arXiv subjects

Xin Sun

Publications and source records attributed to Xin Sun.

At least 199 records · Page 11Linked to original sources

arXiv2020

Volume of metric balls in Liouville quantum gravity

We study the volume of metric balls in Liouville quantum gravity (LQG). For $γ\in (0,2)$, it has been known since the early work of Kahane (1985) and Molchan (1996) that the LQG volume of Euclidean balls has finite moments exactly for $p \in (-\infty, 4/γ^2)$. Here, we prove that the LQG volume of LQG metric balls admits all finite moments. This answers a question of Gwynne and Miller and generalizes a result obtained by Le Gall for the Brownian map, namely, the $γ= \sqrt{8/3}$ case. We use this moment bound to show that on a compact set the volume of metric balls of size $r$ is given by $r^{d_γ+o_r(1)}$, where $d_γ$ is the dimension of the LQG metric space. Using similar techniques, we prove analogous results for the first exit time of Liouville Brownian motion from a metric ball. Gwynne-Miller-Sheffield (2020) prove that the metric measure space structure of $γ$-LQG a.s. determines its conformal structure when $γ=\sqrt{8/3}$; their argument and our estimate yield the result for all $γ\in (0,2)$.

math.PR↗

arXiv2020

Scaling limit of triangulations of polygons

We prove that random triangulations of types I, II, and III with a simple boundary under the critical Boltzmann weight converge in the scaling limit to the Brownian disk. The proof uses a bijection due to Poulalhon and Schaeffer between type III triangulations of the $p$-gon and so-called blossoming forests. A variant of this bijection was also used by Addario-Berry and the first author to prove convergence of type III triangulations to the Brownian map, but new ideas are needed to handle the simple boundary. Our result is an ingredient in the program of the second and third authors on the convergence of uniform triangulations under the Cardy embedding.

math.PR↗

arXiv2020

Equivalence of Liouville measure and Gaussian free field

Given an instance $h$ of the Gaussian free field on a planar domain $D$ and a constant $γ\in (0,2)$, one can use various regularization procedures to make sense of the Liouville quantum gravity area measure $μ:= e^{γh(z)} dz.$ It is known that the field $h$ a.s. determines the measure $μ_h$. We show that the converse is true: namely, $h$ is measurably determined by $μ_h$. More generally, given a random closed fractal subset $\mathcal A$ endowed with a Frostman measure $σ$ whose support is $\mathcal A$ (independent of $h$), a Gaussian multiplicative chaos measure $μ_{σ,h}$ can be constructed. We give a mild condition on $(\mathcal A,σ)$ under which $μ_{σ,h}$ determines $h$ restricted to $\mathcal A$, in the sense that it determines its harmonic extension off $\mathcal A$. Our condition is satisfied by the occupation measures of planar Brownian motion and SLE curves under natural parametrizations. Along the way we obtain general positive moment bounds for Gaussian multiplicative chaos. Contrary to previous results, this does not require any assumption on the underlying measure $σ$ such as scale invariance, and hence may be of independent interest.

math.PR↗

arXiv2020

Weak LQG metrics and Liouville first passage percolation

For $γ\in (0,2)$, we define a weak $γ$-Liouville quantum gravity (LQG) metric to be a function $h\mapsto D_h$ which takes in an instance of the planar Gaussian free field (GFF) and outputs a metric on the plane satisfying a certain list of natural axioms. We show that these axioms are satisfied for any subsequential limits of Liouville first passage percolation. Such subsequential limits were proven to exist by Ding-Dubédat-Dunlap-Falconet (2019). It is also known that these axioms are satisfied for the $\sqrt{8/3}$-LQG metric constructed by Miller and Sheffield (2013-2016). For any weak $γ$-LQG metric, we obtain moment bounds for diameters of sets as well as point-to-point, set-to-set, and point-to-set distances. We also show that any such metric is locally bi-Hölder continuous with respect to the Euclidean metric and compute the optimal Hölder exponents in both directions. Finally, we show that LQG geodesics cannot spend a long time near a straight line or the boundary of a metric ball. These results are used in subsequent work by Gwynne and Miller which proves that the weak $γ$-LQG metric is unique for each $γ\in (0,2)$, which in turn gives the uniqueness of the subsequential limit of Liouville first passage percolation. However, most of our results are new even in the special case when $γ=\sqrt{8/3}$.

