一周活动预告（10.23-10.29）
请查收。
量子人工智能的基本原理与数学基础 （陈泽乾）
A mathematical theory of computational resolution limit and super-resolution （Ping Liu）
河图洛书与组合数学 (张之正)
Acceleration of Reinforcement Learning Facilitated by Decomposable Structures of MDPs（Hao Jin）
Optimal Transport in Machine Learning（孙剑）
On perfect and insulated conductivity problems （董弘桀）
文中BJT为北京时间。
1. 量子人工智能的基本原理与数学基础
报告人: 陈泽乾 （中科院）
报告时间: 2023-10.23 14:00-15:00
报告链接: 腾讯会议ID: 837 501 692
信息来源:
http://www.amss.cas.cn/mzxsbg/202310/t20231019_6903583.html
报告摘要:
本报告介绍近期我们为t' Hooft在2016年提出的新量子力学形式建立的一个数学基础, 并由此阐述他的理论中的态叠加原理就是量子人工智能的基本原理. 基于该原理, 我们用拓扑斯理论(Topos theory)研究量子人工智能的数学基础. 首先, 依据图灵测试对智能给出的科学定义, 我们将人工智能系统定义为由拓扑斯理论所描述的物理系统(Isham等人在2008年建立的物理理论), 它们具有自身的高阶形式语言及逻辑推理系统. 其次, 依据物理原理, 我们将人工智能系统分为经典人工智能系统和量子人工智能系统. 对于经典人工智能系统, 我们用测度论构造相应的拓扑斯描述, 特别是给出了深度学习的拓扑斯描述; 而对于量子人工智能系统, 则用Hilbert空间上算子理论构造相应的拓扑斯以给出它的数学描述. 最后, 我们用量子人工智能系统的拓扑斯理论描述量子机器学习, 特别是给出量子计算的拓扑斯理论模型.
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2. A mathematical theory of computational resolution limit and super-resolution
报告人: Ping Liu （ETH Zurich）
报告时间: 2023-10.23 20:00-21:00
报告链接: 腾讯会议ID: 666 347 256
信息来源:
http://www.amss.cas.cn/mzxsbg/202309/t20230914_6880153.html
报告摘要:
Due to the physical nature of wave propagation and diffraction, there is a fundamental diffraction barrier in optical imaging systems which is called the diffraction limit or resolution limit. Rayleigh investigated this problem and formulated the well-known Rayleigh limit. However, the Rayleigh limit is empirical and only considers the resolving ability of the human visual system. On the other hand, resolving sources separated below the Rayleigh limit to achieve so-called “super-resolution” has been demonstrated in many numerical experiments.
In this talk, we will propose a new concept “computational resolution limit” which reveals the fundamental limits in super-resolving the number and locations of point sources from a data-processing point of view. We will quantitatively characterize the computational resolution limits by the signal-to-noise ratio, the sparsity of sources, and the cutoff frequency of the imaging system. As a direct consequence, it is demonstrated that l_0 optimization achieves the optimal order resolution in solving super-resolution problems. For the case of resolving two point sources, the resolution estimate is improved to an exact formula, which answers the long-standing question of diffraction limit in a general circumstance. We will also propose an optimal algorithm to distinguish images generated by single or two point sources. Generalization of our results to the imaging of positive sources, imaging in multi-dimensional spaces, and multi-illumination imaging will be briefly discussed as well.
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3. 河图洛书与组合数学
报告人: 张之正（洛阳师范学院）
报告时间: 2023-10.24 14:30-15:30
报告链接: 腾讯会议ID: 936 984 488
信息来源:
https://math.bnu.edu.cn/xzbg/ztbg/74df2bef10444bf7bbf59a8bca22d6b8.htm
报告摘要:
组合数学起源于我国先秦文献记载的神话传说“河图”“洛书”，可追溯到四千多年前的大禹治水时代。本报告先从洛阳深厚的文化渊源讲起，讲述组合数学的起源，河图洛书的本源内涵、数学含义以及在当今在数学中的地位，最后讲述我国古代数学家以及当代组合学家的一些杰出贡献等。
张之正，二级教授，博士毕业于大连理工大学，南京大学与南开大学双站博士后；先后主持国家自然科学基金项目7项，其中面上项目5项；为河南省优秀专家，河南省学术技术带头人，河南省五一劳动奖章获得者，河南省高校创新人才培养工程培养对象，教育部国培专家。是中国工业与应用数学学会图论组合及应用专业委员会副主任与编码、密码和相关组合理论专业委员会委员，中国数学会组合数学与图论专业委员会委员，河南省数学会副理事长，河南省中小学数学学科教育教学研究基地首席专家等。
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4. Acceleration of Reinforcement Learning Facilitated by Decomposable Structures of MDPs
报告人: Hao Jin (PKU)
报告时间: 2023-10-26 16:00-17:00
报告地点: 腾讯会议ID: 551-1675-5419
信息来源:
https://www.math.pku.edu.cn/kxyj/xsbg/tlb/informationsciences/153473.htm
报告摘要:
In many real-life applications of reinforcement learning, the learning agent is challenged with either large state space or large action space, which results in high sample complexity. Fortunately, such Markov Decision Processes (MDPs) are usually believed to have decomposable structures. Decomposability enables many distributed algorithms to efficiently solve the learning problems.
In this talk, we introduce various methods for efficiently solving large-scale MDPs. Specifically, we start from traditional techniques of decomposing large-scale MDPs and move on to modern methods of hierarchical reinforcement learning (HRL). Although original algorithms of HRL require a central 'manager' to coordinate 'workers' of subtasks, there is a recent trend to a fully distributed design without a central manger. These distributed HRL algorithms are theoretically shown to achieve lower sample complexity under assumptions on the decomposable structures of MDPs.
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5. Optimal Transport in Machine Learning
Speaker: 孙剑（西安交通大学）
Time: 2023-10-27 14:30-15:30
Venue: Tencent Meeting ID: 455804772 Password: 803534
Info Source:
https://ins.sjtu.edu.cn/seminars/2424
Abstract:
Optimal transport was originally proposed to transport the mass between two probability measures with minimal cost, and has been widely investigated in theory, algorithm and applications. Optimal transport can be taken as a tool for learning distribution transform and designing deep generative model. In this talk, I will briefly introduce the optimal transport from the perspective of machine learning. I will present our research on the optimal transport with keypoints-guidance and its extension to deep generative model, with applications in image synthesis and domain adaptation/generalization.
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6. On perfect and insulated conductivity problems
信息来源: 材料科学中的分析与计算系列短课
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