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Wenbo Sun

Publications and source records attributed to Wenbo Sun.

At least 55 records · Page 3Linked to original sources

SEE-OoD: Supervised Exploration For Enhanced Out-of-Distribution Detection

Current techniques for Out-of-Distribution (OoD) detection predominantly rely on quantifying predictive uncertainty and incorporating model regularization during the training phase, using either real or synthetic OoD samples. However, methods that utilize real OoD samples lack exploration and are prone to overfit the OoD samples at hand. Whereas synthetic samples are often generated based on features extracted from training data, rendering them less effective when the training and OoD data are highly overlapped in the feature space. In this work, we propose a Wasserstein-score-based generative adversarial training scheme to enhance OoD detection accuracy, which, for the first time, performs data augmentation and exploration simultaneously under the supervision of limited OoD samples. Specifically, the generator explores OoD spaces and generates synthetic OoD samples using feedback from the discriminator, while the discriminator exploits both the observed and synthesized samples for OoD detection using a predefined Wasserstein score. We provide theoretical guarantees that the optimal solutions of our generative scheme are statistically achievable through adversarial training in empirical settings. We then demonstrate that the proposed method outperforms state-of-the-art techniques on various computer vision datasets and exhibits superior generalizability to unseen OoD data.

cs.LG↗

Optical N-plasmon: Topological hydrodynamic excitations in Graphene from repulsive Hall viscosity

Edge states occurring in Chern and quantum spin-Hall phases are signatures of the topological electronic band structure in two-dimensional (2D) materials. Recently, a new topological electromagnetic phase of graphene characterized by the optical N-invariant has been proposed. Optical N-invariant arises from repulsive Hall viscosity in hydrodynamic many-body electron systems, fundamentally different from the Chern and Z2 invariants. In this paper, we introduce the topologically protected edge excitation -- optical N-plasmon of interacting many-body electron systems in the topological optical N-phase. These optical N-plasmons are signatures of the topological plasmonic band structure in 2D materials. We demonstrate that optical N-plasmons exhibit fundamentally different dispersion relations, stability, and edge profiles from the topologically trivial edge magneto plasmons. Based on the optical N-plasmon, we design an ultra sub-wavelength broadband topological hydrodynamic circulator, which is a chiral quantum radio-frequency circuit component crucial for information routing and interfacing quantum-classical computing systems. Furthermore, we reveal that optical N-plasmons can be effectively tuned by the neighboring dielectric environment without breaking the topological properties. Our work provides a smoking gun signature of repulsive Hall viscosity and opens practical applications of topological electromagnetic phases of two-dimensional materials.

cond-mat.mes-hall↗

Limits to Quantum Gate Fidelity from Near-Field Thermal and Vacuum Fluctuations

High-fidelity quantum gate operations are essential for achieving scalable quantum circuits. In spin qubit quantum computing systems, metallic gates and antennas which are necessary for qubit operation, initialization, and readout, also cause detriments by enhancing fluctuations of electromagnetic fields. Therefore evanescent wave Johnson noise (EWJN) caused by thermal and vacuum fluctuations becomes an important unmitigated noise, which induces the decay of spin qubits and limits the quantum gate operation fidelity. Here, we first develop a quantum electrodynamics theory of EWJN. Then we propose a numerical technique based on volume integral equations to quantify EWJN strength in the vicinity of nanofabricated metallic gates with arbitrary geometry. We study the limits to two spin-qubit gate fidelity from EWJN-induced relaxation processes in two experimentally relevant quantum computing platforms: (a) silicon quantum dot system and (b) NV centers in diamond. Finally, we introduce the Lindbladian engineering method to optimize the control pulse sequence design and show its enhanced performance over Hamiltonian engineering in mitigating the influence of thermal and vacuum fluctuations. Our work leverages advances in computational electromagnetics, fluctuational electrodynamics and open quantum systems to suppress the effects of thermal and vacuum fluctuations and reach the limits of two-spin-qubit gate fidelity.

quant-ph↗

Joint ergodicity for functions of polynomial growth

We provide necessary and sufficient conditions for joint ergodicity results for systems of commuting measure preserving transformations for an iterated Hardy field function of polynomial growth. Our method builds on and improves recent techniques due to Frantzikinakis and Tsinas, who dealt with multiple ergodic averages along Hardy field functions; it also enhances an approach introduced by the authors and Ferré Moragues to study polynomial iterates. The more general expression, in which the iterate is a linear combination of a Hardy field function of polynomial growth and a tempered function, is studied as well.

