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Model-Based Feature Selection for Neural Networks: A Mixed-Integer Programming Approach 1

17th International Conference on Learning and Intelligent Optimization, LION-17 2023

作者： Zhao, Shudian Tsay, Calvin Kronqvist, Jan Optimization and Systems Theory Department of Mathematics KTH Royal Institute of Technology Stockholm Sweden Department of Computing Imperial College London London United Kingdom

ISBN: (数字)9783031445057

ISBN: (纸本)9783031445040

In this work, we develop a novel input feature selection framework for ReLU-based deep neural networks (DNNs), which builds upon a mixed-integer optimization approach. While the method is generally applicable to various classification tasks, we focus on finding input features for image classification for clarity of presentation. The idea is to use a trained DNN, or an ensemble of trained DNNs, to identify the salient input features. The input feature selection is formulated as a sequence of mixed-integer linear programming (MILP) problems that find sets of sparse inputs that maximize the classification confidence of each category. These "inverse" problems are regularized by the number of inputs selected for each category and by distribution constraints. Numerical results on the well-known MNIST and FashionMNIST datasets show that the proposed input feature selection allows us to drastically reduce the size of the input to ∼ 15% while maintaining a good classification accuracy. This allows us to design DNNs with significantly fewer connections, reducing computational effort and producing DNNs that are more robust towards adversarial attacks. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Deep neural networks

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ParMod: A Parallel and Modular Framework for Learning Non-Markovian Tasks

arXiv

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arXiv 2024年

作者： Miao, Ruixuan Lu, Xu Tian, Cong Yu, Bin Duan, Zhenhua Institute of Computing Theory and Technology State Key Laboratory of ISN Xidian University China

The commonly used Reinforcement Learning (RL) model, MDPs (Markov Decision Processes), has a basic premise that rewards depend on the current state and action only. However, many real-world tasks are non-Markovian, which has long-term memory and dependency. The reward sparseness problem is further amplified in non-Markovian scenarios. Hence learning a non-Markovian task (NMT) is inherently more difficult than learning a Markovian one. In this paper, we propose a novel Parallel and Modular RL framework, ParMod, specifically for learning NMTs specified by temporal logic. With the aid of formal techniques, the NMT is modulaized into a series of sub-tasks based on the automaton structure (equivalent to its temporal logic counterpart). On this basis, sub-tasks will be trained by a group of agents in a parallel fashion, with one agent handling one sub-task. Besides parallel training, the core of ParMod lies in: a flexible classification method for modularizing the NMT, and an effective reward shaping method for improving the sample efficiency. A comprehensive evaluation is conducted on several challenging benchmark problems with respect to various metrics. The experimental results show that ParMod achieves superior performance over other relevant studies. Our work thus provides a good synergy among RL, NMT and temporal logic. © 2024, CC BY.

关键词： Contrastive Learning

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Fast Second-order Method for Neural Networks under Small Treewidth Setting

Fast Second-order Method for Neural Networks under Small Tre...

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2024 IEEE International Conference on Big Data, BigData 2024

作者： Li, Xiaoyu Long, Jiangxuan Song, Zhao Zhou, Tianyi Stevens Institute of Technology Department of Computer Science HobokenNJ United States South China University of Technology School of Software Engineering Guangzhou China University of California Berkeley The Simons Institute for the Theory of Computing BerkeleyCA United States University of Southern California Department of Computer Science Los AngelesCA United States

ISBN: (纸本)9798350362480

Training neural networks is a fundamental problem in theoretical machine learning. Second-order methods are rarely used in practice due to their high computational cost, even they converge much faster than first-order methods. The state-of-the-art result for the second-order method to train an over-parameterized neural network can run in O(log(1/ϵ)) iterations and each iteration has O(mnd + n3) running time, where n represent the number of data points, d is the dimension of the feature space of each data and m is the width of the neural network [Brand, Peng, Song and Weinstein ITCS 2021]. In this work, we further improve the convergence rate and the running time for each iteration to O(loglog(1/ϵ)) and O(mdτ2) respectively, where m = Ω(n4) and τ is the treewidth of the data matrix and usually very small. Our algorithm has a quadratic convergence rate, so it can be regarded as a truly second-order algorithm. To the best of our knowledge, our algorithm is the first to achieve a quadratic convergence rate for neural network training, with a per-iteration running time of O(mdτ2). © 2024 IEEE.

