arXiv subjects

Xiaoyu Chen

Publications and source records attributed to Xiaoyu Chen.

At least 145 records · Page 8Linked to original sources

arXiv2021

$H_2$-reducible matrices in six-dimensional mutually unbiased bases

Finding four six-dimensional mutually unbiased bases (MUBs) containing the identity matrix is a long-standing open problem in quantum information. We show that if they exist, then the $H_2$-reducible matrix in the four MUBs has exactly nine $2\times2$ Hadamard submatrices. We apply our result to exclude from the four MUBs some known CHMs, such as symmetric $H_2$-reducible matrix, the Hermitian matrix, Dita family, Bjorck's circulant matrix, and Szollosi family. Our results represent the latest progress on the existence of six-dimensional MUBs.

quant-ph↗

arXiv2021

Distributional Reinforcement Learning for Multi-Dimensional Reward Functions

A growing trend for value-based reinforcement learning (RL) algorithms is to capture more information than scalar value functions in the value network. One of the most well-known methods in this branch is distributional RL, which models return distribution instead of scalar value. In another line of work, hybrid reward architectures (HRA) in RL have studied to model source-specific value functions for each source of reward, which is also shown to be beneficial in performance. To fully inherit the benefits of distributional RL and hybrid reward architectures, we introduce Multi-Dimensional Distributional DQN (MD3QN), which extends distributional RL to model the joint return distribution from multiple reward sources. As a by-product of joint distribution modeling, MD3QN can capture not only the randomness in returns for each source of reward, but also the rich reward correlation between the randomness of different sources. We prove the convergence for the joint distributional Bellman operator and build our empirical algorithm by minimizing the Maximum Mean Discrepancy between joint return distribution and its Bellman target. In experiments, our method accurately models the joint return distribution in environments with richly correlated reward functions, and outperforms previous RL methods utilizing multi-dimensional reward functions in the control setting.

cs.LG↗

arXiv2021

Abstract induced modules for reductive algebraic groups with Frobenius maps

Let ${\bf G}$ be a connected reductive algebraic group defined over a finite field $\mathbb{F}_q$ of $q$ elements, and ${\bf B}$ be a Borel subgroup of ${\bf G}$ defined over $\mathbb{F}_q$. Let $\Bbbk$ be a field and we assume that $\Bbbk=\bar{\mathbb{F}}_q $ when $\text{char}\ \Bbbk=\text{char} \ \mathbb{F}_q$. We show that the abstract induced module $\mathbb{M}(θ)=\Bbbk{\bf G}\otimes_{\Bbbk{\bf B}}θ$ (here $\Bbbk{\bf H}$ is the group algebra of ${\bf H}$ over the field $\Bbbk$ and $θ$ is a character of ${\bf B}$ over $\Bbbk$) has a composition series (of finite length) if $\text{char}\ \Bbbk\ne \text{char} \ \mathbb{F}_q$. In the case $\Bbbk=\bar{\mathbb{F}}_q$ and $θ$ is a rational character, we give a necessary and sufficient condition for the existence of a composition series (of finite length) of $\mathbb{M}(θ)$. We determine all the composition factors whenever a composition series exists. Thus we obtain a large class of abstract infinite-dimensional irreducible $\Bbbk{\bf G}$-modules.

math.RT↗

arXiv2021

Exact algorithms for maximum weighted independent set on sparse graphs

The maximum independent set problem is one of the most important problems in graph algorithms and has been extensively studied in the line of research on the worst-case analysis of exact algorithms for NP-hard problems. In the weighted version, each vertex in the graph is associated with a weight and we are going to find an independent set of maximum total vertex weight. In this paper, we design several reduction rules and a fast exact algorithm for the maximum weighted independent set problem, and use the measure-and-conquer technique to analyze the running time bound of the algorithm. Our algorithm works on general weighted graphs and it has a good running time bound on sparse graphs. If the graph has an average degree at most 3, our algorithm runs in $O^*(1.1443^n)$ time and polynomial space, improving previous running time bounds for the problem in cubic graphs using polynomial space.

