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Estimating hyperparameters has been a long-standing problem in machine learning. We consider the case where the task at hand is modeled as the solution to an optimization problem. Here the exact gradient with respect to the hyperparameters…
We use a simple algebraic method to find a special class of composite p-brane solutions of higher dimensional gravity coupled with matter. These solutions are composed of n constituent p-branes corresponding n independent harmonic…
This paper introduces a novel double regularization scheme for bilevel optimization problems whose lower-level problem is composite and convex, but not necessarily strongly convex, in the lower-level variable. The analysis focuses on the…
The radiation emitted by accelerated fundamental strings and D-branes is studied within the linear approximation to the supergravity limit of string theory. We show that scalar, gauge field and gravitational radiation is generically emitted…
Colliding branes without $Z_{2}$ symmetry and the formation of spacetime singularities in string theory are studied. After developing the general formulas to describe such events, we study a particular class of exact solutions first in the…
A geometric theory of brane-worlds with large or non-compact extra dimensions is presented. It is shown that coordinate gauge independent perturbations of the brane-world correspond to the Einstein-Hilbert dynamics derived from the…
In String Theory compactification, branes are often invoked to get the desired form of the radion effective potential. Current popular way of doing this assumes that the introduction of branes will not modify the background geometry in an…
Computing the gradient of a function provides fundamental information about its behavior. This information is essential for several applications and algorithms across various fields. One common application that require gradients are…
Curved, intersecting brane configurations satisfying the type IIA supergravity equations of motion are found. In eleven dimensions, the models are interpreted in terms of orthogonally intersecting M5--branes, where the world--volumes are…
In this paper, we propose a random gradient-free method for optimization in infinite dimensional Hilbert spaces, applicable to functional optimization in diverse settings. Though such problems are often solved through finite-dimensional…
We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…
We investigate the computation of the gradient of the value function in parametric convex optimization problems. We derive general expression for the gradient of the value function in terms of the cost function, constraints and Lagrange…
Policy gradient methods hold great potential for solving complex continuous control tasks. Still, their training efficiency can be improved by exploiting structure within the optimization problem. Recent work indicates that supervised…
A thick brane in six dimensions is constructed using two scalar fields. The field equations for 6D gravity plus the scalar fields are solved numerically. This thick brane solution shares some features with a previously studied analytic…
In this paper we investigate about several configurations of two intersecting branes at arbitrary angles. We choose the viewpoint of a brane source and a brane probe and use the low-energy dynamics of p-branes. For each p-brane this…
Many statistical estimators for high-dimensional linear regression are M-estimators, formed through minimizing a data-dependent square loss function plus a regularizer. This work considers a new class of estimators implicitly defined…
A method for obtaining solutions to the classical equations for scalars plus gravity in five dimensions is applied to some recent suggestions for brane-world phenomenology. The method involves only first order differential equations. It is…
We suggest simple implementable modifications of conditional gradient and gradient projection methods for smooth convex optimization problems in Hilbert spaces. Usually, the custom methods attain only weak convergence. We prove strong…
We study the self-tuning of general brane junctions and brane networks on the 6-dimensional space-time. For the general brane junctions, there may exist one fine-tuning among the brane tensions. For the brane networks, similar to the…
Local oscillations of the brane world are manifested as masssive vector fields. Their coupling to the Standard Model can be obtained using the method of nonlinear realizations of the spontaneously broken higher dimensional space-time…