Investigation of a non-Hermitian edge burst with time-dependent perturbation theory

Edge burst is a phenomenon in non-Hermitian quantum dynamics discovered by a recent numerical study [W.-T. Xue, et al, Phys. Rev. Lett 2, 128.120401(2022)]. It finds that a large proportion of particle loss occurs at the system boundary in a class of non-Hermitian quantum walk. In this paper, we investigate the evolution of real-space wave functions for this lattice system. We find the wave function of the edge site is distinct from the bulk sites. Using time-dependent perturbation theory, we derive the analytical expression of the real-space wave functions and find that the different evolution behaviors between the edge and bulk sites are due to their different nearest-neighbor site configurations. We also find the edge wave function primarily results from the transition of the two nearest-neighbor non-decay sites. Besides, the numerical diagonalization shows the edge wave function is mainly propagated by a group of eigen-modes with a relatively large imaginary part. Our work provides an analytical method for studying non-Hermitian quantum dynamical problems.Comment: 11 pages, 7 figure

Beyond Attentive Tokens: Incorporating Token Importance and Diversity for Efficient Vision Transformers

Vision transformers have achieved significant improvements on various vision tasks but their quadratic interactions between tokens significantly reduce computational efficiency. Many pruning methods have been proposed to remove redundant tokens for efficient vision transformers recently. However, existing studies mainly focus on the token importance to preserve local attentive tokens but completely ignore the global token diversity. In this paper, we emphasize the cruciality of diverse global semantics and propose an efficient token decoupling and merging method that can jointly consider the token importance and diversity for token pruning. According to the class token attention, we decouple the attentive and inattentive tokens. In addition to preserving the most discriminative local tokens, we merge similar inattentive tokens and match homogeneous attentive tokens to maximize the token diversity. Despite its simplicity, our method obtains a promising trade-off between model complexity and classification accuracy. On DeiT-S, our method reduces the FLOPs by 35% with only a 0.2% accuracy drop. Notably, benefiting from maintaining the token diversity, our method can even improve the accuracy of DeiT-T by 0.1% after reducing its FLOPs by 40%

Instance-specific and Model-adaptive Supervision for Semi-supervised Semantic Segmentation

Recently, semi-supervised semantic segmentation has achieved promising performance with a small fraction of labeled data. However, most existing studies treat all unlabeled data equally and barely consider the differences and training difficulties among unlabeled instances. Differentiating unlabeled instances can promote instance-specific supervision to adapt to the model's evolution dynamically. In this paper, we emphasize the cruciality of instance differences and propose an instance-specific and model-adaptive supervision for semi-supervised semantic segmentation, named iMAS. Relying on the model's performance, iMAS employs a class-weighted symmetric intersection-over-union to evaluate quantitative hardness of each unlabeled instance and supervises the training on unlabeled data in a model-adaptive manner. Specifically, iMAS learns from unlabeled instances progressively by weighing their corresponding consistency losses based on the evaluated hardness. Besides, iMAS dynamically adjusts the augmentation for each instance such that the distortion degree of augmented instances is adapted to the model's generalization capability across the training course. Not integrating additional losses and training procedures, iMAS can obtain remarkable performance gains against current state-of-the-art approaches on segmentation benchmarks under different semi-supervised partition protocols

Augmentation Matters: A Simple-yet-Effective Approach to Semi-supervised Semantic Segmentation

Recent studies on semi-supervised semantic segmentation (SSS) have seen fast progress. Despite their promising performance, current state-of-the-art methods tend to increasingly complex designs at the cost of introducing more network components and additional training procedures. Differently, in this work, we follow a standard teacher-student framework and propose AugSeg, a simple and clean approach that focuses mainly on data perturbations to boost the SSS performance. We argue that various data augmentations should be adjusted to better adapt to the semi-supervised scenarios instead of directly applying these techniques from supervised learning. Specifically, we adopt a simplified intensity-based augmentation that selects a random number of data transformations with uniformly sampling distortion strengths from a continuous space. Based on the estimated confidence of the model on different unlabeled samples, we also randomly inject labelled information to augment the unlabeled samples in an adaptive manner. Without bells and whistles, our simple AugSeg can readily achieve new state-of-the-art performance on SSS benchmarks under different partition protocols.Comment: 10 pages, 8 table

Extended imaginary gauge transformation in a general nonreciprocal lattice

Imaginary gauge transformation (IGT) provides a clear understanding of the non-Hermitian skin effect by transforming the non-Hermitian Hamiltonians with real spectra into Hermitian ones. In this work, we extend this approach to the complex spectrum regime in a general nonreciprocal lattice model. We unveil the validity of IGT hinges on a class of pseudo-Hermitian symmetry. The generalized Brillouin zone of Hamiltonian respect such pseudo-Hermiticity is demonstrated to be a circle, which enables easy access to the continuum bands, localization length of skin modes, and relevant topological numbers. Furthermore, we investigate the applicability of IGT and the underlying pseudo-Hermiticity beyond nearest-neighbour hopping, offering a graphical interpretation. Our theoretical framework is applied to establish bulk-boundary correspondence in the nonreciprocal trimer Su-Schrieffer-Heeger model and analyze the localization behaviors of skin modes in the two-dimensional Hatano-Nelson model.Comment: 16 pages, 6 figure