cs.DS↗

arXiv2021

Adaptively Weighted Top-N Recommendation for Organ Matching

Reducing the shortage of organ donations to meet the demands of patients on the waiting list has being a major challenge in organ transplantation. Because of the shortage, organ matching decision is the most critical decision to assign the limited viable organs to the most suitable patients. Currently, organ matching decisions were only made by matching scores calculated via scoring models, which are built by the first principles. However, these models may disagree with the actual post-transplantation matching performance (e.g., patient's post-transplant quality of life (QoL) or graft failure measurements). In this paper, we formulate the organ matching decision-making as a top-N recommendation problem and propose an Adaptively Weighted Top-N Recommendation (AWTR) method. AWTR improves performance of the current scoring models by using limited actual matching performance in historical data set as well as the collected covariates from organ donors and patients. AWTR sacrifices the overall recommendation accuracy by emphasizing the recommendation and ranking accuracy for top-N matched patients. The proposed method is validated in a simulation study, where KAS [60] is used to simulate the organ-patient recommendation response. The results show that our proposed method outperforms seven state-of-the-art top-N recommendation benchmark methods.

cs.LG↗

arXiv2021

Certifiably Robust Interpretation via Renyi Differential Privacy

Motivated by the recent discovery that the interpretation maps of CNNs could easily be manipulated by adversarial attacks against network interpretability, we study the problem of interpretation robustness from a new perspective of \Renyi differential privacy (RDP). The advantages of our Renyi-Robust-Smooth (RDP-based interpretation method) are three-folds. First, it can offer provable and certifiable top-$k$ robustness. That is, the top-$k$ important attributions of the interpretation map are provably robust under any input perturbation with bounded $\ell_d$-norm (for any $d\geq 1$, including $d = \infty$). Second, our proposed method offers $\sim10\%$ better experimental robustness than existing approaches in terms of the top-$k$ attributions. Remarkably, the accuracy of Renyi-Robust-Smooth also outperforms existing approaches. Third, our method can provide a smooth tradeoff between robustness and computational efficiency. Experimentally, its top-$k$ attributions are {\em twice} more robust than existing approaches when the computational resources are highly constrained.

cs.LG↗

arXiv2021

Distinct Properties of Vortex Bound States Driven by Temperature

We investigate the behavior of vortex bound states in the quantum limit by self-consistently solving the Bogoliubov-de Gennes equation. We find that the energies of the vortex bound states deviates from the analytical result $E_μ=μΔ^2/E_F$ with the half-integer angular momentum $μ$ in the extreme quantum limit. Specifically, the energy ratio for the first three orders is more close to $1:2:3$ instead of $1:3:5$ at extremely low temperature. The local density of states reveals an Friedel-like behavior associated with that of the pair potential in the extreme quantum limit, which will be smoothed out by thermal effect above a certain temperature even the quantum limit condition, namely $T/T_c<Δ/E_F$ is still satisfied. Our studies show that the vortex bound states can exhibit very distinct features in different temperature regimes, which provides a comprehensive understanding and should stimulate more experimental efforts for verifications.

cond-mat.supr-con↗

arXiv2021

Efficient Reinforcement Learning in Factored MDPs with Application to Constrained RL

Reinforcement learning (RL) in episodic, factored Markov decision processes (FMDPs) is studied. We propose an algorithm called FMDP-BF, which leverages the factorization structure of FMDP. The regret of FMDP-BF is shown to be exponentially smaller than that of optimal algorithms designed for non-factored MDPs, and improves on the best previous result for FMDPs~\citep{osband2014near} by a factored of $\sqrt{H|\mathcal{S}_i|}$, where $|\mathcal{S}_i|$ is the cardinality of the factored state subspace and $H$ is the planning horizon. To show the optimality of our bounds, we also provide a lower bound for FMDP, which indicates that our algorithm is near-optimal w.r.t. timestep $T$, horizon $H$ and factored state-action subspace cardinality. Finally, as an application, we study a new formulation of constrained RL, known as RL with knapsack constraints (RLwK), and provides the first sample-efficient algorithm based on FMDP-BF.

