arXiv subjects

Lin Chen

Publications and source records attributed to Lin Chen.

At least 361 records · Page 20Linked to original sources

arXiv2021

Feature Cross Search via Submodular Optimization

In this paper, we study feature cross search as a fundamental primitive in feature engineering. The importance of feature cross search especially for the linear model has been known for a while, with well-known textbook examples. In this problem, the goal is to select a small subset of features, combine them to form a new feature (called the crossed feature) by considering their Cartesian product, and find feature crosses to learn an \emph{accurate} model. In particular, we study the problem of maximizing a normalized Area Under the Curve (AUC) of the linear model trained on the crossed feature column. First, we show that it is not possible to provide an $n^{1/\log\log n}$-approximation algorithm for this problem unless the exponential time hypothesis fails. This result also rules out the possibility of solving this problem in polynomial time unless $\mathsf{P}=\mathsf{NP}$. On the positive side, by assuming the \naive\ assumption, we show that there exists a simple greedy $(1-1/e)$-approximation algorithm for this problem. This result is established by relating the AUC to the total variation of the commutator of two probability measures and showing that the total variation of the commutator is monotone and submodular. To show this, we relate the submodularity of this function to the positive semi-definiteness of a corresponding kernel matrix. Then, we use Bochner's theorem to prove the positive semi-definiteness by showing that its inverse Fourier transform is non-negative everywhere. Our techniques and structural results might be of independent interest.

cs.LG↗

arXiv2021

Bending the Bruhat-Tits Tree I:Tensor Network and Emergent Einstein Equations

As an extended companion paper to [1], we elaborate in detail how the tensor network construction of a p-adic CFT encodes geometric information of a dual geometry even as we deform the CFT away from the fixed point by finding a way to assign distances to the tensor network. In fact we demonstrate that a unique (up to normalizations) emergent graph Einstein equation is satisfied by the geometric data encoded in the tensor network, and the graph Einstein tensor automatically recovers the known proposal in the mathematics literature, at least perturbatively order by order in the deformation away from the pure Bruhat-Tits Tree geometry dual to pure CFTs. Once the dust settles, it becomes apparent that the assigned distance indeed corresponds to some Fisher metric between quantum states encoding expectation values of bulk fields in one higher dimension. This is perhaps a first quantitative demonstration that a concrete Einstein equation can be extracted directly from the tensor network, albeit in the simplified setting of the p-adic AdS/CFT.

hep-th↗

arXiv2021

A complete picture of the four-party linear inequalities in terms of the 0-entropy

Multipartite quantum system is complex. Characterizing the relations among the three bipartite reduced density operators $ρ_{AB}$, $ρ_{AC}$ and $ρ_{BC}$ of a tripartite state $ρ_{ABC}$ has been an open problem in quantum information. One of such relations has been reduced by [Cadney et al, LAA. 452, 153, 2014] to a conjectured inequality in terms of matrix rank, namely $r(ρ_{AB}) \cdot r(ρ_{AC})\ge r(ρ_{BC})$ for any $ρ_{ABC}$. It is denoted as open problem $41$ in the website "Open quantum problems-IQOQI Vienna". We prove the inequality, and thus establish a complete picture of the four-party linear inequalities in terms of the $0$-entropy. Our proof is based on the construction of a novel canonical form of bipartite matrices under local equivalence. We apply our result to the marginal problem and the extension of inequalities in the multipartite systems, as well as the condition when the inequality is saturated.

quant-ph↗

arXiv2021

Multi-linear Monogamy Relations for Three Qubit States

The monogamy of entanglement means that entanglement cannot be freely shared. In 2014, Oliveira et al. [ Oliveira et al., Phys. Rev. A. 89, 034303 (2014)] proposed a monogamy relation in the linear version and considered it in terms of entanglement of formation. Here we generalize the above version and consider a multi-linear monogamy relation for a multi-qubit system in terms of entanglement of formation and concurrence. Based on the above results, we present an entanglement criterion for genuine entangled states, also we consider the absolutely maximally entangled states and present what an absolutely maximally entangled state is for a three-qubit system. At last, we apply our results to a three-qubit pure state in terms of quantum discord.

