arXiv subjects

Jialin Zhang

Publications and source records attributed to Jialin Zhang.

At least 73 records · Page 4Linked to original sources

arXiv2022

Online Influence Maximization under the Independent Cascade Model with Node-Level Feedback

We study the online influence maximization (OIM) problem in social networks, where the learner repeatedly chooses seed nodes to generate cascades, observes the cascade feedback, and gradually learns the best seeds that generate the largest cascade in multiple rounds. In the demand of the real world, we work with node-level feedback instead of the common edge-level feedback in the literature. The edge-level feedback reveals all edges that pass through information in a cascade, whereas the node-level feedback only reveals the activated nodes with timestamps. The node-level feedback is arguably more realistic since in practice it is relatively easy to observe who is influenced but very difficult to observe from which relationship (edge) the influence comes. Previously, there is a nearly optimal $\tilde{O}(\sqrt{T})$-regret algorithm for OIM problem under the linear threshold (LT) diffusion model with node-level feedback. It remains unknown whether the same algorithm exists for the independent cascade (IC) diffusion model. In this paper, we resolve this open problem by presenting an $\tilde{O}(\sqrt{T})$-regret algorithm for OIM problem under the IC model with node-level feedback.

cs.SI↗

arXiv2022

A Normal Test for Independence via Generalized Mutual Information

Testing hypothesis of independence between two random elements on a joint alphabet is a fundamental exercise in statistics. Pearson's chi-squared test is an effective test for such a situation when the contingency table is relatively small. General statistical tools are lacking when the contingency data tables are large or sparse. A test based on generalized mutual information is derived and proposed in this article. The new test has two desired theoretical properties. First, the test statistic is asymptotically normal under the hypothesis of independence; consequently it does not require the knowledge of the row and column sizes of the contingency table. Second, the test is consistent and therefore it would detect any form of dependence structure in the general alternative space given a sufficiently large sample. In addition, simulation studies show that the proposed test converges faster than Pearson's chi-squared test when the contingency table is large or sparse.

math.ST↗

arXiv2022

Efficient quantum circuit synthesis for SAT-oracle with limited ancillary qubit

How to implement quantum oracle with limited resources raises concerns these days. We design two ancilla-adjustable and efficient algorithms to synthesize SAT-oracle, the key component in solving SAT problems. The previous work takes 2m-1 ancillary qubits and O(m) elementary gates to synthesize an m clauses oracle. The first algorithm reduces the number of ancillary qubits to 2\sqrt{m}, with at most an eightfold increase in circuit size. The number of ancillary qubits can be further reduced to 3 with a quadratic increase in circuit size. The second algorithm aims to reduce the circuit depth. By leveraging of the second algorithm, the circuit depth can be reduced to O(log m) with m ancillary qubits.

quant-ph↗

arXiv2022

Quantum Multi-Armed Bandits and Stochastic Linear Bandits Enjoy Logarithmic Regrets

Multi-arm bandit (MAB) and stochastic linear bandit (SLB) are important models in reinforcement learning, and it is well-known that classical algorithms for bandits with time horizon $T$ suffer $Ω(\sqrt{T})$ regret. In this paper, we study MAB and SLB with quantum reward oracles and propose quantum algorithms for both models with $O(\mbox{poly}(\log T))$ regrets, exponentially improving the dependence in terms of $T$. To the best of our knowledge, this is the first provable quantum speedup for regrets of bandit problems and in general exploitation in reinforcement learning. Compared to previous literature on quantum exploration algorithms for MAB and reinforcement learning, our quantum input model is simpler and only assumes quantum oracles for each individual arm.

cs.LG↗

arXiv2022

Asymptotic Normality for Plug-in Estimators of Generalized Shannon's Entropy

Shannon's entropy is one of the building blocks of information theory and an essential aspect of Machine Learning methods (e.g., Random Forests). Yet, it is only finitely defined for distributions with fast decaying tails on a countable alphabet. The unboundedness of Shannon's entropy over the general class of all distributions on an alphabet prevents its potential utility from being fully realized. To fill the void in the foundation of information theory, Zhang (2020) proposed generalized Shannon's entropy, which is finitely defined everywhere. The plug-in estimator, adopted in almost all entropy-based ML method packages, is one of the most popular approaches to estimating Shannon's entropy. The asymptotic distribution for Shannon's entropy's plug-in estimator was well studied in the existing literature. This paper studies the asymptotic properties for the plug-in estimator of generalized Shannon's entropy on countable alphabets. The developed asymptotic properties require no assumptions on the original distribution. The proposed asymptotic properties allow interval estimation and statistical tests with generalized Shannon's entropy.