math.DS↗

Amalur: Data Integration Meets Machine Learning

The data needed for machine learning (ML) model training, can reside in different separate sites often termed data silos. For data-intensive ML applications, data silos pose a major challenge: the integration and transformation of data demand a lot of manual work and computational resources. With data privacy and security constraints, data often cannot leave the local sites, and a model has to be trained in a decentralized manner. In this work, we present a vision on how to bridge the traditional data integration (DI) techniques with the requirements of modern machine learning. We explore the possibilities of utilizing metadata obtained from data integration processes for improving the effectiveness and efficiency of ML models. We analyze two common use cases over data silos, feature augmentation and federated learning. Bringing data integration and machine learning together, we highlight the new research opportunities from the aspects of systems, representations, factorized learning and federated learning.

cs.DB↗

Total joint ergodicity for totally ergodic systems

Examining multiple ergodic averages whose iterates are integer parts of real valued polynomials for totally ergodic systems, we provide various characterizations of total joint ergodicity, meaning that an average converges to the "expected" limit along every arithmetic progression. In particular, we obtain a complete characterization when the number of iterates is at most two, and disprove a conjecture of the first author. We also improve a result of Frantzikinakis on joint ergodicity of Hardy field functions of at most polynomial growth for totally ergodic systems, which extends a conjecture of Bergelson-Moreira-Richter. Our method is to first use the methodology of Frantzikinakis, which allows one to reduce the systems to rotations on abelian groups without using deep tools from ergodic theory, then develop formulas for integrals of exponential functions over subtori, and finally, compute exponential sums for integer parts of real polynomials.

math.DS↗

Seminorms for multiple averages along polynomials and applications to joint ergodicity

Exploiting the recent work of Tao and Ziegler on a concatenation theorem on factors, we find explicit characteristic factors for multiple averages along polynomials on systems with commuting transformations, and use them to study criteria of joint ergodicity for sequences of the form $(T^{p_{1,j}(n)}_{1}\cdot\ldots\cdot T^{p_{d,j}(n)}_{d})_{n\in\mathbb{Z}},$ $1\leq j\leq k$, where $T_{1},\dots,T_{d}$ are commuting measure preserving transformations on a probability measure space and $p_{i,j}$ are integer polynomials. To be more precise, we provide a sufficient condition for such sequences to be jointly ergodic, giving also a characterization for sequences of the form $(T^{p(n)}_{i})_{n\in\mathbb{Z}}, 1\leq i\leq d$ to be jointly ergodic, answering a question due to Bergelson.

math.DS↗

Sarnak's Conjecture for nilsequences on arbitrary number fields and applications

We formulate the generalized Sarnak's Möbius disjointness conjecture for an arbitrary number field $K$, and prove a quantitative disjointness result between polynomial nilsequences $(Φ(g(n)Γ))_{n\in\mathbb{Z}^{D}}$ and aperiodic multiplicative functions on $\mathcal{O}_{K}$, the ring of integers of $K$. Here $D=[K\colon\mathbb{Q}]$, $X=G/Γ$ is a nilmanifold, $g\colon\mathbb{Z}^{D}\to G$ is a polynomial sequence, and $Φ\colon X\to \mathbb{C}$ is a Lipschitz function. The proof uses tools from multi-dimensional higher order Fourier analysis, multi-linear analysis, orbit properties on nilmanifold, and an orthogonality criterion of Kátai in $\mathcal{O}_{K}$. We also use variations of this result to derive applications in number theory and combinatorics: (1) we prove a structure theorem for multiplicative functions on $K$, saying that every bounded multiplicative function can be decomposed into the sum of an almost periodic function (the structural part) and a function with small Gowers uniformity norm of any degree (the uniform part); (2) we give a necessary and sufficient condition for the Gowers norms of a bounded multiplicative function in $\mathcal{O}_{K}$ to be zero; (3) we provide partition regularity results over $K$ for a large class of homogeneous equations in three variables. For example, for $a,b\in\mathbb{Z}\backslash\{0\}$, we show that for every partition of $\mathcal{O}_{K}$ into finitely many cells, where $K=\mathbb{Q}(\sqrt{a},\sqrt{b},\sqrt{a+b})$, there exist distinct and non-zero $x,y$ belonging to the same cell and $z\in\mathcal{O}_{K}$ such that $ax^{2}+by^{2}=z^{2}$.