quant-ph↗

arXiv2021

An Overview of the Compton Scattering Calculation

The Compton scattering process plays significant roles in atomic and molecular physics, condensed matter physics, nuclear physics and material science. It could provide useful information on the electromagnetic interaction between light and matter. Several aspects of many-body physics, such us electronic structures, electron momentum distributions, many-body interactions of bound electrons, \emph{etc}, can be revealed by Compton scattering experiments. In this work, we give a review on \emph{ab initio} calculation of Compton scattering process. Several approaches, including the free electron approximation (FEA), impulse approximation (IA), incoherent scattering function / incoherent scattering factor (ISF) and scattering matrix (SM) are focused in this work. The main features and available ranges for these approaches are discussed. Furthermore, we also briefly introduce the databases and applications for Compton scattering.

cond-mat.other↗

arXiv2021

Entanglement criterion via general symmetric informationally complete measurement

We propose entanglement criteria for multipartite systems via symmetric informationally complete (SIC) measurement and general symmetric informationally complete (GSIC) measurement. We apply these criteria to detect entanglement of multipartite states, such as the convex of Bell states, entangled states mixed with white noise. It is shown that these criteria are stronger than some existing ones.

quant-ph↗

arXiv2021

Deep Neural Tangent Kernel and Laplace Kernel Have the Same RKHS

We prove that the reproducing kernel Hilbert spaces (RKHS) of a deep neural tangent kernel and the Laplace kernel include the same set of functions, when both kernels are restricted to the sphere $\mathbb{S}^{d-1}$. Additionally, we prove that the exponential power kernel with a smaller power (making the kernel less smooth) leads to a larger RKHS, when it is restricted to the sphere $\mathbb{S}^{d-1}$ and when it is defined on the entire $\mathbb{R}^d$.

cs.LG↗

arXiv2021

Infinite-Horizon Offline Reinforcement Learning with Linear Function Approximation: Curse of Dimensionality and Algorithm

In this paper, we investigate the sample complexity of policy evaluation in infinite-horizon offline reinforcement learning (also known as the off-policy evaluation problem) with linear function approximation. We identify a hard regime $dγ^{2}>1$, where $d$ is the dimension of the feature vector and $γ$ is the discount rate. In this regime, for any $q\in[γ^{2},1]$, we can construct a hard instance such that the smallest eigenvalue of its feature covariance matrix is $q/d$ and it requires $Ω\left(\frac{d}{γ^{2}\left(q-γ^{2}\right)\varepsilon^{2}}\exp\left(Θ\left(dγ^{2}\right)\right)\right)$ samples to approximate the value function up to an additive error $\varepsilon$. Note that the lower bound of the sample complexity is exponential in $d$. If $q=γ^{2}$, even infinite data cannot suffice. Under the low distribution shift assumption, we show that there is an algorithm that needs at most $O\left(\max\left\{ \frac{\left\Vert θ^π\right\Vert _{2}^{4}}{\varepsilon^{4}}\log\frac{d}δ,\frac{1}{\varepsilon^{2}}\left(d+\log\frac{1}δ\right)\right\} \right)$ samples ($θ^π$ is the parameter of the policy in linear function approximation) and guarantees approximation to the value function up to an additive error of $\varepsilon$ with probability at least $1-δ$.

cs.LG↗

arXiv2021

The entropy of quantum causal networks

Quantum networks play a key role in many scenarios of quantum information theory. Here we consider the quantum causal networks in the manner of entropy. First we present a revised smooth max-relative entropy of quantum combs, then we present a lower and upper bound of a type II error of the hypothesis testing. Next we present a lower bound of the smooth max-relative entropy for the quantum combs with asymptotic equipartition. At last, we consider the score to quantify the performance of an operator. We present a quantity equaling to the smooth asymptotic version of the performance of a quantum positive operator.

quant-ph↗

arXiv2021

Measuring Discrimination to Boost Comparative Testing for Multiple Deep Learning Models