math.PR↗

arXiv2020

Few-shot Learning for Domain-specific Fine-grained Image Classification

Learning to recognize novel visual categories from a few examples is a challenging task for machines in real-world industrial applications. In contrast, humans have the ability to discriminate even similar objects with little supervision. This paper attempts to address the few shot fine-grained image classification problem. We propose a feature fusion model to explore discriminative features by focusing on key regions. The model utilizes the focus area location mechanism to discover the perceptually similar regions among objects. High-order integration is employed to capture the interaction information among intra-parts. We also design a Center Neighbor Loss to form robust embedding space distributions. Furthermore, we build a typical fine-grained and few-shot learning dataset miniPPlankton from the real-world application in the area of marine ecological environments. Extensive experiments are carried out to validate the performance of our method. The results demonstrate that our model achieves competitive performance compared with state-of-the-art models. Our work is a valuable complement to the model domain-specific industrial applications.

cs.CV↗

arXiv2020

Learning Relation Ties with a Force-Directed Graph in Distant Supervised Relation Extraction

Relation ties, defined as the correlation and mutual exclusion between different relations, are critical for distant supervised relation extraction. Existing approaches model this property by greedily learning local dependencies. However, they are essentially limited by failing to capture the global topology structure of relation ties. As a result, they may easily fall into a locally optimal solution. To solve this problem, in this paper, we propose a novel force-directed graph based relation extraction model to comprehensively learn relation ties. Specifically, we first build a graph according to the global co-occurrence of relations. Then, we borrow the idea of Coulomb's Law from physics and introduce the concept of attractive force and repulsive force to this graph to learn correlation and mutual exclusion between relations. Finally, the obtained relation representations are applied as an inter-dependent relation classifier. Experimental results on a large scale benchmark dataset demonstrate that our model is capable of modeling global relation ties and significantly outperforms other baselines. Furthermore, the proposed force-directed graph can be used as a module to augment existing relation extraction systems and improve their performance.

cs.CL↗

arXiv2020

Bit Commitment for Lottery and Auction on Quantum Blockchain

This paper propose a protocol for lottery and a protocol for auction on quantum Blockchain. Our protocol of lottery satisfies randomness, unpredictability, unforgeability, verifiability, decentralization and unconditional security. Our protocol of auction satisfies bid privacy, posterior privacy, bids' binding, decentralization and unconditional security. Except quantum Block-chain, the main technique involved in both protocols is quantum bit commitment. Since both quantum blockchain and quantum bit commitment can be realized by the current technology, our protocols are practically feasible.

cs.CR↗

arXiv2020

Multi-party Quantum Byzantine Agreement Without Entanglement

In this paper we propose a protocol of quantum communication to achieve Byzantine agreement among multiple parties. The striking feature of our proposal in comparison to the existing protocols is that we do not use entanglement to achieve the agreement. There are two stages in our protocol. In the first stage, a list of numbers that satisfies some special properties is distributed to every participant by a group of semi-honest list distributors via quantum secure communication. Then, in the second stage those participants exchange some information to reach agreement.

cs.CR↗

arXiv2020

Induced graphs of uniform spanning forests

Given a subgraph $H$ of a graph $G$, the induced graph of $H$ is the largest subgraph of $G$ whose vertex set is the same as that of $H$. Our paper concerns the induced graphs of the components of $\operatorname{WSF}(G)$, the wired spanning forest on $G$, and, to a lesser extent, $\operatorname{FSF}(G)$, the free uniform spanning forest. We show that the induced graph of each component of $\operatorname{WSF}(\mathbb Z^d$) is almost surely recurrent when $d\ge 8$. Moreover, the effective resistance between two points on the ray of the tree to infinity within a component grows linearly when $d\ge9$. For any vertex-transitive graph $G$, we establish the following resampling property: Given a vertex $o$ in $G$, let $\mathcal T_o$ be the component of $\operatorname{WSF}(G)$ containing $o$ and $\overline{\mathcal{T}_o}$ be its induced graph. Conditioned on $\overline{\mathcal{T}_o}$, the tree $\mathcal T_o$ is distributed as $\operatorname{WSF}(\overline{\mathcal{T}_o})$. For any graph $G$, we also show that if $\mathcal T_o$ is the component of $\operatorname{FSF}(G)$ containing $o$ and $\overline{\mathcal{T}_o}$ is its induced graph, then conditioned on $\overline{\mathcal{T}_o}$, the tree $\mathcal T_o$ is distributed as $\operatorname{FSF}(\overline{\mathcal{T}_o})$.