math.NT↗

Graph-theoretical approach to robust 3D normal extraction of LiDAR data

Low dimensional primitive feature extraction from LiDAR point clouds (such as planes) forms the basis of majority of LiDAR data processing tasks. A major challenge in LiDAR data analysis arises from the irregular nature of LiDAR data that forces practitioners to either regularize the data using some form of gridding or utilize a triangular mesh such as triangulated irregular network (TIN). While there have been a handful applications using LiDAR data as a connected graph, a principled treatment of utilizing graph-theoretical approach for LiDAR data modelling is still lacking. In this paper, we try to bridge this gap by utilizing graphical approach for normal estimation from LiDAR point clouds. We formulate the normal estimation problem in an optimization framework, where we find the corresponding normal vector for each LiDAR point by utilizing its nearest neighbors and simultaneously enforcing a graph smoothness assumption based on point samples. This is a non-linear constrained convex optimization problem which can then be solved using projected conjugate gradient descent to yield an unique solution. As an enhancement to our optimization problem, we also provide different weighted solutions based on the dot product of the normals and Euclidean distance between the points. In order to assess the performance of our proposed normal extraction method and weighting strategies, we first provide a detailed analysis on repeated randomly generated datasets with four different noise levels and four different tuning parameters. Finally, we benchmark our proposed method against existing state-of-the-art approaches on a large scale synthetic plane extraction dataset. The code for the proposed approach along with the simulations and benchmarking is available at https://github.com/arpan-kusari/graph-plane-extraction-simulation.

cs.CV↗

Additive averages of multiplicative correlation sequences and applications

We study sets of recurrence, in both measurable and topological settings, for actions of $(\mathbb{N},\times)$ and $(\mathbb{Q}^{>0},\times)$. In particular, we show that autocorrelation sequences of positive functions arising from multiplicative systems have positive additive averages. We also give criteria for when sets of the form $\{(an+b)^{\ell}/(cn+d)^{\ell}: n \in \mathbb{N}\}$ are sets of multiplicative recurrence, and consequently we recover two recent results in number theory regarding completely multiplicative functions and the Omega function.

math.DS↗

A Continual Learning Framework for Adaptive Defect Classification and Inspection

Machine-vision-based defect classification techniques have been widely adopted for automatic quality inspection in manufacturing processes. This article describes a general framework for classifying defects from high volume data batches with efficient inspection of unlabelled samples. The concept is to construct a detector to identify new defect types, send them to the inspection station for labelling, and dynamically update the classifier in an efficient manner that reduces both storage and computational needs imposed by data samples of previously observed batches. Both a simulation study on image classification and a case study on surface defect detection via 3D point clouds are performed to demonstrate the effectiveness of the proposed method.

cs.CV↗

Precision Radiotherapy via Information Integration of Expert Human Knowledge and AI Recommendation to Optimize Clinical Decision Making

In the precision medicine era, there is a growing need for precision radiotherapy where the planned radiation dose needs to be optimally determined by considering a myriad of patient-specific information in order to ensure treatment efficacy. Existing artificial-intelligence (AI) methods can recommend radiation dose prescriptions within the scope of this available information. However, treating physicians may not fully entrust the AI's recommended prescriptions due to known limitations or when the AI recommendation may go beyond physicians' current knowledge. This paper lays out a systematic method to integrate expert human knowledge with AI recommendations for optimizing clinical decision making. Towards this goal, Gaussian process (GP) models are integrated with deep neural networks (DNNs) to quantify the uncertainty of the treatment outcomes given by physicians and AI recommendations, respectively, which are further used as a guideline to educate clinical physicians and improve AI models performance. The proposed method is demonstrated in a comprehensive dataset where patient-specific information and treatment outcomes are prospectively collected during radiotherapy of $67$ non-small cell lung cancer patients and retrospectively analyzed.

stat.ML↗

ASC-Net: Unsupervised Medical Anomaly Segmentation Using an Adversarial-based Selective Cutting Network