关键词： Trees (mathematics)

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Design and Implementation of List and Dictionary in XD-M Language 15th

Design and Implementation of List and Dictionary in XD-M...

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15th International Conference on Algorithmic Aspects in Information and Management, AAIM 2021

作者： Wang, Yajie Zhang, Nan Duan, Zhenhua Institute of Computing Theory and Technology and ISN Laboratory Xidian University Xi’an710071 China

ISBN: (纸本)9783030931759

This paper presents the design and implementation of two data types, List and Dictionary, in the programming language XD-M. XD-M is an interpreted language with dynamic data types and its syntax is similar to Python. It is developed from the Modeling Simulation and Verification Language called MSVL. In the main part of the paper, we will discuss data structures, syntax and algorithms of List and Dictionary in XD-M, as well as their abstract syntax trees. Finally, an example is given to illustrate how to use List and Dictionary in XD-M programming. © 2021, Springer Nature Switzerland AG.

关键词： Data structures

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Experimental quantum simulation of a topologically protected Hadamard gate via braiding Fibonacci anyons

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The Innovation 2023年第5期4卷 41-46页

作者： Yu-ang Fan Yingcheng Li Yuting Hu Yishan Li Xinyue Long Hongfeng Liu Xiaodong Yang Xinfang Nie Jun Li Tao Xin Dawei Lu Yidun Wan Shenzhen Institute for Quantum Science and Engineering and Department of Physics Southem University of Science and Technology Shenzhen 518055China State Key Laboratory of Surface Physics Department of PhysicsCenter for Field Theory and Particle Physicsand Institute for Nanoelectronic Devices and Quantum ComputingFudan UniversityShanghai 200433and Shanghai Qi Zhi InstituteShanghai 200030China School of Physics Hangzhou Normal UniversityHangzhou 311121China

Topological quantum computation(TQC)is one of the most striking architectures that can realize fault-tolerant quantum *** TQC,the logical space and the quantum gates are topologically protected,i.e.,robust against local *** topological protection,however,requires complicated lattice models and hard-to-manipulate dynamics;even the simplest system that can realize universal TQC-the Fibonacci anyon system—lacks a physical realization,let alone braiding the non-Abelian ***,we propose a disk model that can simulate the Fibonacci anyon system and construct the topologically protected logical spaces with the Fibonacci *** braiding the Fibonacci anyons,we can implement universal quantum gates on the logical *** disk model merely requires two physical qubits to realize three Fibonacci anyons at the *** 15 sequential braiding operations,we construct a topologically protected Hadamard gate,which is to date the least-resource requirement for *** showcase,we implement a topological Hadamard gate with two nuclear spin qubits,which reaches 97.18%fidelity by randomized *** further prove by experiment that the logical space and Hadamard gate are topologically protected:local disturbances due to thermal fluctuations result in a global phase *** a platform-independent proposal,our work is a proof of principle of TQC and paves the way toward fault-tolerant quantum computation.

