相关论文: Universal Correlators from Geometry
We provide a comprehensive summary of concepts from Calabi-Yau motives relevant to the computation of multi-loop Feynman integrals. From this we derive several consequences for multi-loop integrals in general, and we illustrate them on the…
In this paper we investigate the $\mathbb{Q}$-rational points of a class of simply connected Calabi-Yau threefolds, which were originally studied by Hosono and Takagi in the context of mirror symmetry. These varieties are defined as a…
We establish a global Torelli theorem for the complete family of Calabi-Yau threefolds arising from cyclic triple covers of $\mathbb P^3$ branched along stable hyperplane arrangements.
Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a…
We provide a consistent reduction to five dimensions of the system of D3-branes at Calabi-Yau singularities coupled to D7-branes with world-volume gauge flux. The D3-branes source the dual to would-be conformal quiver theories. The…
The universal approximation theorem states that a neural network with one hidden layer can approximate continuous functions on compact sets with any desired precision. This theorem supports using neural networks for various applications,…
Deep learning employs multi-layer neural networks trained via the backpropagation algorithm. This approach has achieved success across many domains and relies on adaptive gradient methods such as the Adam optimizer. Sequence modeling…
In this paper, we reconsider the study of five-dimensional supersymmetric black branes in the context of the M-theory compactification on a special Calabi-Yau manifold called tetra-quadric, being realized as complete intersections of…
Properties of universality have essential relevance for the theory of random matrices usually called the Wigner ensemble. The issue was analysed up to recent years with detailed and relevant results. We present a slightly different view and…
Matrix models of Yang-Mills type induce an effective gravity theory on 4-dimensional branes, which are considered as models for dynamical space-time. We review recent progress in the understanding of this emergent gravity. The metric is not…
We compute the motivic Euler characteristic of Ayoub's nearby cycles spectrum in terms of strata of a semi-stable reduction, for a degeneration to multiple semi-quasi-homogeneous singularities. This allows us to compare the local picture at…
We describe mirror manifolds in dimensions different from the familiar case of complex threefolds. We emphasize the simplifying features of dimension three and supply more robust methods that do not rely on such special characteristics and…
Following hep-th/0412336 we use the non-linear realisation of the semi-direct product of E11 and its vector representation to construct brane dynamics. The brane moves through a spacetime which arises in the non-linear realisation from the…
The universal enveloping algebra $\mathscr{U}$ of a two-dimensional nonabelian Lie algebra $L$ is a Lie algebra itself with the commutator as Lie bracket. There exists a presentation of $\mathscr{U}$ with generators $x,y$ and relation…
Several recent works have revealed a simplicity in equal-time correlators that is absent in their wavefunction counterparts. In this letter, we show that this arises from the simple fact that the correlator is obtained by integrating…
We extend the spinorial geometry techniques developed for the solution of supergravity Killing spinor equations to the kappa symmetry condition for supersymmetric brane probe configurations in any supergravity background. In particular, we…
In this work we study generalization of neural networks in gradient-based meta-learning by analyzing various properties of the objective landscapes. We experimentally demonstrate that as meta-training progresses, the meta-test solutions,…
We analyse the effect of general brane kinetic terms for bulk scalars, fermions and gauge bosons in theories with extra dimensions, with and without supersymmetry. We find in particular a singular behaviour when these terms contain…
Understanding how the statistical and geometric properties of neural activity relate to performance is a key problem in theoretical neuroscience and deep learning. Here, we calculate how correlations between object representations affect…
We consider correlation functions of topologically twisted, $\mathcal{N}=2$ supersymmetric Yang-Mills theory with gauge group ${\rm SU}(2)$ and $N_f\leq 3$ massive hypermultiplets in the fundamental representation. For a smooth, compact,…