相关论文: Renormalization and Hyperscaling for Self-Avoiding…

We consider a version of dimensional regularization (reduction) in which the dimensionful regularization parameter $\Lambda$ is in general different from the renormalization scale $\mu$. Then in the scheme analogous to the minimal…

Self-Organizing Maps (SOMs) provide topology-preserving projections of high-dimensional data, yet their use as generative models remains largely unexplored. We show that the activation pattern of a SOM -- the squared distances to its…

The proper orthogonal decomposition (POD) -- a popular projection-based model order reduction (MOR) method -- may require significant model dimensionalities to successfully capture a nonlinear solution manifold resulting from a…

Given an observable and its operator product expansion (OPE), we present expressions that carefully disentangle truncated sums of the perturbative series in powers of $\alpha$ from the non-perturbative (NP) corrections. This splitting is…

Parametric human body models are foundational to human reconstruction, animation, and simulation, yet they remain mutually incompatible: SMPL, SMPL-X, MHR, Anny, and related models each diverge in mesh topology, skeletal structure, shape…

Controlling the internal representation space of a neural network is a desirable feature because it allows to generate new data in a supervised manner. In this paper we will show how this can be achieved while building a low-dimensional…

Multiple scales coexist in complex networks. However, the small world property makes them strongly entangled. This turns the elucidation of length scales and symmetries a defiant challenge. Here, we define a geometric renormalization group…

Face swapping has gained significant attention for its varied applications. Most previous face swapping approaches have relied on the seesaw game training scheme, also known as the target-oriented approach. However, this often leads to…

We show how the newly developed method of Periodic Unfolding on Riemannian manifolds can be applied to PDE problems: We consider the homogenization of an elliptic model problem. In the limit, we obtain a generalization of the well-known…

We present a novel approach for model reduction of nonlinear dynamical systems based on proper orthogonal decomposition (POD). Our method, derived from Density Matrix Renormalization Group (DMRG), provides a significant reduction in…

The polarizable embedding (PE) approach is a flexible embedding model where a pre-selected region out of a larger system is described quantum mechanically while the interaction with the surrounding environment is modeled through an…

We propose a theoretical formulation of protected edge modes in the language of quantum field theories based on the contemporary understanding of the renormalization group. We use bulk and boundary renormalization arguments which have never…

We consider the operator product expansion (OPE) of correlation functions in the supersymmetric $O(N)$ non-linear sigma model at sub-leading order in the large $N$ limit in order to study the cancellation between ambiguities coming from…

Detecting out of distribution (OOD) samples is of paramount importance in all Machine Learning applications. Deep generative modeling has emerged as a dominant paradigm to model complex data distributions without labels. However, prior work…

Sharpness-Aware Minimization (SAM) has been demonstrated to improve the generalization performance of overparameterized models by seeking flat minima on the loss landscape through optimizing model parameters that incur the largest loss…

The direct parametrisation method for invariant manifold is a model-order reduction technique that can be applied to nonlinear systems described by PDEs and discretised e.g. with a finite element procedure in order to derive efficient…

We propose a reduced-order modeling approach for nonlinear, parameter-dependent ordinary differential equations (ODE). Dimensionality reduction is achieved using nonlinear maps represented by autoencoders. The resulting low-dimensional ODE…

Object-level SLAM introduces semantic meaningful and compact object landmarks that help both indoor robot applications and outdoor autonomous driving tasks. However, the back end of object-level SLAM suffers from singularity problems…

This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…

Katz and Vafa showed how charged matter can arise geometrically by the deformation of ADE-type orbifold singularities in type IIa, M-theory, and F-theory compactifications. In this paper we use those same basic ingredients, used there to…