arXiv subjects

Bin Guo

Publications and source records attributed to Bin Guo.

At least 145 records · Page 8Linked to original sources

arXiv2022

Equivalence between Time Series Predictability and Bayes Error Rate

Predictability is an emerging metric that quantifies the highest possible prediction accuracy for a given time series, being widely utilized in assessing known prediction algorithms and characterizing intrinsic regularities in human behaviors. Lately, increasing criticisms aim at the inaccuracy of the estimated predictability, caused by the original entropy-based method. In this brief report, we strictly prove that the time series predictability is equivalent to a seemingly unrelated metric called Bayes error rate that explores the lowest error rate unavoidable in classification. This proof bridges two independently developed fields, and thus each can immediately benefit from the other. For example, based on three theoretical models with known and controllable upper bounds of prediction accuracy, we show that the estimation based on Bayes error rate can largely solve the inaccuracy problem of predictability.

cs.IT↗

arXiv2022

Uniform entropy and energy bounds for fully non-linear equations

Energy bounds which are uniform in the background metric are obtained from upper bounds for entropy-like quantities. The argument is based on auxiliary Monge-Ampère equations involving sublevel sets, and bypasses the Alexandrov-Bakelman-Pucci maximum principle. In particular, it implies uniform $L^\infty$ bounds for systems coupling a fully non-linear equation to its linearization, generalizing the cscK equation.

math.DG↗

arXiv2022

Enabling Harmonious Human-Machine Interaction with Visual-Context Augmented Dialogue System: A Review

The intelligent dialogue system, aiming at communicating with humans harmoniously with natural language, is brilliant for promoting the advancement of human-machine interaction in the era of artificial intelligence. With the gradually complex human-computer interaction requirements (e.g., multimodal inputs, time sensitivity), it is difficult for traditional text-based dialogue system to meet the demands for more vivid and convenient interaction. Consequently, Visual Context Augmented Dialogue System (VAD), which has the potential to communicate with humans by perceiving and understanding multimodal information (i.e., visual context in images or videos, textual dialogue history), has become a predominant research paradigm. Benefiting from the consistency and complementarity between visual and textual context, VAD possesses the potential to generate engaging and context-aware responses. For depicting the development of VAD, we first characterize the concepts and unique features of VAD, and then present its generic system architecture to illustrate the system workflow. Subsequently, several research challenges and representative works are detailed investigated, followed by the summary of authoritative benchmarks. We conclude this paper by putting forward some open issues and promising research trends for VAD, e.g., the cognitive mechanisms of human-machine dialogue under cross-modal dialogue context, and knowledge-enhanced cross-modal semantic interaction.

cs.AI↗

arXiv2022

Bootstrapping the effect of the twist operator in symmetric orbifold CFTs

We study the 2D symmetric orbifold CFT of two copies of free bosons. The twist operator can join the two separated copies in the untwisted sector into a joined copy in the twisted sector. Starting with a state with any number of quanta in the untwisted sector, the state in the twisted sector obtained by the action of the twist operator can be computed by using the covering map method. We develop a new method to compute the effect of a twist operator by using the Bogoliubov ansatz and conformal symmetry. This may lead to more efficient tools to compute correlation functions involving twist operators.

hep-th↗

arXiv2022

Are there echoes of gravitational waves?

In several approaches to evading the information paradox, the semiclassical black hole is replaced by an Exotic Compact Object (ECO). It has been conjectured that gravitational waves emitted by the merger of ECOs can reflect off the ECOs and produce a detectable `echo'. We argue that while a part of the wave can indeed reflect off the surface of an ECO, this reflected wave will get trapped by a new closed trapped surface produced by its own backreaction. Thus no detectable signal of the echo will emerge to infinity. The only assumption in this analysis is that causality is maintained to leading order in gently curved spacetime. Thus if echoes are actually detected, then we would face a profound change in our understanding of physics.