math.PR↗

arXiv2020

A mating-of-trees approach for graph distances in random planar maps

We introduce a general technique for proving estimates for certain random planar maps which belong to the $γ$-Liouville quantum gravity (LQG) universality class for $γ\in (0,2)$. The family of random planar maps we consider are those which can be encoded by a two-dimensional random walk with i.i.d.\ increments via a mating-of-trees bijection, and includes the uniform infinite planar triangulation (UIPT; $γ=\sqrt{8/3}$); and planar maps weighted by the number of different spanning trees ($γ=\sqrt 2$), bipolar orientations ($γ=\sqrt{4/3}$), or Schnyder woods ($γ=1$) that can be put on the map. Using our technique, we prove estimates for graph distances in the above family of random planar maps. In particular, we obtain non-trivial upper and lower bounds for the cardinality of a graph distance ball consistent with the Watabiki (1993) prediction for the Hausdorff dimension of $γ$-LQG and we establish the existence of an exponent for certain distances in the map. The basic idea of our approach is to compare a given random planar map $M$ to a mated-CRT map---a random planar map constructed from a correlated two-dimensional Brownian motion---using a strong coupling (Zaitsev, 1998) of the encoding walk for $M$ and the Brownian motion used to construct the mated-CRT map. This allows us to deduce estimates for graph distances in $M$ from the estimates for graph distances in the mated-CRT map which we proved (using continuum theory) in a previous work. In the special case when $γ=\sqrt{8/3}$, we instead deduce estimates for the $\sqrt{8/3}$-mated-CRT map from known results for the UIPT. The arguments of this paper do not directly use SLE/LQG, and can be read without any knowledge of these objects.

math.PR↗

arXiv2020

LibriVoxDeEn: A Corpus for German-to-English Speech Translation and German Speech Recognition

We present a corpus of sentence-aligned triples of German audio, German text, and English translation, based on German audiobooks. The speech translation data consist of 110 hours of audio material aligned to over 50k parallel sentences. An even larger dataset comprising 547 hours of German speech aligned to German text is available for speech recognition. The audio data is read speech and thus low in disfluencies. The quality of audio and sentence alignments has been checked by a manual evaluation, showing that speech alignment quality is in general very high. The sentence alignment quality is comparable to well-used parallel translation data and can be adjusted by cutoffs on the automatic alignment score. To our knowledge, this corpus is to date the largest resource for German speech recognition and for end-to-end German-to-English speech translation.

cs.CL↗

arXiv2020

MIMO-NOMA Networks Relying on Reconfigurable Intelligent Surface: A Signal Cancellation Based Design

Reconfigurable intelligent surface (RIS) technique stands as a promising signal enhancement or signal cancellation technique for next generation networks. We design a novel passive beamforming weight at RISs in a multiple-input multiple-output (MIMO) non-orthogonal multiple access (NOMA) network for simultaneously serving paired users, where a signal cancellation based (SCB) design is employed. In order to implement the proposed SCB design, we first evaluate the minimal required number of RISs in both the diffuse scattering and anomalous reflector scenarios. Then, new channel statistics are derived for characterizing the effective channel gains. In order to evaluate the network's performance, we derive the closed-form expressions both for the outage probability (OP) and for the ergodic rate (ER). The diversity orders as well as the high-signal-to-noise (SNR) slopes are derived for engineering insights. The network's performance of a finite resolution design has been evaluated. Our analytical results demonstrate that: i) the inter-cluster interference can be eliminated with the aid of large number of RIS elements; ii) the line-of-sight of the BS-RIS and RIS-user links are required for the diffuse scattering scenario, whereas the LoS links are not compulsory for the anomalous reflector scenario.

cs.IT↗

arXiv2020

High-Order Paired-ASPP Networks for Semantic Segmenation

Current semantic segmentation models only exploit first-order statistics, while rarely exploring high-order statistics. However, common first-order statistics are insufficient to support a solid unanimous representation. In this paper, we propose High-Order Paired-ASPP Network to exploit high-order statistics from various feature levels. The network first introduces a High-Order Representation module to extract the contextual high-order information from all stages of the backbone. They can provide more semantic clues and discriminative information than the first-order ones. Besides, a Paired-ASPP module is proposed to embed high-order statistics of the early stages into the last stage. It can further preserve the boundary-related and spatial context in the low-level features for final prediction. Our experiments show that the high-order statistics significantly boost the performance on confusing objects. Our method achieves competitive performance without bells and whistles on three benchmarks, i.e, Cityscapes, ADE20K and Pascal-Context with the mIoU of 81.6%, 45.3% and 52.9%.

cs.CV↗

arXiv2020

NOMA Enhanced Terrestrial and Aerial IoT Networks with Partial CSI

This article investigates a non-orthogonal multiple access (NOMA) enhanced Internet of Things (IoT) network. In order to provide connectivity, a novel cluster strategy is proposed, where multiple devices can be served simultaneously. Two potential scenarios are investigated: 1) NOMA enhanced terrestrial IoT networks and 2) NOMA enhanced aerial IoT networks. We utilize stochastic geometry tools to model the spatial randomness of both terrestrial and aerial devices. New channel statistics are derived for both terrestrial and aerial devices. The exact and the asymptotic expressions in terms of coverage probability are derived. In order to obtain further engineering insights, short-packet communication scenarios are investigated. From our analysis, we show that the performance of NOMA enhanced IoT networks is capable of outperforming OMA enhanced IoT networks. Moreover, based on simulation results, there exists an optimal value of the transmit power that maximizes the coverage probability.

