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Considerable efforts have been devoted to Oriented Object Detection (OOD). However, one lasting issue regarding the discontinuity in Oriented Bounding Box (OBB) representation remains unresolved, which is an inherent bottleneck for extant OOD methods. This paper endeavors to completely solve this issue in a theoretically guaranteed manner and puts an end to the ad-hoc efforts in this direction. Prior studies typically can only address one of the two cases of discontinuity: rotation and aspect ratio, and often inadvertently introduce decoding discontinuity, e.g. Decoding Incompleteness (DI) and Decoding Ambiguity (DA) as discussed in literature. Specifically, we propose a novel representation method called Continuous OBB (COBB), which can be readily integrated into existing detectors e.g. Faster-RCNN as a plugin. It can theoretically ensure continuity in bounding box regression which to our best knowledge, has not been achieved in literature for rectangle-based object representation. For fairness and transparency of experiments, we have developed a modularized benchmark based on the open-source deep learning framework Jittor's detection toolbox JDet for OOD evaluation. On the popular DOTA dataset, by integrating Faster-RCNN as the same baseline model, our new method outperforms the peer method Gliding Vertex by 1.13% mAP50 (relative improvement 1.54%), and 2.46% mAP75 (relative improvement 5.91%), without any tricks., Comment: 17 pages, 12 tables, 8 figures. Accepted by CVPR'24. Code: https://github.com/514flowey/JDet-COBB

Great progress has been made in learning-based object detection methods in the last decade. Two-stage detectors often have higher detection accuracy than one-stage detectors, due to the use of region of interest (RoI) feature extractors which extract transformation-invariant RoI features for different RoI proposals, making refinement of bounding boxes and prediction of object categories more robust and accurate. However, previous RoI feature extractors can only extract invariant features under limited transformations. In this paper, we propose a novel RoI feature extractor, termed Semantic RoI Align (SRA), which is capable of extracting invariant RoI features under a variety of transformations for two-stage detectors. Specifically, we propose a semantic attention module to adaptively determine different sampling areas by leveraging the global and local semantic relationship within the RoI. We also propose a Dynamic Feature Sampler which dynamically samples features based on the RoI aspect ratio to enhance the efficiency of SRA, and a new position embedding, \ie Area Embedding, to provide more accurate position information for SRA through an improved sampling area representation. Experiments show that our model significantly outperforms baseline models with slight computational overhead. In addition, it shows excellent generalization ability and can be used to improve performance with various state-of-the-art backbones and detection methods.

Online learning of quantum states with the logarithmic loss (LL-OLQS) is a quantum generalization of online portfolio selection (OPS), a classic open problem in online learning for over three decades. This problem also emerges in designing stochastic optimization algorithms for maximum-likelihood quantum state tomography. Recently, Jezequel et al. (arXiv:2209.13932) proposed the VB-FTRL algorithm, the first regret-optimal algorithm for OPS with moderate computational complexity. In this paper, we generalize VB-FTRL for LL-OLQS. Let $d$ denote the dimension and $T$ the number of rounds. The generalized algorithm achieves a regret rate of $O ( d^2 \log ( d + T ) )$ for LL-OLQS. Each iteration of the algorithm consists of solving a semidefinite program that can be implemented in polynomial time by, for example, cutting-plane methods. For comparison, the best-known regret rate for LL-OLQS is currently $O ( d^2 \log T )$, achieved by an exponential weight method. However, no explicit implementation is available for the exponential weight method for LL-OLQS. To facilitate the generalization, we introduce the notion of VB-convexity. VB-convexity is a sufficient condition for the volumetric barrier associated with any function to be convex and is of independent interest., Comment: 24 pages. This version explicitly addresses complex quantum density matrices

This paper gives concrete examples to exhibit how to use the replica trick to calculate the quantum (quasi-)distances holographically. First, we consider the fidelity and relative entropy between thermal states that are dual to the Schwarzschild-AdS black holes. Then we generalize our method into the RN-AdS black holes by adding a U(1) gauge field. We also investigate the fidelity between states excited by scalar operator in probe limit. In this case, it is surprising that the fidelity in standard quantization will suffer from new UV divergence though the usual holographic renormalization has been applied. We call for deep understanding for such divergence in the future. We also discover a holographic method to check whether the density matrices of two holographic states are commutative., Comment: 30 pages, 5 figures

In order to study the pseudo entropy of time-like subregions holographically, the previous smooth space-like extremal surface was recently generalized to mix space-like and time-like segments and the area becomes complex value. This paper finds that, if one tries to use such kind of piecewise smooth extremal surfaces to compute time-like entanglement entropy holographically, the complex area is not unique in general. We then generalize the original holographic proposal of space-like entanglement entropy to pick up a unique area from all allowed ``space-like+time-like'' piecewise smooth extremal surfaces for a time-like subregion. We will give some concrete examples to show the correctness of our proposal., Comment: Corrected a few typos of figures and main text; Added a brief discussion on the ambiguity of the imaginary part from the choice of branch. Accepted by JHEP

The recent holographic deduction of Penrose inequality only assumes null energy condition while the weak or dominant energy condition is required in usual geometric proof. This paper makes a step toward filling up gap between these two approaches. For planar/spherically symmetrically asymptotically Schwarzschild anti-de Sitter (AdS) black holes, we give a purely geometric proof for Penrose inequality by assuming the null energy condition. We also point out that two naive generalizations of charged Penrose inequality are not generally true and propose two new candidates. When the spacetime is asymptotically AdS but not Schwarzschild-AdS, the total mass is defined according to holographic renormalization and depends on scheme of quantization. In this case, the holographic argument implies that the Penrose inequality should still be valid but this paper use concrete example to show that whether the Penrose inequality holds or not will depend on what kind of quantization scheme we employ., Comment: 15 pages, 3 figures