相关论文: Gradient formula for linearly self-interacting bra…

We give a model-independent derivation of general intersecting rules for spacelike branes (S-branes) in arbitrary dimensions $d$. This is achieved by directly solving bosonic field equations for supergravity coupled to a dilaton and…

A common belief in high-dimensional data analysis is that data are concentrated on a low-dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on…

In this thesis we study the dynamics of higher-dimensional gravity in a universe emerging from a brane collision. We develop a set of powerful analytic methods which, we believe, render braneworld cosmological perturbation theory solvable.…

This article provides a self contained overview of the geometry and dynamics of relativistic brane models, of the category that includes point particle, string, and membrane representations for phenomena that can be considered as being…

We present a general rule determining how extremal branes can interesect in a configuration with zero binding energy. The rule is derived in a model independent way and in arbitrary spacetime dimensions $D$ by solving the equations of…

It is generic for the bulk fields sourced by branes having codimension two and higher to diverge at the brane position, much as does the Coulomb potential at the position of its source charge. This complicates finding the relation between…

We propose a new technique that boosts the convergence of training generative adversarial networks. Generally, the rate of training deep models reduces severely after multiple iterations. A key reason for this phenomenon is that a deep…

Empirical observation of high dimensional phenomena, such as the double descent behaviour, has attracted a lot of interest in understanding classical techniques such as kernel methods, and their implications to explain generalization…

Bilevel reinforcement learning (RL), which features intertwined two-level problems, has attracted growing interest recently. The inherent non-convexity of the lower-level RL problem is, however, to be an impediment to developing bilevel…

The equations of motion for a self-interacting self-dual tensor in six dimensions are extracted from the equations describing the M-theory five-brane. These equations are presented in a self-contained, six-dimensional Lorentz-covariant…

In this work we deal with thick brane solutions in the warped five-dimensional braneworld scenario with a single extra spatial dimension of infinite extent, for a class of modified theories of gravity with a Lagrange multiplier. We first…

We give a full nonlinear numerical treatment of time-dependent 5d braneworld geometry, which is determined self-consistently by potentials for the scalar field in the bulk and at two orbifold branes, supplemented by boundary conditions at…

Gradients have been used to quantify feature importance in machine learning models. Unfortunately, in nonlinear deep networks, not only individual neurons but also the whole network can saturate, and as a result an important input feature…

We discuss the backreaction of a massless, minimally coupled, quantized scalar field on a thick, two-dimensional de Sitter (dS) brane as an extension of our previous work. We show that a finite brane thickness naturally regularizes the…

This paper proposes a novel kernel approach to linear dimension reduction for supervised learning. The purpose of the dimension reduction is to find directions in the input space to explain the output as effectively as possible. The…

A theory for studying the dynamic scaling properties of branes and relativistic topological defect networks is presented. The theory, based on a relativistic version of the level set method, well-known in other contexts, possesses…

This paper presents a study of brane formation in six-dimensional space. There is no a priori assumption of the brane(s) existence. However, the analysis of the generalized Einstein equations reveals that there are a set of metrics…

Tuning hyperparameters of learning algorithms is hard because gradients are usually unavailable. We compute exact gradients of cross-validation performance with respect to all hyperparameters by chaining derivatives backwards through the…

We review various aspects of configurations of intersecting branes, including the conditions for preservation of supersymmetry. In particular, we discuss the projection conditions on the Killing spinors for given brane configurations and…

We compute the gravitational response of six dimensional gauged, chiral supergravity to localized stress energy on one of two space-filling branes, including the effects of compactifying the extra dimensions and brane back-reaction. We find…