关键词： Fibonacci Hadamard TQC

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Quantum frontiers in high energy physics

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Science China(Physics,Mechanics & Astronomy) 2025年第6期Mechanics & Astronomy) .卷 53-75页

作者： Yaquan Fang Christina Gao Ying-Ying Li Jing Shu Yusheng Wu Hongxi Xing Bin Xu Lailin Xu Chen Zhou Institute of High Energy Physics Chinese Academy of Sciences University of Chinese Academy of Sciences Department of Physics Southern University of Science and Technology Interdisciplinary Center for Theoretical Study University of Science and Technology of China Peng Huanwu Center for Fundamental Theory State Key Laboratory of Nuclear Physics and Technology School of Physics Peking University Center for High Energy Physics Peking University Beijing Laser Acceleration Innovation Center State Key Laboratory of Particle Detection and Electronics Department of Modern Physics University of Science and Technology of China Key Laboratory of Atomic and Subatomic Structure and Quantum Control (MOE) Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter Institute of Quantum MatterSouth China Normal University Guangdong-Hong Kong Joint Laboratory of Quantum Matter Guangdong Provincial Key Laboratory of Nuclear ScienceSouthern Nuclear Science Computing Center South China Normal University Southern Center for Nuclear-Science Theory Institute of Modern Physics Chinese Academy of Sciences

Numerous challenges persist in high energy physics(HEP), the addressing of which requires advancements in detection technology, computational methods, data analysis frameworks, and phenomenological designs. We provide a concise yet comprehensive overview of recent progress across these areas, in line with advances in quantum technology. We will discuss the potential of quantum devices in detecting subtle effects indicative of new physics BSM, the transformative role of quantum algorithms and large-scale quantum computers in studying real-time non-perturbative dynamics in the early universe and at colliders, as well as in analyzing complex HEP data. Additionally, we emphasize the importance of integrating quantum properties into HEP experiments to test quantum mechanics at unprecedented high-energy scales and search for hints of new physics. Looking ahead, the continued integration of resources to fully harness these evolving technologies will enhance our efforts to deepen our understanding of the fundamental laws of nature.

关键词： high energy physics quantum sensing quantum simulations quantum machine learning quantum information

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Quantum control for time-dependent noise by inverse geometric optimization

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Science China(Physics,Mechanics & Astronomy) 2024年第9期67卷 51-57页

作者： Xiaodong Yang Yingcheng Li Ran Liu Xinfang Nie Tao Xin Dawei Lu Jun Li Institute of Quantum Precision Measurement State Key Laboratory of Radio Frequency Heterogeneous IntegrationCollege of Physics and Optoelectronic EngineeringShenzhen UniversityShenzhen 518060China State Key Laboratory of Surface Physics Department of PhysicsCenter for Field Theory and Particle Physicsand Institute for Nanoelectronic Devices and Quantum ComputingFudan UniversityShanghai 200433China Shenzhen Institute for Quantum Science and Engineering and Department of Physics Southern University of Science and TechnologyShenzhen 518055China Guangdong Provincial Key Laboratory of Quantum Science and Engineering Southern University of Science and TechnologyShenzhen 518055China Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area(Guangdong) Shenzhen 518045China

Quantum systems are exceedingly difficult to engineer because they are sensitive to various types of *** particular,timedependent noises are frequently encountered in experiments but how to overcome them remains a challenging *** this work,we propose a flexible robust control technique to resist time-dependent noises based on inverse geometric optimization working in the filter-function *** basic idea is to parameterize the control filter function geometrically and minimize its overlap with the noise spectral *** then effectively reduces the noise susceptibility of the controlled system *** show that the proposed method can produce high-quality robust pulses for realizing desired quantum evolutions under realistic noise ***,we demonstrate this method in examples including dynamical decoupling and quantum sensing protocols to enhance their performances.

关键词： time-dependent noise robust control quantum gates and states dynamical decoupling quantum sensing

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Online Flexible Busy Time Scheduling on Heterogeneous Machines 32

Online Flexible Busy Time Scheduling on Heterogeneous Machin...