math.ST↗

arXiv2022

Bounded Memory Adversarial Bandits with Composite Anonymous Delayed Feedback

We study the adversarial bandit problem with composite anonymous delayed feedback. In this setting, losses of an action are split into $d$ components, spreading over consecutive rounds after the action is chosen. And in each round, the algorithm observes the aggregation of losses that come from the latest $d$ rounds. Previous works focus on oblivious adversarial setting, while we investigate the harder non-oblivious setting. We show non-oblivious setting incurs $Ω(T)$ pseudo regret even when the loss sequence is bounded memory. However, we propose a wrapper algorithm which enjoys $o(T)$ policy regret on many adversarial bandit problems with the assumption that the loss sequence is bounded memory. Especially, for $K$-armed bandit and bandit convex optimization, we have $\mathcal{O}(T^{2/3})$ policy regret bound. We also prove a matching lower bound for $K$-armed bandit. Our lower bound works even when the loss sequence is oblivious but the delay is non-oblivious. It answers the open problem proposed in \cite{wang2021adaptive}, showing that non-oblivious delay is enough to incur $\tildeΩ(T^{2/3})$ regret.

cs.LG↗

arXiv2022

Does acceleration assist entanglement harvesting?

We explore whether acceleration assists entanglement harvesting for a pair of uniformly accelerated detectors in three different acceleration scenarios, i.e., parallel, anti-parallel and mutually perpendicular acceleration, both in the sense of the entanglement harvested and harvesting-achievable separation between the two detectors. Within the framework of entanglement harvesting protocols and the Unruh-DeWitt model of detectors locally interacting with massless scalar fields via a Gaussian switching function with an interaction duration parameter, we find that, in the sense of the entanglement harvested, acceleration is a mixed blessing insofar as it increases the harvested entanglement for a large detector energy gap relative to the interaction duration parameter, whilst inhibiting the entanglement harvested for a small energy gap. Regarding the harvesting-achievable separation range between the detectors, we further find that for very small acceleration and large energy gap, both relative to the duration parameter, acceleration-assisted enhancement can happen in all three acceleration scenarios. This is in sharp contrast to what was argued previously: that the harvesting-achievable range can be enhanced only for anti-parallel acceleration. However, for a not too small acceleration relative to the duration parameter and an energy gap larger than the acceleration, we find that only detectors in parallel acceleration possess a harvesting-achievable range larger than those at rest.

quant-ph↗

arXiv2022

Harvesting Entanglement by non-identical detectors with different energy gaps

It has been shown that the vacuum state of a free quantum field is entangled and such vacuum entanglement can be harvested by a pair of initially uncorrelated detectors interacting locally with the vacuum field for a finite time. In this paper, we examine the entanglement harvesting phenomenon of two non-identical inertial detectors with different energy gaps locally interacting with massless scalar fields via a Gaussian switching function. We focus on how entanglement harvesting depends on the energy gap difference from two perspectives: the amount of entanglement harvested and the harvesting-achievable separation between the two detectors. In the sense of the amount of entanglement, we find that as long as the inter-detector separation is not too small with respect to the interaction duration parameter, two non-identical detectors could extract more entanglement from the vacuum state than the identical detectors. There exists an optimal value of the energy gap difference when the inter-detector separation is sufficiently large that renders the harvested entanglement to peak. Regarding the harvesting-achievable separation, we further find that the presence of an energy gap difference generally enlarges the harvesting-achievable separation range. Our results suggest that the non-identical detectors may be advantageous to extracting entanglement from vacuum in certain circumstances as compared to identical detectors.

quant-ph↗

arXiv2022

Quantum Algorithm for Online Convex Optimization

We explore whether quantum advantages can be found for the zeroth-order online convex optimization problem, which is also known as bandit convex optimization with multi-point feedback. In this setting, given access to zeroth-order oracles (that is, the loss function is accessed as a black box that returns the function value for any queried input), a player attempts to minimize a sequence of adversarially generated convex loss functions. This procedure can be described as a $T$ round iterative game between the player and the adversary. In this paper, we present quantum algorithms for the problem and show for the first time that potential quantum advantages are possible for problems of online convex optimization. Specifically, our contributions are as follows. (i) When the player is allowed to query zeroth-order oracles $O(1)$ times in each round as feedback, we give a quantum algorithm that achieves $O(\sqrt{T})$ regret without additional dependence of the dimension $n$, which outperforms the already known optimal classical algorithm only achieving $O(\sqrt{nT})$ regret. Note that the regret of our quantum algorithm has achieved the lower bound of classical first-order methods. (ii) We show that for strongly convex loss functions, the quantum algorithm can achieve $O(\log T)$ regret with $O(1)$ queries as well, which means that the quantum algorithm can achieve the same regret bound as the classical algorithms in the full information setting.

