix functional theory, where the key quantity is the first-order reduced density matrix (1-RDM). In…

In offline reinforcement learning (RL) we have no opportunity to explore so we must make assumptions that the data is sufficient to guide picking a good policy, taking the form of assuming some coverage, realizability, Bellman completeness,…

The $N$-representability problem places fundamental constraints on reduced density matrices (RDMs) that originate from physical many-fermion quantum states. Motivated by recent developments in functional theories, we introduce a hierarchy…