The popular $mathcal{AB}$/push-pull method for distributed optimization problem may unify much of the existing decentralized first-order methods based on gradient tracking technique. More recently, the stochastic gradient variant of $mathcal{AB}$/Pus
h-Pull method ($mathcal{S}$-$mathcal{AB}$) has been proposed, which achieves the linear rate of converging to a neighborhood of the global minimizer when the step-size is constant. This paper is devoted to the asymptotic properties of $mathcal{S}$-$mathcal{AB}$ with diminishing stepsize. Specifically, under the condition that each local objective is smooth and the global objective is strongly-convex, we first present the boundedness of the iterates of $mathcal{S}$-$mathcal{AB}$ and then show that the iterates converge to the global minimizer with the rate $mathcal{O}left(1/sqrt{k}right)$. Furthermore, the asymptotic normality of Polyak-Ruppert averaged $mathcal{S}$-$mathcal{AB}$ is obtained and applications on statistical inference are discussed. Finally, numerical tests are conducted to demonstrate the theoretic results.
The notion of word embedding plays a fundamental role in natural language processing (NLP). However, pre-training word embedding for very large-scale vocabulary is computationally challenging for most existing methods. In this work, we show that with
merely a small fraction of contexts (Q-contexts)which are typical in the whole corpus (and their mutual information with words), one can construct high-quality word embedding with negligible errors. Mutual information between contexts and words can be encoded canonically as a sampling state, thus, Q-contexts can be fast constructed. Furthermore, we present an efficient and effective WEQ method, which is capable of extracting word embedding directly from these typical contexts. In practical scenarios, our algorithm runs 11$sim$13 times faster than well-established methods. By comparing with well-known methods such as matrix factorization, word2vec, GloVeand fasttext, we demonstrate that our method achieves comparable performance on a variety of downstream NLP tasks, and in the meanwhile maintains run-time and resource advantages over all these baselines.
As new kinds of stabilizer code models, fracton models have been promising in realizing quantum memory or quantum hard drives. However, it has been shown that the fracton topological order of 3D fracton models occurs only at zero temperature. In this
Letter, we show that higher dimensional fracton models can support a fracton topological order below a nonzero critical temperature $T_c$. Focusing on a typical 4D X-cube model, we show that there is a finite critical temperature $T_c$ by analyzing its free energy from duality. We also obtained the expectation value of the t Hooft loops in the 4D X-cube model, which directly shows a confinement-deconfinement phase transition at finite temperature. This finite-temperature phase transition can be understood as spontaneously breaking the $mathbb{Z}_2$ one-form subsystem symmetry. Moreover, we propose a new no-go theorem for finite-temperature quantum fracton topological order.
We investigate the 1/f noise of the Five-hundred-meter Aperture Spherical Telescope (FAST) receiver system using drift-scan data from an intensity mapping pilot survey. All the 19 beams have 1/f fluctuations with similar structures. Both the temporal
and the 2D power spectrum densities are estimated. The correlations directly seen in the time series data at low frequency $f$ are associated with the sky signal, perhaps due to a coupling between the foreground and the system response. We use Singular Value Decomposition (SVD) to subtract the foreground. By removing the strongest components, the measured 1/f noise power can be reduced significantly. With 20 modes subtraction, the knee frequency of the 1/f noise in a 10 MHz band is reduced to $1.8 times 10^{-3}Hz$, well below the thermal noise over 500-seconds time scale. The 2D power spectra show that the 1/f-type variations are restricted to a small region in the time-frequency space and the correlations in frequency can be suppressed with SVD modes subtraction. The residual 1/f noise after the SVD mode subtraction is uncorrelated in frequency, and a simple noise diode frequency-independent calibration of the receiver gain at 8s interval does not affect the results. The 1/f noise can be important for HI intensity mapping, we estimate that the 1/f noise has a knee frequency $(f_{k}) sim$ 6 $times$ 10$^{-4}$Hz, and time and frequency correlation spectral indices $(alpha) sim 0.65$, $(beta) sim 0.8$ after the SVD subtraction of 30 modes. This can bias the HI power spectrum measurement by 10 percent.
It is ubiquitously accepted that during the autonomous navigation of the quadrotors, one of the most widely adopted unmanned aerial vehicles (UAVs), safety always has the highest priority. However, it is observed that the ego airflow disturbance can
be a significant adverse factor during flights, causing potential safety issues, especially in narrow and confined indoor environments. Therefore, we propose a novel method to estimate and adapt indoor ego airflow disturbance of quadrotors, meanwhile applying it to trajectory planning. Firstly, the hover experiments for different quadrotors are conducted against the proximity effects. Then with the collected acceleration variance, the disturbances are modeled for the quadrotors according to the proposed formulation. The disturbance model is also verified under hover conditions in different reconstructed complex environments. Furthermore, the approximation of Hamilton-Jacobi reachability analysis is performed according to the estimated disturbances to facilitate the safe trajectory planning, which consists of kinodynamic path search as well as B-spline trajectory optimization. The whole planning framework is validated on multiple quadrotor platforms in different indoor environments.