quant-ph↗

arXiv2022

Network Inference and Influence Maximization from Samples

Influence maximization is the task of selecting a small number of seed nodes in a social network to maximize the influence spread from these seeds. It has been widely investigated in the past two decades. In the canonical setting, the social network and its diffusion parameters are given as input. In this paper, we consider the more realistic sampling setting where the network is unknown and we only have a set of passively observed cascades that record the sets of activated nodes at each diffusion step. We study the task of influence maximization from these cascade samples (IMS) and present constant approximation algorithms for it under mild conditions on the seed set distribution. To achieve the optimization goal, we also provide a novel solution to the network inference problem, that is, learning diffusion parameters and the network structure from the cascade data. Compared with prior solutions, our network inference algorithms require weaker assumptions and do not rely on maximum-likelihood estimation and convex programming. Our IMS algorithms enhance the learning-and-then-optimization approach by allowing a constant approximation ratio even when the diffusion parameters are hard to learn, and we do not need any assumption related to the network structure or diffusion parameters.

cs.SI↗

arXiv2022

Online Scheduling of Time-Critical Tasks to Minimize the Number of Calibrations

We study the online scheduling problem where the machines need to be calibrated before processing any jobs. To calibrate a machine, it will take $λ$ time steps as the activation time, and then the machine will remain calibrated status for $T$ time steps. The job can only be processed by the machine that is in calibrated status. Given a set of jobs arriving online, each of the jobs is characterized by a release time, a processing time, and a deadline. We assume that there is an infinite number of machines for usage. The objective is to minimize the total number of calibrations while feasibly scheduling all jobs. For the case that all jobs have unit processing times, we propose an $\mathcal{O}(λ)$-competitive algorithm, which is asymptotically optimal. When $λ=0$, the problem is degraded to rent minimization, where our algorithm achieves a competitive ratio of $3e+7(\approx 15.16)$ which improves upon the previous results for such problems.

cs.DS↗

arXiv2022

Higher order monotonicity and submodularity of influence in social networks: from local to global

Kempe, Kleinberg and Tardos (KKT) proposed the following conjecture about the general threshold model in social networks: local monotonicity and submodularity imply global monotonicity and submodularity. That is, if the threshold function of every node is monotone and submodular, then the spread function $σ(S)$ is monotone and submodular, where $S$ is a seed set and the spread function $σ(S)$ denotes the expected number of active nodes at termination of a diffusion process starting from $S$. The correctness of this conjecture has been proved by Mossel and Roch. In this paper, we first provide the concept AD-k (Alternating Difference-$k$) as a generalization of monotonicity and submodularity. Specifically, a set function $f$ is called \adk if all the $\ell$-th order differences of $f$ on all inputs have sign $(-1)^{\ell+1}$ for every $\ell\leq k$. Note that AD-1 corresponds to monotonicity and AD-2 corresponds to monotonicity and submodularity. We propose a refined version of KKT's conjecture: in the general threshold model, local AD-k implies global AD-k. The original KKT conjecture corresponds to the case for AD-2, and the case for AD-1 is the trivial one of local monotonicity implying global monotonicity. By utilizing continuous extensions of set functions as well as social graph constructions, we prove the correctness of our conjecture when the social graph is a directed acyclic graph (DAG). Furthermore, we affirm our conjecture on general social graphs when $k=\infty$.

cs.SI↗

arXiv2021

General Quantum Bernoulli Factory: Framework Analysis and Experiments

The unremitting pursuit for quantum advantages gives rise to the discovery of a quantum-enhanced randomness processing named quantum Bernoulli factory (QBF). This quantum enhanced process can show its priority over the corresponding classical process through readily available experimental resources, thus in the near term it may be capable of accelerating the applications of classical Bernoulli factories, such as the widely used sampling algorithms. In this work, we provide the framework analysis of the QBF. We thoroughly analyze the quantum state evolution in this process, discovering the field structure of the constructible quantum states. Our framework analysis shows that naturally, the previous works can be described as specific instances of this framework. Then, as a proof of principle, we experimentally demonstrate this framework via an entangled two-photon source along with a reconfigurable photonic logic, and show the advantages of the QBF over the classical model through a classically infeasible instance. These results may stimulate the discovery of advantages of the quantum randomness processing in a wider range of tasks, as well as its potential applications.

quant-ph↗

arXiv2021

Profiling Neural Blocks and Design Spaces for Mobile Neural Architecture Search

Neural architecture search automates neural network design and has achieved state-of-the-art results in many deep learning applications. While recent literature has focused on designing networks to maximize accuracy, little work has been conducted to understand the compatibility of architecture design spaces to varying hardware. In this paper, we analyze the neural blocks used to build Once-for-All (MobileNetV3), ProxylessNAS and ResNet families, in order to understand their predictive power and inference latency on various devices, including Huawei Kirin 9000 NPU, RTX 2080 Ti, AMD Threadripper 2990WX, and Samsung Note10. We introduce a methodology to quantify the friendliness of neural blocks to hardware and the impact of their placement in a macro network on overall network performance via only end-to-end measurements. Based on extensive profiling results, we derive design insights and apply them to hardware-specific search space reduction. We show that searching in the reduced search space generates better accuracy-latency Pareto frontiers than searching in the original search spaces, customizing architecture search according to the hardware. Moreover, insights derived from measurements lead to notably higher ImageNet top-1 scores on all search spaces investigated.