cs.LG↗

arXiv2021

Friedel Oscillations of Vortex Bound States Under Extreme Quantum Limit in KCa2Fe4As4F2

We report the observation of discrete vortex bound states with the energy levels deviating from the widely believed ratio of 1:3:5 in the vortices of an iron based superconductor KCa2Fe4As4F2 through scanning tunneling microcopy (STM). Meanwhile Friedel oscillations of vortex bound states are also observed for the first time in related vortices. By doing self-consistent calculations of Bogoliubov-de Gennes equations, we find that at extreme quantum limit, the superconducting order parameter exhibits a Friedel-like oscillation, which modifies the energy levels of the vortex bound states and explains why it deviates from the ratio of 1:3:5. The observed Friedel oscillations of the bound states can also be roughly interpreted by the theoretical calculations, however some features at high energies could not be explained. We attribute this discrepancy to the high energy bound states with the influence of nearby impurities. Our combined STM measurement and the self-consistent calculations illustrate a generalized feature of the vortex bound states in type-II superconductors.

cond-mat.supr-con↗

arXiv2021

Single particle tunneling spectroscopy and superconducting gaps in layered iron based superconductor KCa$_{2}$Fe$_{4}$As$_{4}$F$_{2}$

We perform scanning tunneling microscopy/spectroscopy study on the layered iron based superconductor KCa$_2$Fe$_4$As$_4$F$_2$ with a critical temperature of about 33.5 K. Two types of terminated surfaces are generally observed after cleaving the samples in vacuum. On one commonly obtained surface, we observe a full gap feature with energy gap values close to 4.6 meV. This type of spectrum shows a clean and uniform full gap in space, which indicates the absence of gap nodes in this superconductor. Quasiparticle interference patterns have also been measured, which show no scattering patterns between the hole and tiny electron pockets, but rather an intra-band scattering pattern is observed possibly due to the hole-like $α$ pocket. The Fermi energy of this band is only about $24\pm6$ meV as derived from the energy dispersion result. Meanwhile, impurity induced bound-state peaks can be observed at about $\pm2.2$ meV on some spectra, and the peak value seems to be independent to magnetic field. On the second type of surface which is rarely obtained, the fully gapped feature can still be observed on the tunneling spectra, although multiple gaps are obtained either from a single spectrum or separate ones, and the gap values determined from coherence peaks locate mainly in the range from 4 to 8 meV. Our results clearly indicate multiple and nodeless superconducting gap nature in this layered superconductor KCa$_2$Fe$_4$As$_4$F$_2$, and the superfluid is mainly contributed by the hole-like Fermi surfaces near $Γ$ point. This would inspire further consideration on the effect of the shallow and incipient bands near M point, and help to understand the pairing mechanism in this highly layered iron-based superconductor.

cond-mat.supr-con↗

arXiv2021

Near-optimal Representation Learning for Linear Bandits and Linear RL

This paper studies representation learning for multi-task linear bandits and multi-task episodic RL with linear value function approximation. We first consider the setting where we play $M$ linear bandits with dimension $d$ concurrently, and these bandits share a common $k$-dimensional linear representation so that $k\ll d$ and $k \ll M$. We propose a sample-efficient algorithm, MTLR-OFUL, which leverages the shared representation to achieve $\tilde{O}(M\sqrt{dkT} + d\sqrt{kMT} )$ regret, with $T$ being the number of total steps. Our regret significantly improves upon the baseline $\tilde{O}(Md\sqrt{T})$ achieved by solving each task independently. We further develop a lower bound that shows our regret is near-optimal when $d > M$. Furthermore, we extend the algorithm and analysis to multi-task episodic RL with linear value function approximation under low inherent Bellman error \citep{zanette2020learning}. To the best of our knowledge, this is the first theoretical result that characterizes the benefits of multi-task representation learning for exploration in RL with function approximation.