The boom of DL technology leads to massive DL models built and shared, which facilitates the acquisition and reuse of DL models. For a given task, we encounter multiple DL models available with the same functionality, which are considered as candidates to achieve this task. Testers are expected to compare multiple DL models and select the more suitable ones w.r.t. the whole testing context. Due to the limitation of labeling effort, testers aim to select an efficient subset of samples to make an as precise rank estimation as possible for these models. To tackle this problem, we propose Sample Discrimination based Selection (SDS) to select efficient samples that could discriminate multiple models, i.e., the prediction behaviors (right/wrong) of these samples would be helpful to indicate the trend of model performance. To evaluate SDS, we conduct an extensive empirical study with three widely-used image datasets and 80 real world DL models. The experimental results show that, compared with state-of-the-art baseline methods, SDS is an effective and efficient sample selection method to rank multiple DL models.

cs.SE↗

arXiv2021

Bending the Bruhat-Tits Tree II: the p-adic BTZ Black hole and Local Diffeomorphism on the Bruhat-Tits Tree

In this sequel to [1], we take up a second approach in bending the Bruhat-Tits tree. Inspired by the BTZ black hole connection, we demonstrate that one can transplant it to the Bruhat-Tits tree, at the cost of defining a novel "exponential function" on the p-adic numbers that is hinted by the BT tree. We demonstrate that the PGL$(2,Q_p)$ Wilson lines [2] evaluated on this analogue BTZ connection is indeed consistent with correlation functions of a CFT at finite temperatures. We demonstrate that these results match up with the tensor network reconstruction of the p-adic AdS/CFT with a different cutoff surface at the asymptotic boundary, and give explicit coordinate transformations that relate the analogue p-adic BTZ background and the "pure" Bruhat-Tits tree background. This is an interesting demonstration that despite the purported lack of descendents in p-adic CFTs, there exists non-trivial local Weyl transformations in the CFT corresponding to diffeomorphism in the Bruhat-Tits tree.

hep-th↗

arXiv2021

Emergent Einstein Equation in p-adic CFT Tensor Networks

We take the tensor network describing explicit p-adic CFT partition functions proposed in [1], and considered boundary conditions of the network describing a deformed Bruhat-Tits (BT) tree geometry. We demonstrate that this geometry satisfies an emergent graph Einstein equation in a unique way that is consistent with the bulk effective matter action encoding the same correlation function as the tensor network, at least in the perturbative limit order by order away from the pure BT tree. Moreover, the (perturbative) definition of the graph curvature in the Mathematics literature naturally emerges from the consistency requirements of the emergent Einstein equation. This could provide new insights into the understanding of gravitational dynamics potentially encoded in more general tensor networks.

hep-th↗

arXiv2021

The construction and local distinguishability of multiqubit unextendible product bases

An important problem in quantum information is to construct multiqubit unextendible product bases (UPBs). By using the unextendible orthogonal matrices, we construct a 7-qubit UPB of size 11. It solves an open problem in [Quantum Information Processing 19:185 (2020)]. Next, we graph-theoretically show that the UPB is locally indistinguishable in the bipartite systems of two qubits and five qubits, respectively. It turns out that the UPB corresponds to a complete graph with 11 vertices constructed by three sorts of nonisomorphic graphs. Taking the graphs as product vectors, we show that they are in three different orbits up to local unitary equivalence. Moreover, we also present the number of sorts of nonisomorphic graphs of complete graphs of some known UPBs and their orbits.

quant-ph↗

arXiv2021

Detection of genuine multipartite entanglement based on local sum uncertainty relations

Genuine multipartite entanglement (GME) offers more significant advantages in quantum information compared with entanglement. We propose a sufficient criterion for the detection of GME based on local sum uncertainty relations for chosen observables of subsystems. We apply the criterion to detect the GME properties of noisy $n$-partite W state when $n = 3, 4, 5$ and $6$, and find that the criterion can detect more noisy W states when $n$ ranges from 4 to 6. Moreover, the criterion is also used to detect the genuine entanglement of $3$-qutrit state. The result is stronger than that based on GME concurrence and fisher information.