In this paper we consider the problem of unsupervised anomaly segmentation in medical images, which has attracted increasing attention in recent years due to the expensive pixel-level annotations from experts and the existence of a large amount of unannotated normal and abnormal image scans. We introduce a segmentation network that utilizes adversarial learning to partition an image into two cuts, with one of them falling into a reference distribution provided by the user. This Adversarial-based Selective Cutting network (ASC-Net) bridges the two domains of cluster-based deep segmentation and adversarial-based anomaly/novelty detection algorithms. Our ASC-Net learns from normal and abnormal medical scans to segment anomalies in medical scans without any masks for supervision. We evaluate this unsupervised anomly segmentation model on three public datasets, i.e., BraTS 2019 for brain tumor segmentation, LiTS for liver lesion segmentation, and MS-SEG 2015 for brain lesion segmentation, and also on a private dataset for brain tumor segmentation. Compared to existing methods, our model demonstrates tremendous performance gains in unsupervised anomaly segmentation tasks. Although there is still room to further improve performance compared to supervised learning algorithms, the promising experimental results and interesting observations shed light on building an unsupervised learning algorithm for medical anomaly identification using user-defined knowledge.

eess.IV↗

WOOD: Wasserstein-based Out-of-Distribution Detection

The training and test data for deep-neural-network-based classifiers are usually assumed to be sampled from the same distribution. When part of the test samples are drawn from a distribution that is sufficiently far away from that of the training samples (a.k.a. out-of-distribution (OOD) samples), the trained neural network has a tendency to make high confidence predictions for these OOD samples. Detection of the OOD samples is critical when training a neural network used for image classification, object detection, etc. It can enhance the classifier's robustness to irrelevant inputs, and improve the system resilience and security under different forms of attacks. Detection of OOD samples has three main challenges: (i) the proposed OOD detection method should be compatible with various architectures of classifiers (e.g., DenseNet, ResNet), without significantly increasing the model complexity and requirements on computational resources; (ii) the OOD samples may come from multiple distributions, whose class labels are commonly unavailable; (iii) a score function needs to be defined to effectively separate OOD samples from in-distribution (InD) samples. To overcome these challenges, we propose a Wasserstein-based out-of-distribution detection (WOOD) method. The basic idea is to define a Wasserstein-distance-based score that evaluates the dissimilarity between a test sample and the distribution of InD samples. An optimization problem is then formulated and solved based on the proposed score function. The statistical learning bound of the proposed method is investigated to guarantee that the loss value achieved by the empirical optimizer approximates the global optimum. The comparison study results demonstrate that the proposed WOOD consistently outperforms other existing OOD detection methods.

cs.LG↗

Decomposition of multicorrelation sequences and joint ergodicity

We show that, under finitely many ergodicity assumptions, any multicorrelation sequence defined by invertible measure preserving $\mathbb{Z}^d$-actions with multivariable integer polynomial iterates is the sum of a nilsequence and a null sequence, extending a recent result of the second author. To this end, we develop a new seminorm bound estimate for multiple averages by improving the results in a previous work of the first, third and fourth authors. We also use this approach to obtain new criteria for joint ergodicity of multiple averages with multivariable polynomial iterates on $\mathbb{Z}^{d}$-systems.

math.DS↗

Optimal lower bounds for multiple recurrence

Let $(X, \mathcal{B},μ,T)$ be an ergodic measure preserving system, $A \in \mathcal{B}$ and $ε>0$. We study the largeness of sets of the form \begin{equation*} \begin{split} S = \left\{ n\in\mathbb{N}\colonμ(A\cap T^{-f_1(n)}A\cap T^{-f_2(n)}A\cap\ldots\cap T^{-f_k(n)}A)> μ(A)^{k+1} - ε\right\} \end{split} \end{equation*} for various families $\{f_1,\dots,f_k\}$ of sequences $f_i\colon \mathbb{N} \to \mathbb{N}$. For $k \leq 3$ and $f_{i}(n)=i f(n)$, we show that $S$ has positive density if $f(n)=q(p_n)$ where $q \in \mathbb{Z}[x]$ satisfies $q(1)$ or $q(-1) =0$ and $p_n$ denotes the $n$-th prime; or when $f$ is a certain Hardy field sequence. If $T^q$ is ergodic for some $q \in \mathbb{N}$, then for all $r \in \mathbb{Z}$, $S$ is syndetic if $f(n) = qn + r$. For $f_{i}(n)=a_{i}n$, where $a_{i}$ are distinct integers, we show that $S$ can be empty for $k\geq 4$, and for $k = 3$ we found an interesting relation between the largeness of $S$ and the abundance of solutions to certain linear equations in sparse sets of integers. We also provide some partial results when the $f_{i}$ are distinct polynomials.

