This paper focuses on the Layered Packet Erasure Broadcast Channel (LPE-BC) with Channel Output Feedback (COF) available at the transmitter. The LPE-BC is a high-SNR approximation of the fading Gaussian BC recently proposed by Tse and Yates, who char
acterized the capacity region for any number of users and any number of layers when there is no COF. This paper provides a comparative overview of this channel model along the following lines: First, inner and outer bounds to the capacity region (set of achievable rates with backlogged arrivals) are presented: a) a new outer bound based on the idea of the physically degraded broadcast channel, and b) an inner bound of the LPE-BC with COF for the case of two users and any number of layers. Next, an inner bound on the stability region (set of exogenous arrival rates for which packet arrival queues are stable) for the same model is derived. The capacity region inner bound generalizes past results for the two-user erasure BC, which is a special case of the LPE-BC with COF with only one layer. The novelty lies in the use of inter-user and inter-layer network coding retransmissions (for those packets that have only been received by the unintended user), where each random linear combination may involve packets intended for any user originally sent on any of the layers. For the case of $K = 2$ users and $Q geq 1$ layers, the inner bounds to the capacity region and the stability region coincide; both strategically employ the novel retransmission protocol. For the case of $Q = 2$ layers, sufficient conditions are derived by Fourier-Motzkin elimination for the inner bound on the stability region to coincide with the capacity outer bound, thus showing that in those cases the capacity and stability regions coincide.
We measure the evolution of the $M_{rm BH}-M_*$ relation using 584 uniformly-selected SDSS quasars at $0.2<z<0.8$. The black-hole masses ($M_{rm BH}$) are derived from the single-epoch virial mass estimator using the H$beta$ emission line, and span t
he range $7.0<{rm log},M_{rm BH}/M_odot<9.5$. The host-galaxy stellar masses ($M_*$), which cover the interval $10.0<{rm log},M_* / M_odot <11.5$, are determined by performing two-dimensional quasar-host decomposition of the Hyper Suprime-Cam images and spectral energy distribution fitting. To quantify sample-selection biases and measurement uncertainties on the mass terms, a mock quasar sample is constructed to jointly constrain the redshift evolution of the $M_{rm BH}-M_*$ relation and its intrinsic scatter ($sigma_mu$) through forward modeling. We find that the level of evolution is degenerate with $sigma_mu$, such that both positive mild evolution (i.e, $M_{rm BH}/M_*$ increases with redshift) with a small $sigma_mu$, and negative mild evolution with a larger $sigma_mu$ are consistent with our data. The posterior distribution of $sigma_mu$ enables us to put a strong constraint on the intrinsic scatter of the $M_{rm BH}-M_*$ relation, which has a best inference of $0.25_{-0.04}^{+0.03}$ dex, consistent with the local value. The redshift evolution of the $M_{rm BH}-M_*$ relation relative to the local relation is constrained to be $(1+z)^{0.12_{-0.27}^{+0.28}}$, in agreement with no significant evolution since $zsim0.8$. The tight and non-evolving $M_{rm BH}-M_*$ relation is suggestive of a coupling through AGN feedback or/and a common gas supply at work, thus restricting the mass ratio of galaxies and their black holes to a limited range. Given the considerable stellar disk component, the $M_{rm BH}-M_{rm bulge}$ relation may evolve as previously seen at higher redshifts.
In a recent work of Wu, Wang, Sun and Liu, a second-order explicit symplectic integrator was proposed for the integrable Kerr spacetime geometry. It is still suited for simulating the nonintegrable dynamics of charged particles moving around the Kerr
black hole embedded in an external magnetic field. Its successful construction is due to the contribution of a time transformation. The algorithm exhibits a good long-term numerical performance in stable Hamiltonian errors and computational efficiency. As its application, the dynamics of order and chaos of charged particles is surveyed. In some circumstances, an increase of the dragging effects of the spacetime seems to weaken the extent of chaos from the global phase-space structure on Poincare sections. However, an increase of the magnetic parameter strengthens the chaotic properties. On the other hand, fast Lyapunov indicators show that there is no universal rule for the dependence of the transition between different dynamical regimes on the black hole spin. The dragging effects of the spacetime do not always weaken the extent of chaos from a local point of view.
The domain shift between the source and target domain is the main challenge in Cross-Domain Few-Shot Learning (CD-FSL). However, the target domain is absolutely unknown during the training on the source domain, which results in lacking directed guida
nce for target tasks. We observe that since there are similar backgrounds in target domains, it can apply self-labeled samples as prior tasks to transfer knowledge onto target tasks. To this end, we propose a task-expansion-decomposition framework for CD-FSL, called Self-Taught (ST) approach, which alleviates the problem of non-target guidance by constructing task-oriented metric spaces. Specifically, Weakly Supervised Object Localization (WSOL) and self-supervised technologies are employed to enrich task-oriented samples by exchanging and rotating the discriminative regions, which generates a more abundant task set. Then these tasks are decomposed into several tasks to finish the task of few-shot recognition and rotation classification. It helps to transfer the source knowledge onto the target tasks and focus on discriminative regions. We conduct extensive experiments under the cross-domain setting including 8 target domains: CUB, Cars, Places, Plantae, CropDieases, EuroSAT, ISIC, and ChestX. Experimental results demonstrate that the proposed ST approach is applicable to various metric-based models, and provides promising improvements in CD-FSL.
