Twisted Gauge Theory Model of Topological Phases in Three Dimensions

We propose an exactly solvable lattice Hamiltonian model of topological phases in $3+1$ dimensions, based on a generic finite group $G$ and a $4$-cocycle $\omega$ over $G$. We show that our model has topologically protected degenerate ground states and obtain the formula of its ground state degeneracy on the $3$-torus. In particular, the ground state spectrum implies the existence of purely three-dimensional looplike quasi-excitations specified by two nontrivial flux indices and one charge index. We also construct other nontrivial topological observables of the model, namely the $SL(3,\mathbb{Z})$ generators as the modular $S$ and $T$ matrices of the ground states, which yield a set of topological quantum numbers classified by $\omega$ and quantities derived from $\omega$. Our model fulfills a Hamiltonian extension of the $3+1$-dimensional Dijkgraaf-Witten topological gauge theory with a gauge group $G$. This work is presented to be accessible for a wide range of physicists and mathematicians.Comment: 37 pages, 9 figures, 4 tables; revised to improve the clarity; references adde

LeNo: Adversarial Robust Salient Object Detection Networks with Learnable Noise

Pixel-wise predction with deep neural network has become an effective paradigm for salient object detection (SOD) and achieved remakable performance. However, very few SOD models are robust against adversarial attacks which are visually imperceptible for human visual attention. The previous work robust salient object detection against adversarial attacks (ROSA) shuffles the pre-segmented superpixels and then refines the coarse saliency map by the densely connected CRF. Different from ROSA that rely on various pre- and post-processings, this paper proposes a light-weight Learnble Noise (LeNo) to against adversarial attacks for SOD models. LeNo preserves accuracy of SOD models on both adversarial and clean images, as well as inference speed. In general, LeNo consists of a simple shallow noise and noise estimation that embedded in the encoder and decoder of arbitrary SOD networks respectively. Inspired by the center prior of human visual attention mechanism, we initialize the shallow noise with a cross-shaped gaussian distribution for better defense against adversarial attacks. Instead of adding additional network components for post-processing, the proposed noise estimation modifies only one channel of the decoder. With the deeply-supervised noise-decoupled training on state-of-the-art RGB and RGB-D SOD networks, LeNo outperforms previous works not only on adversarial images but also clean images, which contributes stronger robustness for SOD.Comment: 8 pages, 5 figures, submitted to AAA