Collision avoidance is an essential concern for the autonomous operations of aerial vehicles in dynamic and uncertain urban environments. This paper introduces a risk-bounded path planning algorithm for unmanned aerial vehicles (UAVs) operating in su
ch environments. This algorithm advances the rapidly-exploring random tree (RRT) with chance constraints to generate probabilistically guaranteed collision-free paths that are robust to vehicle and environmental obstacle uncertainties. Assuming all uncertainties follow Gaussian distributions, the chance constraints are established through converting dynamic and probabilistic constraints into equivalent static and deterministic constraints. By incorporating chance constraints into the RRT algorithm, the proposed algorithm not only inherits the computational advantage of sampling-based algorithms but also guarantees a probabilistically feasible flying zone at every time step. Simulation results show the promising performance of the proposed algorithm.
It is well known that spectral Tur{a}n type problem is one of the most classical {problems} in graph theory. In this paper, we consider the spectral Tur{a}n type problem. Let $G$ be a graph and let $mathcal{G}$ be a set of graphs, we say $G$ is texti
t{$mathcal{G}$-free} if $G$ does not contain any element of $mathcal{G}$ as a subgraph. Denote by $lambda_1$ and $lambda_2$ the largest and the second largest eigenvalues of the adjacency matrix $A(G)$ of $G,$ respectively. In this paper we focus on the characterization of graphs without short odd cycles according to the adjacency eigenvalues of the graphs. Firstly, an upper bound on $lambda_1^{2k}+lambda_2^{2k}$ of $n$-vertex ${C_3,C_5,ldots,C_{2k+1}}$-free graphs is established, where $k$ is a positive integer. All the corresponding extremal graphs are identified. Secondly, a sufficient condition for non-bipartite graphs containing an odd cycle of length at most $2k+1$ in terms of its spectral radius is given. At last, we characterize the unique graph having the maximum spectral radius among the set of $n$-vertex non-bipartite graphs with odd girth at least $2k+3,$ which solves an open problem proposed by Lin, Ning and Wu [Eigenvalues and triangles in graphs, Combin. Probab. Comput. 30 (2) (2021) 258-270].
Human conversations naturally evolve around different topics and fluently move between them. In research on dialog systems, the ability to actively and smoothly transition to new topics is often ignored. In this paper we introduce TIAGE, a new topic-
shift aware dialog benchmark constructed utilizing human annotations on topic shifts. Based on TIAGE, we introduce three tasks to investigate different scenarios of topic-shift modeling in dialog settings: topic-shift detection, topic-shift triggered response generation and topic-aware dialog generation. Experiments on these tasks show that the topic-shift signals in TIAGE are useful for topic-shift response generation. On the other hand, dialog systems still struggle to decide when to change topic. This indicates further research is needed in topic-shift aware dialog modeling.
Neural conversation models have shown great potentials towards generating fluent and informative responses by introducing external background knowledge. Nevertheless, it is laborious to construct such knowledge-grounded dialogues, and existing models
usually perform poorly when transfer to new domains with limited training samples. Therefore, building a knowledge-grounded dialogue system under the low-resource setting is a still crucial issue. In this paper, we propose a novel three-stage learning framework based on weakly supervised learning which benefits from large scale ungrounded dialogues and unstructured knowledge base. To better cooperate with this framework, we devise a variant of Transformer with decoupled decoder which facilitates the disentangled learning of response generation and knowledge incorporation. Evaluation results on two benchmarks indicate that our approach can outperform other state-of-the-art methods with less training data, and even in zero-resource scenario, our approach still performs well.
Deep learning has achieved remarkable progress for visual recognition on large-scale balanced datasets but still performs poorly on real-world long-tailed data. Previous methods often adopt class re-balanced training strategies to effectively allevia
te the imbalance issue, but might be a risk of over-fitting tail classes. The recent decoupling method overcomes over-fitting issues by using a multi-stage training scheme, yet, it is still incapable of capturing tail class information in the feature learning stage. In this paper, we show that soft label can serve as a powerful solution to incorporate label correlation into a multi-stage training scheme for long-tailed recognition. The intrinsic relation between classes embodied by soft labels turns out to be helpful for long-tailed recognition by transferring knowledge from head to tail classes. Specifically, we propose a conceptually simple yet particularly effective multi-stage training scheme, termed as Self Supervised to Distillation (SSD). This scheme is composed of two parts. First, we introduce a self-distillation framework for long-tailed recognition, which can mine the label relation automatically. Second, we present a new distillation label generation module guided by self-supervision. The distilled labels integrate information from both label and data domains that can model long-tailed distribution effectively. We conduct extensive experiments and our method achieves the state-of-the-art results on three long-tailed recognition benchmarks: ImageNet-LT, CIFAR100-LT and iNaturalist 2018. Our SSD outperforms the strong LWS baseline by from $2.7%$ to $4.5%$ on various datasets. The code is available at https://github.com/MCG-NJU/SSD-LT.
