Related papers: A renormalization-group inspired lattice-based fra…
We present a renormalization group (RG) procedure which works naturally on a wide class of interacting one-dimension models based on perturbed (possibly strongly) continuum conformal and integrable models. This procedure integrates Kenneth…
From benign overfitting in overparameterized models to rich power-law scalings in performance, simple ridge regression displays surprising behaviors sometimes thought to be limited to deep neural networks. This balance of phenomenological…
We consider the analysis of continuous repeated measurement outcomes that are collected through time, also known as longitudinal data. A standard framework for analysing data of this kind is a linear Gaussian mixed-effects model within…
The paper contains the generalization of usual lattice model of multicomponent systems. The generalization is related to account the following factors: 1. The short-range parts of interatomic repulsions. These repulsions are not identical…
The renormalization group (RG) is known to provide information about radiative corrections beyond the order in perturbation theory to which one has calculated explicitly. We first demonstrate the effect of the renormalization scheme used on…
This paper considers generalized linear models using rule-based features, also referred to as rule ensembles, for regression and probabilistic classification. Rules facilitate model interpretation while also capturing nonlinear dependences…
Using particle-scale models to accurately describe property enhancements and phase transitions in macroscopic behavior is a major engineering challenge in composite materials science. To address some of these challenges, we use the graph…
The Renormalization Group (RG) methods are still far from being completely understood in quenched disordered systems. In order to gain insight into the nature of the phase transition of these systems, it is common to investigate simple…
Probabilistic graphical models provide a powerful tool to describe complex statistical structure, with many real-world applications in science and engineering from controlling robotic arms to understanding neuronal computations. A major…
Motivated by the large strain shear of loose granular materials we introduced a model which consists of consecutive optimization and restructuring steps leading to a self organization of a density field. The extensive connections to other…
We review the variational principle in the density matrix renormalization group (DMRG) method, which maximizes an approximate partition function within a restricted degrees of freedom; at zero temperature, DMRG mini- mizes the ground state…
We explain how to use diffusion models to learn inverse renormalization group flows of statistical and quantum field theories. Diffusion models are a class of machine learning models which have been used to generate samples from complex…
A possible path to the interpretability of neural networks is to (approximately) represent them in the regional format of piecewise linear functions, where regions of inputs are associated to linear functions computing the network outputs.…
We develop a rigorous algebraic framework for deep convolutional architectures, CNNs, ResNets, and encoder--decoder networks such as UNet, grounded in lattice theory and mathematical morphology. The central tool is the…
We introduce a generalized additive model for location, scale, and shape (GAMLSS) next of kin aiming at distribution-free and parsimonious regression modelling for arbitrary outcomes. We replace the strict parametric distribution…
We propose a renormalization group (RG) approach to compare and collapse eigenvalue densities of random matrix models of complex systems across different system sizes. The approach is to fix a natural spectral scale by letting the model…
Generalized linear and additive models are very efficient regression tools but the selection of relevant terms becomes difficult if higher order interactions are needed. In contrast, tree-based methods also known as recursive partitioning…
We discuss the averaging hypothesis tacitly assumed in standard cosmology. Our approach is implemented in a "3+1" formalism and invokes the coarse graining arguments, provided and supported by the real-space Renormalization Group (RG)…
At low energies, the microscopic characteristics and changes of physical systems as viewed at different distance scales are described by universal scale invariant properties investigated by the Renormalization Group (RG) apparatus, an…
We propose an $L_{2}$-based penalization algorithm for functional linear regression models, where the coefficient function is shrunk towards a data-driven shape template $\gamma$, which is constrained to belong to a class of piecewise…