math.DS↗

Weak ergodic averages over dilated measures

Let $m\in\mathbb{N}$ and $\textbf{X}=(X,\mathcal{X},μ,(T_α)_{α\in\mathbb{R}^{m}})$ be a measure preserving system with an $\mathbb{R}^{m}$-action. We say that a Borel measure $ν$ on $\mathbb{R}^{m}$ is weakly equidistributed for $\textbf{X}$ if there exists $A\subseteq\mathbb{R}$ of density 1 such that for all $f\in L^{\infty}(μ)$, we have $$\lim_{t\in A,t\to\infty}\int_{\mathbb{R}^{m}}f(T_{t α}x)\,dν(α)=\int_{X}f\,dμ$$ for $μ$-a.e. $x\in X$. Let $W(\textbf{X})$ denote the collection of all $α\in\mathbb{R}^{m}$ such that the $\mathbb{R}$-action $(T_{tα})_{t\in\mathbb{R}}$ is not ergodic. Under the assumption of the pointwise convergence of double Birkhoff ergodic average, we show that a Borel measure $ν$ on $\mathbb{R}^{m}$ is weakly equidistributed for an ergodic system $\textbf{X}$ if and only if $ν(W(\textbf{X})+β)=0$ for every $β\in\mathbb{R}^{m}$. Under the same assumption, we also show that $ν$ is weakly equidistributed for all ergodic measure preserving systems with $\mathbb{R}^{m}$-actions if and only if $ν(\ell)=0$ for all hyperplanes $\ell$ of $\mathbb{R}^{m}$. Unlike many equidistribution results in literature whose proofs use methods from harmonic analysis, our results adopt a purely ergodic theoretic approach.

math.DS↗

Under- and over-independence in measure preserving systems

We introduce the notions of over- and under-independence for weakly mixing and (free) ergodic measure preserving actions and establish new results which complement and extend the theorems obtained in [BoFW] and [A]. Here is a sample of results obtained in this paper: $\cdot$ (Existence of density-1 UI and OI set) Let $(X,\mathcal{B},μ,T)$ be an invertible probability measure preserving weakly mixing system. Then for any $d\in\mathbb{N}$, any non-constant integer-valued polynomials $p_{1},p_{2},\dots,p_{d}$ such that $p_{i}-p_{j}$ are also non-constant for all $i\neq j$, (i) there is $A\in\mathcal{B}$ such that the set $$\{n\in\mathbb{N}\colonμ(A\cap T^{p_{1}(n)}A\cap\dots\cap T^{p_{d}(n)}A)<μ(A)^{d+1}\}$$ is of density 1. (ii) there is $A\in\mathcal{B}$ such that the set $$\{n\in\mathbb{N}\colonμ(A\cap T^{p_{1}(n)}A\cap\dots\cap T^{p_{d}(n)}A)>μ(A)^{d+1}\}$$ is of density 1. $\cdot$ (Existence of Cesàro OI set) Let $(X,\mathcal{B},μ,T)$ be a free, invertible, ergodic probability measure preserving system and $M\in\mathbb{N}$. %Suppose that $X$ contains an ergodic component which is aperiodic. Then there is $A\in\mathcal{B}$ such that $$\frac{1}{N}\sum_{n=M}^{N+M-1}μ(A\cap T^{n}A)>μ(A)^{2}$$ for all $N\in\mathbb{N}$. $\cdot$ (Nonexistence of Cesàro UI set) Let $(X,\mathcal{B},μ,T)$ be an invertible probability measure preserving system. For any measurable set $A$ satisfying $μ(A) \in (0,1)$, there exist infinitely many $N \in \mathbb{N}$ such that $$\frac{1}{N} \sum_{n=0}^{N-1} μ( A \cap T^{n}A) > μ(A)^2.$$

math.DS↗