Large-scale global optimization of ultra-high dimensional non-convex landscapes based on generative neural networks

We present a non-convex optimization algorithm metaheuristic, based on the training of a deep generative network, which enables effective searching within continuous, ultra-high dimensional landscapes. During network training, populations of sampled local gradients are utilized within a customized loss function to evolve the network output distribution function towards one peak at high-performing optima. The deep network architecture is tailored to support progressive growth over the course of training, which allows the algorithm to manage the curse of dimensionality characteristic of high-dimensional landscapes. We apply our concept to a range of standard optimization problems with dimensions as high as one thousand and show that our method performs better with fewer function evaluations compared to state-of-the-art algorithm benchmarks. We also discuss the role of deep network over-parameterization, loss function engineering, and proper network architecture selection in optimization, and why the required batch size of sampled local gradients is independent of problem dimension. These concepts form the foundation for a new class of algorithms that utilize customizable and expressive deep generative networks to solve non-convex optimization problems

Giant Wilson Loops and AdS2_2/dCFT1_1

The 1/2-BPS Wilson loop in $\mathcal{N}=4$ supersymmetric Yang-Mills theory is an important and well-studied example of conformal defect. In particular, much work has been done for the correlation functions of operator insertions on the Wilson loop in the fundamental representation. In this paper, we extend such analyses to Wilson loops in the large-rank symmetric and antisymmetric representations, which correspond to probe D3 and D5 branes with $AdS_2 \times S^2$ and $AdS_2 \times S^4$ worldvolume geometries, ending at the $AdS_5$ boundary along a one-dimensional contour. We first compute the correlation functions of protected scalar insertions from supersymmetric localization, and obtain a representation in terms of multiple integrals that are similar to the eigenvalue integrals of the random matrix, but with important differences. Using ideas from the Fermi Gas formalism and the Clustering method, we evaluate their large $N$ limit exactly as a function of the 't Hooft coupling. The results are given by simple integrals of polynomials that resemble the $Q$-functions of the Quantum Spectral Curve, with integration measures depending on the number of insertions. Next, we study the correlation functions of fluctuations on the probe D3 and D5 branes in AdS. We compute a selection of three- and four-point functions from perturbation theory on the D-branes, and show that they agree with the results of localization when restricted to supersymmetric kinematics. We also explain how the difference of the internal geometries of the D3 and D5 branes manifests itself in the localization computation.Comment: 91 pages, 19 figure

Visualizing Morphogenesis through Instability Formation in 4-D Printing.

Heterogeneous growth in a myriad of biological systems can lead to the formation of distinct morphologies during the maturation processes of different species. We demonstrate that the distinct circumferential buckling observed in pumpkins can be reproduced by a core-shell barrel structure using four-dimensional (4D) printing, taking advantage of digital light processing (DLP)-based three-dimensional (3D) printing and stimulus-responsive hydrogels. The mechanical mismatch between the stiff core and compliant shell results in buckling instability on the surface. The initiation and development of the buckling are governed by the ratio of core/shell radius, the ratio of core/shell swelling ratios, and the mismatch between the core and shell in stiffness. Furthermore, the rigid core not only acts as a source of circumferential confinement but also sets a boundary at the poles of the entire structure. The heterogeneous structures with controllable buckling geometrically and structurally behave much like plants' fruits. This replicates the biological morphologic change and elucidates the general mechanism and dynamics of the complex instability formation of heterogeneous 3D objects