Related papers: Collective Kernel EFT for Pre-activation ResNets

A method to quantitatively assess the consistency of power-counting proposals in Effective Field Theories (EFT) which are non-perturbative at leading order is presented. The Renormalisation Group evolution of an observable predicts the…

In this thesis we elaborate on two different aspects of the Effective Field Theory (EFT) approach to a Binary Coalescing system in General Relativity (GR). First, we consider the issue of hereditary effects in the Post-Newtonian (PN)…

We consider the capacity of \emph{treelike committee machines} (TCM) neural networks. Relying on Random Duality Theory (RDT), \cite{Stojnictcmspnncaprdt23} recently introduced a generic framework for their capacity analysis. An upgrade…

The energy density functional (EDF) method is currently the only microscopic theoretical approach able to tackle the entire nuclear chart. Nevertheless, it suffers from limitations resulting from its empirical character and deteriorating…

We develop an efficient approach to evaluate range-separated exact exchange for grid or plane-wave based representations within the Generalized Kohn-Sham DFT (GKS-DFT) framework. The Coulomb kernel is fragmented in reciprocal space, and we…

Feature learning, or the ability of deep neural networks to automatically learn relevant features from raw data, underlies their exceptional capability to solve complex tasks. However, feature learning seems to be realized in different ways…

Density functional theory (DFT) is a widespread and effective tool in electronic structure calculations for ground-state electron systems. Its success has prompted exploration into the use of DFT for non-collective excited states. The delta…

In this study, we propose a quantum-classical hybrid scheme for performing orbital-free density functional theory (OFDFT) using probabilistic imaginary-time evolution (PITE), designed for the era of fault-tolerant quantum computers (FTQC),…

Feature transformation plays a critical role in enhancing machine learning model performance by optimizing data representations. Recent state-of-the-art approaches address this task as a continuous embedding optimization problem, converting…

We present a novel scheme to accurately predict atomic forces as vector quantities, rather than sets of scalar components, by Gaussian Process (GP) Regression. This is based on matrix-valued kernel functions, on which we impose the…

Kernel density estimation (KDE) is a popular statistical technique for estimating the underlying density distribution with minimal assumptions. Although they can be shown to achieve asymptotic estimation optimality for any input…

Error entropy is a important nonlinear similarity measure, and it has received increasing attention in many practical applications. The default kernel function of error entropy criterion is Gaussian kernel function, however, which is not…

Rotation equivariant graph neural networks, i.e. networks designed to guarantee certain geometric relations between their inputs and outputs, yield state of the art performance on spatial deep learning tasks. They exhibit high data…

General formulation for the effective field theory with differential operator technique and the decoupling approximation with larger finite clusters (namely EFT-$N$ formulation) has been derived, for S-1/2 bulk systems. The effect of the…

Federated learning must address heterogeneity, strict communication and computation limits, and privacy while ensuring performance. We propose an operator-theoretic framework that maps the $L^2$-optimal solution into a reproducing kernel…

Predictive power in theoretical nuclear physics has been a major concern in the study of nuclear structure and reactions. The Effective Field Theory (EFT) based on chiral expansions provides a model independent hierarchy for many body…

Whilst deep neural networks have shown great empirical success, there is still much work to be done to understand their theoretical properties. In this paper, we study the relationship between random, wide, fully connected, feedforward…

Conformal field theory (CFT) is an extremely powerful tool for explicitly computing critical exponents and correlation functions of statistical mechanics systems at a second order phase transition, or of condensed matter systems at a…

We implement the effective field theory (EFT) approach to dark energy and modified gravity in the public Einstein-Boltzmann solver CAMB. The resulting code, which we dub EFTCAMB, is a powerful and versatile tool that can be used for several…

The asymptotically precise estimation of the generalization of kernel methods has recently received attention due to the parallels between neural networks and their associated kernels. However, prior works derive such estimates for training…