quant-ph↗

arXiv2021

Nonlinear Blockchain Scalability: a Game-Theoretic Perspective

Recent advances in the blockchain research have been made in two important directions. One is refined resilience analysis utilizing game theory to study the consequences of selfish behaviors of users (miners), and the other is the extension from a linear (chain) structure to a non-linear (graphical) structure for performance improvements, such as IOTA and Graphcoin. The first question that comes to people's minds is what improvements that a blockchain system would see by leveraging these new advances. In this paper, we consider three major metrics for a blockchain system: full verification, scalability, and finality-duration. We { establish a formal framework and} prove that no blockchain system can achieve full verification, high scalability, and low finality-duration simultaneously. We observe that classical blockchain systems like Bitcoin achieves full verification and low finality-duration, Harmony and Ethereum 2.0 achieve low finality-duration and high scalability. As a complementary, we design a non-linear blockchain system that achieves full verification and scalability. We also establish, for the first time, the trade-off between scalability and finality-duration.

cs.CR↗

arXiv2021

Mutant reduction evaluation: what is there and what is missing?

Background. Many mutation reduction strategies, which aim to reduce the number of mutants, have been proposed. Problem. It is important to measure the ability of a mutation reduction strategy to maintain test suite effectiveness evaluation. However, existing evaluation indicators are unable to measure the "order-preserving ability". Objective. We aim to propose evaluation indicators to measure the "order-preserving ability" of a mutation reduction strategy, which is important but missing in our community. Method. Given a test suite on a Software Under Test (SUT) with a set of original mutants, we leverage the test suite to generate a group of test suites that have a partial order relationship in fault detecting potential. When evaluating a reduction strategy, we first construct two partial order relationships among the generated test suites in terms of mutation score, one with the original mutants and another with the reduced mutants. Then, we measure the extent to which the two partial order relationships are consistent. The more consistent the two partial order relationships are, the stronger the Order Preservation (OP) of the mutation reduction strategy is, and the more effective the reduction strategy is. Furthermore, we propose Effort-aware Relative Order Preservation (EROP) to measure how much gain a mutation reduction strategy can provide compared with a random reduction strategy. Result. The experimental results show that OP and EROP are able to efficiently measure the "order-preserving ability" of a mutation reduction strategy. As a result, they have a better ability to distinguish various mutation reduction strategies compared with the existing evaluation indicators. Conclusion. We suggest, for the researchers, that OP and EROP should be used to measure the effectiveness of a mutant reduction strategy.

cs.SE↗

arXiv2021

Genuine entanglement, distillability and quantum information masking under noise

Genuineness and distillability of entanglement play a key role in quantum information tasks, and they are easily disturbed by the noise. We construct a family of multipartite states without genuine entanglement and distillability sudden death across every bipartition, respectively. They are realized by establishing the noise as the multipartite high dimensional Pauli channels. Further, we construct a locally unitary channel as another noise such that the multipartite Greenberger-Horne-Zeilinger state becomes the D{ü}r's multipartite state. We also show that the quantum information masking still works under the noise we constructed, and thus show a novel quantum secret sharing scheme under noise. The evolution of a family of three-qutrit genuinely entangled states distillable across every bipartition under noise is also investigated.

quant-ph↗

arXiv2021

An extensive empirical study of inconsistent labels in multi-version-project defect data sets

The label quality of defect data sets has a direct influence on the reliability of defect prediction models. In this study, for multi-version-project defect data sets, we propose an approach to automatically detecting instances with inconsistent labels (i.e. the phenomena of instances having the same source code but different labels over multiple versions of a software project) and understand their influence on the evaluation and interpretation of defect prediction models. Based on five multi-version-project defect data sets (either widely used or the most up-to-date in the literature) collected by diverse approaches, we find that: (1) most versions in the investigated defect data sets contain inconsistent labels with varying degrees; (2) the existence of inconsistent labels in a training data set may considerably change the prediction performance of a defect prediction model as well as can lead to the identification of substantially different true defective modules; and (3) the importance ranking of independent variables in a defect prediction model can be substantially shifted due to the existence of inconsistent labels. The above findings reveal that inconsistent labels in defect data sets can profoundly change the prediction ability and interpretation of a defect prediction model. Therefore, we strongly suggest that practitioners should detect and exclude inconsistent labels in defect data sets to avoid their potential negative influence on defect prediction models. What is more, it is necessary for researchers to improve existing defect label collection approaches to reduce inconsistent labels. Furthermore, there is a need to re-examine the experimental conclusions of previous studies using multi-version-project defect data sets with a high ratio of inconsistent labels.

cs.SE↗