cs.LG↗

arXiv2021

Modeling Method for the Coupling Relations of Microgrid Cyber-Physical Systems Driven by Hybrid Spatiotemporal Events

The essence of the microgrid cyber-physical system (CPS) lies in the cyclical conversion of information flow and energy flow. Most of the existing coupling models are modeled with static networks and interface structures, in which the closed-loop data flow characteristic is not fully considered. It is difficult for these models to accurately describe spatiotemporal deduction processes, such as microgrid CPS attack identification, risk propagation, safety assessment, defense control, and cascading failure. To address this problem, a modeling method for the coupling relations of microgrid CPS driven by hybrid spatiotemporal events is proposed in the present work. First, according to the topological correlation and coupling logic of the microgrid CPS, the cyclical conversion mechanism of information flow and energy flow is analyzed, and a microgrid CPS architecture with multi-agents as the core is constructed. Next, the spatiotemporal evolution characteristic of the CPS is described by hybrid automata, and the task coordination mechanism of the multi-agent CPS terminal is designed. On this basis, a discrete-continuous correlation and terminal structure characteristic representation method of the CPS based on heterogeneous multi-groups are then proposed. Finally, four spatiotemporal events, namely state perception, network communication, intelligent decision-making, and action control, are defined. Considering the constraints of the temporal conversion of information flow and energy flow, a microgrid CPS coupling model is established, the effectiveness of which is verified by simulating false data injection attack (FDIA) scenarios.

eess.SP↗

arXiv2020

Compositional Prototype Network with Multi-view Comparision for Few-Shot Point Cloud Semantic Segmentation

Point cloud segmentation is a fundamental visual understanding task in 3D vision. A fully supervised point cloud segmentation network often requires a large amount of data with point-wise annotations, which is expensive to obtain. In this work, we present the Compositional Prototype Network that can undertake point cloud segmentation with only a few labeled training data. Inspired by the few-shot learning literature in images, our network directly transfers label information from the limited training data to unlabeled test data for prediction. The network decomposes the representations of complex point cloud data into a set of local regional representations and utilizes them to calculate the compositional prototypes of a visual concept. Our network includes a key Multi-View Comparison Component that exploits the redundant views of the support set. To evaluate the proposed method, we create a new segmentation benchmark dataset, ScanNet-$6^i$, which is built upon ScanNet dataset. Extensive experiments show that our method outperforms baselines with a significant advantage. Moreover, when we use our network to handle the long-tail problem in a fully supervised point cloud segmentation dataset, it can also effectively boost the performance of the few-shot classes.

cs.CV↗

arXiv2020

Relation Extraction with Contextualized Relation Embedding (CRE)

Relation extraction is the task of identifying relation instance between two entities given a corpus whereas Knowledge base modeling is the task of representing a knowledge base, in terms of relations between entities. This paper proposes an architecture for the relation extraction task that integrates semantic information with knowledge base modeling in a novel manner. Existing approaches for relation extraction either do not utilize knowledge base modelling or use separately trained KB models for the RE task. We present a model architecture that internalizes KB modeling in relation extraction. This model applies a novel approach to encode sentences into contextualized relation embeddings, which can then be used together with parameterized entity embeddings to score relation instances. The proposed CRE model achieves state of the art performance on datasets derived from The New York Times Annotated Corpus and FreeBase. The source code has been made available.