gr-qc↗

arXiv2022

Efficient Parallel Graph Trimming by Arc-Consistency

Given a large data graph, trimming techniques can reduce the search space by removing vertices without outgoing edges. One application is to speed up the parallel decomposition of graphs into strongly connected components (SCC decomposition), which is a fundamental step for analyzing graphs. We observe that graph trimming is essentially a kind of arc-consistency problem, and AC-3, AC-4, and AC-6 are the most relevant arc-consistency algorithms for application to graph trimming. The existing parallel graph trimming methods require worst-case $\mathcal O(nm)$ time and worst-case $\mathcal O(n)$ space for graphs with $n$ vertices and $m$ edges. We call these parallel AC-3-based as they are much like the AC-3 algorithm. In this work, we propose AC-4-based and AC-6-based trimming methods. That is, AC-4-based trimming has an improved worst-case time of $\mathcal O(n+m)$ but requires worst-case space of $\mathcal O(n+m)$; compared with AC-4-based trimming, AC-6-based has the same worst-case time of $\mathcal O(n+m)$ but an improved worst-case space of $\mathcal O(n)$. We parallelize the AC-4-based and AC-6-based algorithms to be suitable for shared-memory multi-core machines. The algorithms are designed to minimize synchronization overhead. For these algorithms, we also prove the correctness and analyze time complexities with the work-depth model. In experiments, we compare these three parallel trimming algorithms over a variety of real and synthetic graphs. Specifically, for the maximum number of traversed edges per worker by using 16 workers, AC-3-based traverses up to 58.3 and 36.5 times more edges than AC-6-based trimming and AC-4-based trimming, respectively.

cs.DC↗

arXiv2022

Human-in-the-loop Machine Learning: A Macro-Micro Perspective

Though technical advance of artificial intelligence and machine learning has enabled many promising intelligent systems, many computing tasks are still not able to be fully accomplished by machine intelligence. Motivated by the complementary nature of human and machine intelligence, an emerging trend is to involve humans in the loop of machine learning and decision-making. In this paper, we provide a macro-micro review of human-in-the-loop machine learning. We first describe major machine learning challenges which can be addressed by human intervention in the loop. Then we examine closely the latest research and findings of introducing humans into each step of the lifecycle of machine learning. Finally, we analyze current research gaps and point out future research directions.

cs.HC↗

arXiv2022

Green's functions and complex Monge-Ampère equations

Uniform $L^1$ and lower bounds are obtained for the Green's function on compact Kähler manifolds. Unlike in the classic theorem of Cheng-Li for Riemannian manifolds, the lower bounds do not depend directly on the Ricci curvature, but only on integral bounds for the volume form and certain of its derivatives. In particular, a uniform lower bound for the Green's function on Kähler manifolds is obtained which depends only on a lower bound for the scalar curvature and on an $L^q$ norm for the volume form for some $q>1$. The proof relies on auxiliary Monge-Ampère equations, and is fundamentally non-linear. The lower bounds for the Green's function imply in turn $C^1$ and $C^2$ estimates for complex Monge-Ampère equations with a sharper dependence on the function on the right hand side.

math.DG↗

arXiv2022

Simplified Algorithms for Order-Based Core Maintenance

Graph analytics attract much attention from both research and industry communities. Due to the linear time complexity, the $k$-core decomposition is widely used in many real-world applications such as biology, social networks, community detection, ecology, and information spreading. In many such applications, the data graphs continuously change over time. The changes correspond to edge insertion and removal. Instead of recomputing the $k$-core, which is time-consuming, we study how to maintain the $k$-core efficiently. That is, when inserting or deleting an edge, we need to identify the affected vertices by searching for more vertices. The state-of-the-art order-based method maintains an order, the so-called $k$-order, among all vertices, which can significantly reduce the searching space. However, this order-based method is complicated for understanding and implementation, and its correctness is not formally discussed. In this work, we propose a simplified order-based approach by introducing the classical Order Data Structure to maintain the $k$-order, which significantly improves the worst-case time complexity for both edge insertion and removal algorithms. Also, our simplified method is intuitive to understand and implement; it is easy to argue the correctness formally. Additionally, we discuss a simplified batch insertion approach. The experiments evaluate our simplified method over 12 real and synthetic graphs with billions of vertices. Compared with the existing method, our simplified approach achieves high speedups up to 7.7x and 9.7x for edge insertion and removal, respectively.

