Semantic Graph Convolutional Networks for 3D Human Pose Regression

In this paper, we study the problem of learning Graph Convolutional Networks (GCNs) for regression. Current architectures of GCNs are limited to the small receptive field of convolution filters and shared transformation matrix for each node. To address these limitations, we propose Semantic Graph Convolutional Networks (SemGCN), a novel neural network architecture that operates on regression tasks with graph-structured data. SemGCN learns to capture semantic information such as local and global node relationships, which is not explicitly represented in the graph. These semantic relationships can be learned through end-to-end training from the ground truth without additional supervision or hand-crafted rules. We further investigate applying SemGCN to 3D human pose regression. Our formulation is intuitive and sufficient since both 2D and 3D human poses can be represented as a structured graph encoding the relationships between joints in the skeleton of a human body. We carry out comprehensive studies to validate our method. The results prove that SemGCN outperforms state of the art while using 90% fewer parameters.Comment: In CVPR 2019 (13 pages including supplementary material). The code can be found at https://github.com/garyzhao/SemGC

Non-Fermi Liquid Behavior of the tt-JJ Model in the Strange Metal Phase: U(1)U(1) Gauge Theory with Local Constraints

We use the Becchi-Rouet-Stora-Tyutin (BRST) method to quantize the $t$-$J$ model in the $U(1)$ gauge slave boson representation. While the temporal component of the gauge field plays a role of a Lagrange multiplier to enforce the no double occupancy constraint, the spatial components do that to enforce the zero counterflow constraint of the spinon and holon currents. The BRST quantization guarantees the gauge invariance of the theory and removes the redundant gauge degrees of freedom by proper gauge fixing conditions while the no double occupancy and zero counterflow constraints are exactly retained. Furthermore, Fradkin-Vilkovisky gauge fixing conditions endow the gauge field with dynamics. This turns the strongly correlated electron model into a weakly coupled slave boson model, most of whose physical observables can be calculated by the conventional quantum many-body perturbation theory. We focus on the properties of the strange metal phase in the $t$-$J$ model. The electron momentum distribution and the spectral function are calculated, and their non-Fermi liquid behavior agrees with the angle resolved photoemission spectroscopy measurements for the cuprate materials. We also study the responses of the strange metal state to the external electromagnetic fields. The non-Fermi liquid anomalies observed in cuprates are captured by our calculations. Especially, we find that the Hall resistivity decreases as temperature raises and the sign of the Hall resistivity varies from negative to positive when the dopant concentration varies from the optimal doping one to underdoping one when the temperature $T>T^*$.Comment: v1: 20 pages; v2: 21 pages, 8 figures. A few changes and new references added. All comments are welcom