cs.IT↗

arXiv2019

Reconfigurable Intelligent Surface Aided NOMA Networks

Reconfigurable intelligent surfaces (RISs) constitute a promising performance enhancement for next-generation (NG) wireless networks in terms of enhancing both their spectrum efficiency (SE) and energy efficiency (EE). We conceive a system for serving paired power-domain non-orthogonal multiple access (NOMA) users by designing the passive beamforming weights at the RISs. In an effort to evaluate the network performance, we first derive the best-case and worst-case of new channel statistics for characterizing the effective channel gains. Then, we derive the best-case and worst-case of our closed-form expressions derived both for the outage probability and for the ergodic rate of the prioritized user. For gleaning further insights, we investigate both the diversity orders of the outage probability and the high-signal-to-noise (SNR) slopes of the ergodic rate. We also derive both the SE and EE of the proposed network. Our analytical results demonstrate that the base station (BS)-user links have almost no impact on the diversity orders attained when the number of RISs is high enough. Numerical results are provided for confirming that: i) the high-SNR slope of the RIS-aided network is one; ii) the proposed RIS-aided NOMA network has superior network performance compared to its orthogonal counterpart.

eess.SP↗

arXiv2019

Multi-level Similarity Learning for Low-Shot Recognition

Low-shot learning indicates the ability to recognize unseen objects based on very limited labeled training samples, which simulates human visual intelligence. According to this concept, we propose a multi-level similarity model (MLSM) to capture the deep encoded distance metric between the support and query samples. Our approach is achieved based on the fact that the image similarity learning can be decomposed into image-level, global-level, and object-level. Once the similarity function is established, MLSM will be able to classify images for unseen classes by computing the similarity scores between a limited number of labeled samples and the target images. Furthermore, we conduct 5-way experiments with both 1-shot and 5-shot setting on Caltech-UCSD datasets. It is demonstrated that the proposed model can achieve promising results compared with the existing methods in practical applications.

cs.CV↗

arXiv2019

Highlight Every Step: Knowledge Distillation via Collaborative Teaching

High storage and computational costs obstruct deep neural networks to be deployed on resource-constrained devices. Knowledge distillation aims to train a compact student network by transferring knowledge from a larger pre-trained teacher model. However, most existing methods on knowledge distillation ignore the valuable information among training process associated with training results. In this paper, we provide a new Collaborative Teaching Knowledge Distillation (CTKD) strategy which employs two special teachers. Specifically, one teacher trained from scratch (i.e., scratch teacher) assists the student step by step using its temporary outputs. It forces the student to approach the optimal path towards the final logits with high accuracy. The other pre-trained teacher (i.e., expert teacher) guides the student to focus on a critical region which is more useful for the task. The combination of the knowledge from two special teachers can significantly improve the performance of the student network in knowledge distillation. The results of experiments on CIFAR-10, CIFAR-100, SVHN and Tiny ImageNet datasets verify that the proposed knowledge distillation method is efficient and achieves state-of-the-art performance.

cs.CV↗

arXiv2019

Non-Orthogonal Multiple Access in UAV-to-Everything (U2X) Networks

This article investigates the non-orthogonal multiple access (NOMA) enhanced unmanned aerial vehicle (UAV)-to-Everything (U2X) frameworks. A novel 3-Dimension framework for providing wireless services to randomly roaming NOMA receivers (Rxs) in the sphere space is proposed by utilizing stochastic geometry tools. In an effort to evaluate the performance of the proposed framework, we first derive closed-form expressions for the outage probability and the ergodic rate of paired NOMA Rxs. For obtaining more insights, we investigate the diversity order and the high signal-to-noise (SNR) slope of NOMA enhanced U2X frameworks. We also derive the spectrum efficiency in both NOMA and orthogonal multiple access (OMA) enhanced U2X frameworks. Our analytical results demonstrate that the diversity order and the high SNR slope of the proposed framework are $m$ and one, respectively. Numerical results are provided to confirm that: i) the proposed NOMA enhanced U2X frameworks have superior outage performance and spectrum efficiency compared with the OMA-enhanced U2X frameworks; and ii) for the case of fixed LoS probability, the outage performance of paired NOMA Rxs mainly depends on users with poor channel conditions.

cs.IT↗