cs.DB↗

arXiv2021

A freely falling graviton in the D1D5 CFT

We study a freely falling graviton propagating in AdS in the context of the D1D5 CFT, where we introduce an interaction by turning on a deformation operator. We start with one left and right moving boson in the CFT. After applying two deformation operators, the initial bosons split into three left moving and three right moving bosons. We compute the amplitude for various energies and extrapolate the result to the large energy region. At early times, the amplitude is linear in time. This corresponds to an infalling graviton becoming redshifted in AdS. At late times, the amplitude is periodic, which agrees with the fact that a freely falling graviton will not be thermalized.

hep-th↗

arXiv2021

Partial Spectral Flow in the D1D5 CFT

The two-dimensional $\mathcal{N}=4$ superconformal algebra has a free field realization with four bosons and four fermions. There is an automorphism of the algebra called spectral flow. Under spectral flow, the four fermions are transformed together. In this paper, we study {\it partial spectral flow} where only two of the four fermions are transformed. Partial spectral flow is applied to the D1D5 CFT where a marginal deformation moves the CFT away from the free point. The partial spectral flow is broken by the deformation. We show that this effect can be studied due to a transformation of the deformation which is well-defined under partial spectral flow. As a result in the spectrum, we demonstrate how to compute the second-order energy lift of D1D5P states from their partial spectral flowed states. We find that D1D5P states related by partial spectral flow do not have the same lift in general.

hep-th↗

arXiv2021

On the modulus of continuity of solutions to complex Monge-Ampère equations

In this paper, we prove a uniform and sharp estimate for the modulus of continuity of solutions to complex Monge-Ampère equations, using the PDE-based approach developed by the first three authors in their approach to supremum estimates for fully non-linear equations in Kähler geometry. As an application, we derive a uniform diameter bound for Kähler metrics satisfying certain Monge-Ampère equations.

math.DG↗

arXiv2021

On $L^\infty$ estimates for Monge-Ampère and Hessian equations on nef classes

The PDE approach developed earlier by the first three authors for $L^\infty$ estimates for fully non-linear equations on Kähler manifolds is shown to apply as well to Monge-Ampère and Hessian equations on nef classes. In particular, one obtains a new proof of the estimates of Boucksom-Eyssidieux-Guedj-Zeriahi and Fu-Guo-Song for the Monge-Ampère equation, together with their generalization to Hessian equations.

math.DG↗

arXiv2021

Contrasting the fuzzball and wormhole paradigms for black holes

We examine an interesting set of recent proposals describing a `wormhole paradigm' for black holes. These proposals require that in some effective variables, semiclassical low-energy dynamics emerges at the horizon. We prove the `effective small corrections theorem' to show that such an effective horizon behavior is not compatible with the requirement that the black hole radiate like a piece of coal as seen from outside. This theorem thus concretizes the fact that the proposals within the wormhole paradigm require some nonlocality linking the hole and its distant radiation. We try to illustrate various proposals for nonlocality by making simple bit models to encode the nonlocal effects. In each case, we find either nonunitarity of evolution in the black hole interior or a nonlocal Hamiltonian interaction between the hole and infinity; such an interaction is not present for burning coal. We examine recent arguments about the Page curve and observe that the quantity that is argued to follow the Page curve of a normal body is not the entanglement entropy but a different quantity. It has been suggested that this replacement of the quantity to be computed arises from the possibility of topology change in gravity which can generate replica wormholes. We examine the role of topology change in quantum gravity but do not find any source of connections between different replica copies in the path integral for the Rényi entropy. We also contrast the wormhole paradigm with the fuzzball paradigm, where the fuzzball does radiate like a piece of coal. Just as in the case of a piece of coal, the fuzzball does not have low-energy semiclassical dynamics at its surface at energies $E\sim T$ (effective dynamics at energies $E\gg T$ is possible under the conjecture of fuzzball complementarity, but these $E\gg T$ modes have no relevance to the Page curve or the information paradox).

