Related papers: Gradient formula for linearly self-interacting bra…
In this article, we show that solving the system of linear equations by manipulating the kernel and the range space is equivalent to solving the problem of least squares error approximation. This establishes the ground for a gradient-free…
The optimisation of neural networks can be sped up by orthogonalising the gradients before the optimisation step, ensuring the diversification of the learned representations. We orthogonalise the gradients of the layer's components/filters…
We systematically investigate open strings in the plane wave background of type IIB string theory. We carefully analyze possible boundary conditions for open strings and find static as well as time-dependent branes. The branes fall into…
Many statistical $M$-estimators are based on convex optimization problems formed by the combination of a data-dependent loss function with a norm-based regularizer. We analyze the convergence rates of projected gradient and composite…
Combining the benefits of D-branes and background fluxes in string compactifications opens up the possibility to explore phenomenologically interesting brane world models with stabilized moduli. However, it is difficult to determine…
Distributional sources of matter on codimension-two and higher branes are only well-defined as regularized objects. Nevertheless, intuition from effective field theory suggests that the low-energy physics on such branes should be…
The structures in target space geometry that correspond to conformally invariant boundary conditions in WZW theories are determined both by studying the scattering of closed string states and by investigating the algebra of open string…
In this paper, we investigate about two physically distinct classes of the `one-dimensional' worldvolume solutions describing the status of an arbitrary brane in the presence of another arbitrary (flat) brane which supplies the required…
The effective four-dimensional, linearised gravity of a brane world model with one extra dimension and a single brane is analysed. The model includes higher order curvature terms (such as the Gauss-Bonnet term) and a conformally coupled…
For Dirac operators, which have discrete spectra, the concept of eigenvalues gradient is given and formulae for this gradients are obtained in terms of normalized eigenfunctions. It is shown how the gradient is being used to describe…
Using a formalism developed to include collective coordinates, we calculate the contributions to S-matrix elements due to off-shell D-branes in a string coupling expansion. The formalism is further used to establish a two-dimensional…
We comment on the brane solutions for the boundary H3+ model that have been proposed so far and point out that they should be distinguished according to the patterns regular/irregular and discrete/continuous. In the literature, mostly…
Performance of optimization on quadratic problems sensitively depends on the low-lying part of the spectrum. For large (effectively infinite-dimensional) problems, this part of the spectrum can often be naturally represented or approximated…
Selecting hyperparameters in deep learning greatly impacts its effectiveness but requires manual effort and expertise. Recent works show that Bayesian model selection with Laplace approximations can allow to optimize such hyperparameters…
The string and brane tensions do not have to be put in by hand, they can be dynamically generated, as in the case when we formulate string and brane theories in the modified measure formalism. Then string and brane tensions appears, but as…
We show how non-near horizon p-brane theories can be obtained from two embedding constraints in a flat higher dimensional space with 2 time directions. In particular this includes the construction of D3 branes from a flat 12-dimensional…
We study the effective gravitational theory on a brane in a six-dimensional Einstein-Maxwell model of flux compactification, regularizing a conical defect as a codimension-one brane. We employ the gradient expansion technique valid at low…
It is shown that two gravitating scalar fields may form a thick brane in 5D spacetime. The necessary condition for the existence of such a regular solution is that the scalar fields potential must have local and global minima.
We address the challenging problem of deep representation learning--the efficient adaption of a pre-trained deep network to different tasks. Specifically, we propose to explore gradient-based features. These features are gradients of the…
We find broad classes of solutions to the field equations for d-dimensional gravity coupled to an antisymmetric tensor of arbitrary rank and a scalar field with non-vanishing potential. Our construction generates these configurations from…