引用

32nd Annual European Symposium on Algorithms, ESA 2024

作者： Călinescu, Gruia Davies, Sami Khuller, Samir Zhang, Shirley Department of Computer Science Illinois Institute of Technology ChicagoIL United States Department of EECS The Simons Institute for the Theory of Computing UC Berkeley CA United States Computer Science Department Northwestern University EvanstonIL United States Computer Science Department Harvard University CambridgeMA United States

ISBN: (纸本)9783959773386

We study the online busy time scheduling model on heterogeneous machines. In our setting, jobs with uniform length arrive online with a deadline that becomes known to the algorithm at the job's arrival time. An algorithm has access to machines, each with different associated capacities and costs. The goal is to schedule jobs on machines by their deadline, so that the total cost incurred by the scheduling algorithm is minimized. While busy time scheduling has been well-studied, relatively little is known when machines are heterogeneous (i.e., have different costs and capacities), despite this natural theoretical generalization being the most practical model for clients using cloud computing services. We make significant progress in understanding this model by designing an 8-competitive algorithm for the problem on unit-length jobs and provide a lower bound of 2 on the competitive ratio. The lower bound is tight in the setting when jobs form non-nested intervals. Our 8-competitive algorithm generalizes to one with competitive ratio 8(2p − 1)/p © Gruia Călinescu, Sami Davies, Samir Khuller, and Shirley Zhang;licensed under Creative Commons License CC-BY 4.0.

关键词： Scheduling algorithms

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Using Experience Classification for Training Non-Markovian Tasks

arXiv

引用

arXiv 2023年

作者： Miao, Ruixuan Lu, Xu Tian, Cong Yu, Bin Duan, Zhenhua Institute of Computing Theory and Technology State Key Laboratory of Integrated Services Networks Xidian University China

Unlike the standard Reinforcement Learning (RL) model, many real-world tasks are non-Markovian, whose rewards are predicated on state history rather than solely on the current state. Solving a non-Markovian task, frequently applied in practical applications such as autonomous driving, financial trading, and medical diagnosis, can be quite challenging. We propose a novel RL approach to achieve non-Markovian rewards expressed in temporal logic LTLf (Linear Temporal Logic over Finite Traces). To this end, an encoding of linear complexity from LTLf into MDPs (Markov Decision Processes) is introduced to take advantage of advanced RL algorithms. Then, a prioritized experience replay technique based on the automata structure (semantics equivalent to LTLf specification) is utilized to improve the training process. We empirically evaluate several benchmark problems augmented with non-Markovian tasks to demonstrate the feasibility and effectiveness of our approach. Copyright © 2023, The Authors. All rights reserved.

关键词： Reinforcement learning

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Distributed exact Grover’s algorithm

引用

Frontiers of physics 2023年第5期18卷 255-279页

作者： Xu Zhou Daowen Qiu Le Luo Institute of Quantum Computing and Computer Theory School of Computer Science and EngineeringSun Yat-sen UniversityGuangzhou 510006China The Guangdong Key Laboratory of Information Security Technology Sun Yat-sen UniversityGuangzhou 510006China School of Physics and Astronomy Sun Yat-sen UniversityZhuhai 519082China QUDOOR Co Ltd.Beijing 100089China

Distributed quantum computation has gained extensive *** this paper,we consider a search problem that includes only one target item in the unordered *** that,we propose a distributed exact Grover’s algorithm(DEGA),which decomposes the original search problem into■n/2■***,(i)our algorithm is as exact as the modified version of Grover’s algorithm by Long,which means the theoretical probability of finding the objective state is 100%;(ii)the actual depth of our circuit is 8(n mod 2)+9,which is less than the circuit depths of the original and modified Grover’s algorithms,1+8■π/4√2^(n)■and 9+8■π/4√2^(n)-1/2■,*** only depends on the parity of n,and it is not deepened as n increases;(iii)we provide particular situations of the DEGA on MindQuantum(a quantum software)to demonstrate the practicality and validity of our *** our circuit is shallower,it will be more resistant to the depolarization channel noise.

关键词： distributed quantum computation search problem distributed exact Grover’s algorithm(DEGA) MindQuantum the depolarization channel noise

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