Semantic information provides intra-class consistency and inter-class discriminability beyond visual concepts, which has been employed in Few-Shot Learning (FSL) to achieve further gains. However, semantic information is only available for labeled sa
mples but absent for unlabeled samples, in which the embeddings are rectified unilaterally by guiding the few labeled samples with semantics. Therefore, it is inevitable to bring a cross-modal bias between semantic-guided samples and nonsemantic-guided samples, which results in an information asymmetry problem. To address this problem, we propose a Modal-Alternating Propagation Network (MAP-Net) to supplement the absent semantic information of unlabeled samples, which builds information symmetry among all samples in both visual and semantic modalities. Specifically, the MAP-Net transfers the neighbor information by the graph propagation to generate the pseudo-semantics for unlabeled samples guided by the completed visual relationships and rectify the feature embeddings. In addition, due to the large discrepancy between visual and semantic modalities, we design a Relation Guidance (RG) strategy to guide the visual relation vectors via semantics so that the propagated information is more beneficial. Extensive experimental results on three semantic-labeled datasets, i.e., Caltech-UCSD-Birds 200-2011, SUN Attribute Database, and Oxford 102 Flower, have demonstrated that our proposed method achieves promising performance and outperforms the state-of-the-art approaches, which indicates the necessity of information symmetry.
In the question answering(QA) task, multi-hop reasoning framework has been extensively studied in recent years to perform more efficient and interpretable answer reasoning on the Knowledge Graph(KG). However, multi-hop reasoning is inapplicable for a
nswering n-ary fact questions due to its linear reasoning nature. We discover that there are two feasible improvements: 1) upgrade the basic reasoning unit from entity or relation to fact; and 2) upgrade the reasoning structure from chain to tree. Based on these, we propose a novel fact-tree reasoning framework, through transforming the question into a fact tree and performing iterative fact reasoning on it to predict the correct answer. Through a comprehensive evaluation on the n-ary fact KGQA dataset introduced by this work, we demonstrate that the proposed fact-tree reasoning framework has the desired advantage of high answer prediction accuracy. In addition, we also evaluate the fact-tree reasoning framework on two binary KGQA datasets and show that our approach also has a strong reasoning ability compared with several excellent baselines. This work has direct implications for exploring complex reasoning scenarios and provides a preliminary baseline approach.
Decentralized optimization and communication compression have exhibited their great potential in accelerating distributed machine learning by mitigating the communication bottleneck in practice. While existing decentralized algorithms with communicat
ion compression mostly focus on the problems with only smooth components, we study the decentralized stochastic composite optimization problem with a potentially non-smooth component. A underline{Prox}imal gradient underline{L}inunderline{EA}r convergent underline{D}ecentralized algorithm with compression, Prox-LEAD, is proposed with rigorous theoretical analyses in the general stochastic setting and the finite-sum setting. Our theorems indicate that Prox-LEAD works with arbitrary compression precision, and it tremendously reduces the communication cost almost for free. The superiorities of the proposed algorithms are demonstrated through the comparison with state-of-the-art algorithms in terms of convergence complexities and numerical experiments. Our algorithmic framework also generally enlightens the compressed communication on other primal-dual algorithms by reducing the impact of inexact iterations, which might be of independent interest.
Recently deep learning has achieved significant progress on point cloud analysis tasks. Learning good representations is of vital importance to these tasks. Most current methods rely on massive labelled data for training. We here propose a point disc
riminative learning method for unsupervised representation learning on 3D point clouds, which can learn local and global geometry features. We achieve this by imposing a novel point discrimination loss on the middle level and global level point features produced in the backbone network. This point discrimination loss enforces the features to be consistent with points belonging to the shape surface and inconsistent with randomly sampled noisy points. Our method is simple in design, which works by adding an extra adaptation module and a point consistency module for unsupervised training of the encoder in the backbone network. Once trained, these two modules can be discarded during supervised training of the classifier or decoder for down-stream tasks. We conduct extensive experiments on 3D object classification, 3D part segmentation and shape reconstruction in various unsupervised and transfer settings. Both quantitative and qualitative results show that our method learns powerful representations and achieves new state-of-the-art performance.
Communication cost is one major bottleneck for the scalability for distributed learning. One approach to reduce the communication cost is to compress the gradient during communication. However, directly compressing the gradient decelerates the conver
gence speed, and the resulting algorithm may diverge for biased compression. Recent work addressed this problem for stochastic gradient descent by adding back the compression error from the previous step. This idea was further extended to one class of variance reduced algorithms, where the variance of the stochastic gradient is reduced by taking a moving average over all history gradients. However, our analysis shows that just adding the previous steps compression error, as done in existing work, does not fully compensate the compression error. So, we propose ErrorCompensatedX, which uses the compression error from the previous two steps. We show that ErrorCompensatedX can achieve the same asymptotic convergence rate with the training without compression. Moreover, we provide a unified theoretical analysis framework for this class of variance reduced algorithms, with or without error compensation.
The spin-orbit coupling plays an important role in the spin Hall effect and the topological insulators. In addition, the spin-orbit coupled Bose-Einstein condensates show remarkable quantum many-body phase transition. In this work we tune the exciton
polariton condensate by virtue of the Rashba-Dresselhaus (RD) spin-orbit coupling in a liquid-crystal filled microcavity where perovskite CsPbBr3 microplates act as the gain material at room temperature. We realize an artificial gauge field on the CsPbBr3 exciton polariton condensate, which splits the condensates with opposite spins in both momentum and real spaces. Our work paves the way to manipulate the exciton polariton condensate with a synthetic gauge field based on the RD spin-orbit coupling at room temperature.