cs.CL↗

arXiv2020

Noisy Agents: Self-supervised Exploration by Predicting Auditory Events

Humans integrate multiple sensory modalities (e.g. visual and audio) to build a causal understanding of the physical world. In this work, we propose a novel type of intrinsic motivation for Reinforcement Learning (RL) that encourages the agent to understand the causal effect of its actions through auditory event prediction. First, we allow the agent to collect a small amount of acoustic data and use K-means to discover underlying auditory event clusters. We then train a neural network to predict the auditory events and use the prediction errors as intrinsic rewards to guide RL exploration. Experimental results on Atari games show that our new intrinsic motivation significantly outperforms several state-of-the-art baselines. We further visualize our noisy agents' behavior in a physics environment and demonstrate that our newly designed intrinsic reward leads to the emergence of physical interaction behaviors (e.g. contact with objects).

cs.CV↗

arXiv2020

(Locally) Differentially Private Combinatorial Semi-Bandits

In this paper, we study Combinatorial Semi-Bandits (CSB) that is an extension of classic Multi-Armed Bandits (MAB) under Differential Privacy (DP) and stronger Local Differential Privacy (LDP) setting. Since the server receives more information from users in CSB, it usually causes additional dependence on the dimension of data, which is a notorious side-effect for privacy preserving learning. However for CSB under two common smoothness assumptions \cite{kveton2015tight,chen2016combinatorial}, we show it is possible to remove this side-effect. In detail, for $B_{\infty}$-bounded smooth CSB under either $\varepsilon$-LDP or $\varepsilon$-DP, we prove the optimal regret bound is $Θ(\frac{mB^2_{\infty}\ln T } {Δε^2})$ or $\tildeΘ(\frac{mB^2_{\infty}\ln T} { Δε})$ respectively, where $T$ is time period, $Δ$ is the gap of rewards and $m$ is the number of base arms, by proposing novel algorithms and matching lower bounds. For $B_1$-bounded smooth CSB under $\varepsilon$-DP, we also prove the optimal regret bound is $\tildeΘ(\frac{mKB^2_1\ln T} {Δε})$ with both upper bound and lower bound, where $K$ is the maximum number of feedback in each round. All above results nearly match corresponding non-private optimal rates, which imply there is no additional price for (locally) differentially private CSB in above common settings.

cs.LG↗

arXiv2020

Multivariate Regression of Mixed Responses for Evaluation of Visualization Designs

Information visualization significantly enhances human perception by graphically representing complex data sets. The variety of visualization designs makes it challenging to efficiently evaluate all possible designs catering to users' preferences and characteristics. Most of existing evaluation methods perform user studies to obtain multivariate qualitative responses from users via questionnaires and interviews. However, these methods cannot support online evaluation of designs as they are often time-consuming. A statistical model is desired to predict users' preferences on visualization designs based on non-interference measurements (i.e., wearable sensor signals). In this work, we propose a multivariate regression of mixed responses (MRMR) to facilitate quantitative evaluation of visualization designs. The proposed MRMR method is able to provide accurate model prediction with meaningful variable selection. A simulation study and a user study of evaluating visualization designs with 14 effective participants are conducted to illustrate the merits of the proposed model.

stat.ME↗

arXiv2019

Dynamic 3-D measurement based on fringe-to-fringe transformation using deep learning

Fringe projection profilometry (FPP) has become increasingly important in dynamic 3-D shape measurement. In FPP, it is necessary to retrieve the phase of the measured object before shape profiling. However, traditional phase retrieval techniques often require a large number of fringes, which may generate motion-induced error for dynamic objects. In this paper, a novel phase retrieval technique based on deep learning is proposed, which uses an end-to-end deep convolution neural network to transform a single or two fringes into the phase retrieval required fringes. When the object's surface is located in a restricted depth, the presented network only requires a single fringe as the input, which otherwise requires two fringes in an unrestricted depth. The proposed phase retrieval technique is first theoretically analyzed, and then numerically and experimentally verified on its applicability for dynamic 3-D measurement.

eess.IV↗