Holographic Tests for Giant Graviton Expansion

It has been proposed that the superconformal index admits a novel reformulation, called giant graviton expansion. In this paper, we investigate the properties of dual $AdS_5$ black holes using the giant graviton expansion framework. First, we compute the entropy of black holes in $AdS_5\times S^5$ with fixed charges through a large $N$ saddle point analysis on the giant graviton index and further extremize it in the wrapping number. We identify a specific regime of fugacities where our saddle point analysis is valid. It turns out that this condition ensures the absence of closed-time-like curves and the stability of dual black hole solutions with equal charges. In addition, the giant graviton expansion of the index provides insights into how small black holes in AdS can be interpreted as bound states of branes. We extend our study to include the giant graviton expansion with the insertion of a half-BPS surface defect in $\mathcal{N}=4$ SYM with a $U(N)$ gauge group. Finally, we test the giant graviton expansion in various holographic theories whose dual geometries are $AdS_5\times S^5/\mathbb{Z}_k$ and $AdS_5\times SE_5$.Comment: 23+10 pages, 4 figures, 1 table, JHEP styl

Two-dimensional higher-order topology in monolayer graphdiyne

Based on first-principles calculations and tight-binding model analysis, we propose monolayer graphdiyne as a candidate material for a two-dimensional higher-order topological insulator protected by inversion symmetry. Despite the absence of chiral symmetry, the higher-order topology of monolayer graphdiyne is manifested in the filling anomaly and charge accumulation at two corners. Although its low energy band structure can be properly described by the tight-binding Hamiltonian constructed by using only the $p_z$ orbital of each atom, the corresponding bulk band topology is trivial. The nontrivial bulk topology can be correctly captured only when the contribution from the core levels derived from $p_{x,y}$ and $s$ orbitals are included, which is further confirmed by the Wilson loop calculations. We also show that the higher-order band topology of a monolayer graphdyine gives rise to the nontrivial band topology of the corresponding three-dimensional material, ABC-stacked graphdiyne, which hosts monopole nodal lines and hinge states.Comment: 19 pages, 4 figures, new titl

Deep Virtual Networks for Memory Efficient Inference of Multiple Tasks

Deep networks consume a large amount of memory by their nature. A natural question arises can we reduce that memory requirement whilst maintaining performance. In particular, in this work we address the problem of memory efficient learning for multiple tasks. To this end, we propose a novel network architecture producing multiple networks of different configurations, termed deep virtual networks (DVNs), for different tasks. Each DVN is specialized for a single task and structured hierarchically. The hierarchical structure, which contains multiple levels of hierarchy corresponding to different numbers of parameters, enables multiple inference for different memory budgets. The building block of a deep virtual network is based on a disjoint collection of parameters of a network, which we call a unit. The lowest level of hierarchy in a deep virtual network is a unit, and higher levels of hierarchy contain lower levels' units and other additional units. Given a budget on the number of parameters, a different level of a deep virtual network can be chosen to perform the task. A unit can be shared by different DVNs, allowing multiple DVNs in a single network. In addition, shared units provide assistance to the target task with additional knowledge learned from another tasks. This cooperative configuration of DVNs makes it possible to handle different tasks in a memory-aware manner. Our experiments show that the proposed method outperforms existing approaches for multiple tasks. Notably, ours is more efficient than others as it allows memory-aware inference for all tasks.Comment: CVPR 201

Deep Elastic Networks with Model Selection for Multi-Task Learning

In this work, we consider the problem of instance-wise dynamic network model selection for multi-task learning. To this end, we propose an efficient approach to exploit a compact but accurate model in a backbone architecture for each instance of all tasks. The proposed method consists of an estimator and a selector. The estimator is based on a backbone architecture and structured hierarchically. It can produce multiple different network models of different configurations in a hierarchical structure. The selector chooses a model dynamically from a pool of candidate models given an input instance. The selector is a relatively small-size network consisting of a few layers, which estimates a probability distribution over the candidate models when an input instance of a task is given. Both estimator and selector are jointly trained in a unified learning framework in conjunction with a sampling-based learning strategy, without additional computation steps. We demonstrate the proposed approach for several image classification tasks compared to existing approaches performing model selection or learning multiple tasks. Experimental results show that our approach gives not only outstanding performance compared to other competitors but also the versatility to perform instance-wise model selection for multiple tasks.Comment: ICCV 201

The shape of non-graviton operators for SU(2)SU(2)

The BPS spectrum of AdS/CFT exhibits multi-gravitons at low energies, while having black hole states at higher energies. This can be studied concretely in AdS$_5$/CFT$_4$ in terms of classical cohomologies, even in the quantum regimes at finite $1/N$. Recently, Chang and Lin found a threshold for non-graviton states in the $SU(2)$ maximal super-Yang-Mills theory. We explicitly construct and present this threshold cohomology.Comment: 8 page

From giant gravitons to black holes

We study AdS$_5$ black holes from a recently suggested giant graviton expansion formula for the index of $U(N)$ maximal super-Yang-Mills theory. We compute the large $N$ entropy at fixed charges and giant graviton numbers $n_I$ by a saddle point analysis, and further maximize it in $n_I$. This agrees with the dual black hole entropy in the small black hole limit. To get black holes at general sizes, one should note that various giant graviton indices cancel because gauge theory does not suffer from a Hagedorn-like pathology by an infinite baryonic tower. With one assumption on the mechanism of this cancellation, we account for the dual black hole entropy at general sizes. We interpret our results as analytic continuations of the large $N$ free energies of SCFTs, and based on it compute the entropies of AdS$_{4,7}$ black holes from M5, M2 giant gravitons.Comment: 27 pages, 4 figure