hep-th↗

arXiv2021

The Dual of a Tidal Force in the D1D5 CFT

It was demonstrated that a string probe falling radially within a superstratum geometry would experience tidal forces. These tidal forces were shown to excite the string by converting its kinetic energy into stringy excitations. Using the AdS/CFT correspondence we seek to understand this behavior from the perspective of the dual D1D5 CFT. To study this process we turn on an interaction of the theory which is described by a deformation operator. We start with an initial state which is dual to a graviton probe moving within the superstratum geometry. We then use two deformation operators to compute transition amplitudes between this state and a final state that corresponds to stringy excitations. We show that this amplitude grows as $t^2$ with $t$ being the amount of time for which the deformation operators are turned on. We argue that this process in the CFT is suggestive of the tidal effects experienced by the probe propagating within the dual superstratum geometry.

hep-th↗

arXiv2021

On the Hessian-cscK equations

In this paper, we propose a coupled system of complex Hessian equations which generalizes the equation for constant scalar curvature Kähler (cscK) metrics. We show this system can be realized variationally as the Euler-Lagrange equation of a Hessian version of the Mabuchi K-energy in an infinite dimensional space of $k$-Hessian potentials, which can be seen as an infinite dimensional Riemannian manifold with negative sectional curvature. Finally, we prove an a priori $C^0$-estimate for this system which depends on the Entropy, which generalizes a fundamental result of Chen and Cheng for cscK metrics.

math.DG↗

arXiv2021

AskMe: Joint Individual-level and Community-level Behavior Interaction for Question Recommendation

Questions in Community Question Answering (CQA) sites are recommended to users, mainly based on users' interest extracted from questions that users have answered or have asked. However, there is a general phenomenon that users answer fewer questions while pay more attention to follow questions and vote answers. This can impact the performance when recommending questions to users (for obtaining their answers) by using their historical answering behaviors on existing studies. To address the data sparsity issue, we propose AskMe, which aims to leverage the rich, hybrid behavior interactions in CQA to improve the question recommendation performance. On the one hand, we model the rich correlations between the users' diverse behaviors (e.g., answer, follow, vote) to obtain the individual-level behavior interaction. On the other hand, we model the sophisticated behavioral associations between similar users to obtain the community-level behavior interaction. Finally, we propose the way of element-level fusion to mix these two kinds of interactions together to predict the ranking scores. A dataset collected from Zhihu (1126 users, 219434 questions) is utilized to evaluate the performance of the proposed model, and the experimental results show that our model has gained the best performance compared to baseline methods, especially when the historical answering behaviors data is scarce.

cs.IR↗

arXiv2021

Multiway sparse distance weighted discrimination

Modern data often take the form of a multiway array. However, most classification methods are designed for vectors, i.e., 1-way arrays. Distance weighted discrimination (DWD) is a popular high-dimensional classification method that has been extended to the multiway context, with dramatic improvements in performance when data have multiway structure. However, the previous implementation of multiway DWD was restricted to classification of matrices, and did not account for sparsity. In this paper, we develop a general framework for multiway classification which is applicable to any number of dimensions and any degree of sparsity. We conducted extensive simulation studies, showing that our model is robust to the degree of sparsity and improves classification accuracy when the data have multiway structure. For our motivating application, magnetic resonance spectroscopy (MRS) was used to measure the abundance of several metabolites across multiple neurological regions and across multiple time points in a mouse model of Friedreich's ataxia, yielding a four-way data array. Our method reveals a robust and interpretable multi-region metabolomic signal that discriminates the groups of interest. We also successfully apply our method to gene expression time course data for multiple sclerosis treatment. An R implementation is available in the package MultiwayClassification at http://github.com/lockEF/MultiwayClassification .

stat.ME↗