cs.LG↗

arXiv2021

Entanglement harvesting in the presence of a reflecting boundary

We study, in the framework of the entanglement harvesting protocol, the entanglement harvesting of both a pair of inertial and uniformly accelerated detectors locally interacting with vacuum massless scalar fields subjected to a perfectly reflecting plane boundary. We find that the presence of the boundary generally degrades the harvested entanglement when two detectors are very close to the boundary. However, when the distance between detectors and the boundary becomes comparable to the interaction duration parameter, the amount of the harvested entanglement approaches a peak, which even goes beyond that without a boundary. Remarkably, the parameter space of the detectors' separation and the magnitude of acceleration that allows entanglement harvesting to occur is enlarged due to the presence of the boundary. In this sense, the boundary plays a double-edged role on entanglement harvesting, degrading in general the harvested entanglement while enlarging the entanglement harvesting-achievable parameter space. A comparison of three different acceleration scenarios of the detectors with respect to the boundary, i.e., parallel, anti-parallel and mutually perpendicular acceleration, shows that the phenomenon of entanglement harvesting crucially depends on the acceleration, the separation between two detectors and the detectors' distance from the boundary.

quant-ph↗

arXiv2021

Rapid interrogation of special nuclear materials by combining scattering and transmission nuclear resonance fluorescence spectroscopy

The smuggling of special nuclear materials (SNMs) across national borders is becoming a serious threat to nuclear nonproliferation. This paper presents a feasibility study on the rapid interrogation of concealed SNMs by combining scattering and transmission nuclear resonance fluorescence (sNRF and tNRF) spectroscopy. In sNRF spectroscopy, SNMs such as $^{235, 238}$U are excited by a wide-band photon beam of appropriate energy and exhibit unique NRF signatures. Monte Carlo simulations show that one-dimensional scans can realize isotopic identification of concealed $^{235, 238}$U when the detector array used for interrogation has sufficiently high energy resolution. The simulated isotopic ratio $^{235}U/^{238}U$ is in good agreement with the theoretical value when the SNMs are enclosed in relatively thin iron. This interrogation is followed by tNRF spectroscopy using a narrow-band photon beam with the goal of obtaining tomographic images of the concealed SNMs. The reconstructed image clearly reveals the position of the isotope $^{235}$U inside an iron rod. It is shown that the interrogation time of sNRF and tNRF spectroscopy is one order of magnitude lower than that when only tNRF spectroscopy is used and results in a missed-detection rate of 10$^{-3}$. The proposed method can also be applied for isotopic imaging of other SNMs such as $^{239, 240}$Pu and $^{237}$Np.

physics.app-ph↗

arXiv2021

Thermodynamical multihair and phase transitions of 4-dimensional charged Taub-NUT-AdS spacetimes

We study the behavior of phase transitions for the four-dimensional charged Taub-NUT-AdS spacetime with the Newman-Unti-Tamburino (NUT) parameter interpreted as the thermodynamic multihair in the extended thermodynamic phase space, and mainly focus on the effects of the NUT parameter on the phase transitions. We find that there is an upper bound on the value of the NUT parameter beyond which the corresponding physical inflection point or critical point will not exist, and the thermodynamic trihair interpretation of the NUT parameter would admit a little larger upper bound than the thermodynamic bihair interpretation. Moreover, as long as the NUT parameter is vanishingly small, the analogy to the van der Waals liquid/gas phase transition is valid irrespective of the multihair characteristics of the NUT parameter. However, as the NUT parameter increases to be comparable to the electric charge, such analogy to the van der Waals system will be broken, and the corresponding inflection point is not a thermodynamic critical point any more. For a large NUT parameter, there are frequent occurrences of the zeroth order phase transition in the case of the thermodynamic bihair interpretation, while only the first order phase transition happens in the case of the thermodynamic trihair interpretation.

gr-qc↗

arXiv2020

Quantum Search with Prior Knowledge

Search-base algorithms have widespread applications in different scenarios. Grover's quantum search algorithms and its generalization, amplitude amplification, provide a quadratic speedup over classical search algorithms for unstructured search. We consider the problem of searching with prior knowledge. More preciously, search for the solution among N items with a prior probability distribution. This letter proposes a new generalization of Grover's search algorithm which performs better than the standard Grover algorithm in average under this setting. We prove that our new algorithm achieves the optimal expected success probability of finding the solution if the number of queries is fixed.

quant-ph↗