Floquet Non-Abelian Topological Insulator and Multifold Bulk-Edge Correspondence

Topological phases characterized by non-Abelian charges are beyond the scope of the paradigmatic tenfold way and have gained increasing attention recently. Here we investigate topological insulators with multiple tangled gaps in Floquet settings and identify uncharted Floquet non-Abelian topological insulators without any static or Abelian analog. We demonstrate that the bulk-edge correspondence is multifold and follows the multiplication rule of the quaternion group $Q_8$. The same quaternion charge corresponds to several distinct edge-state configurations that are fully determined by phase-band singularities of the time evolution. In the anomalous non-Abelian phase, edge states appear in all bandgaps despite trivial quaternion charge. Furthermore, we uncover an exotic swap effect -- the emergence of interface modes with swapped driving, which is a signature of the non-Abelian dynamics and absent in Floquet Abelian systems. Our work, for the first time, presents Floquet topological insulators characterized by non-Abelian charges and opens up exciting possibilities for exploring the rich and uncharted territory of non-equilibrium topological phases.Comment: 8+7 page

Defense against Adversarial Attacks Using High-Level Representation Guided Denoiser

Neural networks are vulnerable to adversarial examples, which poses a threat to their application in security sensitive systems. We propose high-level representation guided denoiser (HGD) as a defense for image classification. Standard denoiser suffers from the error amplification effect, in which small residual adversarial noise is progressively amplified and leads to wrong classifications. HGD overcomes this problem by using a loss function defined as the difference between the target model's outputs activated by the clean image and denoised image. Compared with ensemble adversarial training which is the state-of-the-art defending method on large images, HGD has three advantages. First, with HGD as a defense, the target model is more robust to either white-box or black-box adversarial attacks. Second, HGD can be trained on a small subset of the images and generalizes well to other images and unseen classes. Third, HGD can be transferred to defend models other than the one guiding it. In NIPS competition on defense against adversarial attacks, our HGD solution won the first place and outperformed other models by a large margin

Anderson transition and mobility edges on hyperbolic lattices

Hyperbolic lattices, formed by tessellating the hyperbolic plane with regular polygons, exhibit a diverse range of exotic physical phenomena beyond conventional Euclidean lattices. Here, we investigate the impact of disorder on hyperbolic lattices and reveal that the Anderson localization occurs at strong disorder strength, accompanied by the presence of mobility edges. Taking the hyperbolic $\{p,q\}=\{3,8\}$ and $\{p,q\}=\{4,8\}$ lattices as examples, we employ finite-size scaling of both spectral statistics and the inverse participation ratio to pinpoint the transition point and critical exponents. Our findings indicate that the transition points tend to increase with larger values of $\{p,q\}$ or curvature. In the limiting case of $\{\infty, q\}$, we further determine its Anderson transition using the cavity method, drawing parallels with the random regular graph. Our work lays the cornerstone for a comprehensive understanding of Anderson transition and mobility edges in non-Euclidean lattices.Comment: 7+6 pages, 5+3 figure

Multiuser Resource Allocation for Semantic-Relay-Aided Text Transmissions

Semantic communication (SemCom) is an emerging technology that extracts useful meaning from data and sends only relevant semantic information. Thus, it has the great potential to improve the spectrum efficiency of conventional wireless systems with bit transmissions, especially in low signal-to-noise ratio (SNR) and small bandwidth regions. However, the existing works have mostly overlooked the constraints of mobile devices, which may not have sufficient capabilities to implement resource-demanding semantic encoder/decoder based on deep learning. To address this issue, we propose in this paper a new semantic relay (SemRelay), which is equipped with a semantic receiver to assist multiuser text transmissions. Specifically, the SemRelay decodes semantic information from a base station and forwards it to the users using conventional bit transmission, hence effectively improving text transmission efficiency. To study the multiuser resource allocation, we formulate an optimization problem to maximize the multiuser weighted sum-rate by jointly designing the SemRelay transmit power allocation and system bandwidth allocation. Although this problem is non-convex and hence challenging to solve, we propose an efficient algorithm to obtain its high-quality suboptimal solution by using the block coordinate descent method. Last, numerical results show the effectiveness of the proposed algorithm as well as superior performance of the proposed SemRelay over the conventional decode-and-forward (DF) relay, especially in small bandwidth region.Comment: 6 pages, 3 figures, accepted for IEEE Global Communication Conference (GLOBECOM) 2023 Workshop on Semantic Communication for 6