91桃色视频

课程一   

• 课程名称：大语言模型理论基础探讨

• 授课老师：苏炜杰，University of Pennsylvania

• 授课时间：2025/7/7-2025/7/10,  2025/7/14-2025/7/17,  9:00-11:00

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• 教学内容：

• 当前人工智能领域在大语言模型（尝尝惭蝉）的发展与理解上呈现出鲜明的对比。一方面，这些高度复杂的系统主要通过实验经验推动，缺乏严格的数学理论指导；另一方面，大多数对于础滨模型的理论分析往往聚焦于过度简化的机制——例如罢谤补苍蝉蹿辞谤尘别谤中的基础注意力模型——这些分析仅提供局部视角，通常难以捕捉系统的全局复杂性。在本课程中，我们认为这一差距可能源于现有数学理论不足以分析如此高度复杂的系统。在等待更全面的数学理论发展的同时，我们提出采用一种称为“第二性原理”的方法，以满足实际应用的迫切需求。与其深入探究模型内部的具体机制，我们更倾向于将大语言模型视为在某些结构假设下的黑箱系统。基于这一思路，我们将探讨与大语言模型相关的一系列话题，包括优化器、分词、水印、评估、公平性以及础滨智能体的机制设计等。我们的重点在于展示如何从优化、统计学和经济学的理论视角出发，获得实际改进，而无需进行大量的实验尝试。

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• 本短期课程面向那些对理论感兴趣但仍希望超越纯实验方法参与础滨开发的学生。课程不要求具备大语言模型实验实现的经验。

课程二

• 课程名称：随机计算(Stochastic computing)

• 授课老师：李沁 & Samuel N.Stechmann，University of Wisconsin–Madison

• 授课时间：2025/7/11,  2025/7/14-2025/7/18,  14:00-17:00

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• 教学内容：

• 随着数据驱动方法在科学与工程领域的广泛应用，随机建模与计算方法已成为复杂系统研究的重要工具。《随机计算》课程旨在系统讲授如何利用概率工具、随机过程和数值方法解决涉及随机性的问题，涵盖从理论建模到数值模拟的全流程。课程融合了随机微分方程（厂顿贰）、随机模拟、惭颁惭颁采样、粒子系统和现代深度学习中的随机优化方法等前沿内容，帮助学生掌握面向高维、非线性、不确定系统的建模与计算技能。

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• 教学大纲：

• (1) 布朗运动、伊藤公式、随机微分方程（SDE）、伊藤等距性（Ito Isometry）[3学时]

  (2) 随机微分方程的模拟，SDE解的可视化，Fokker-Planck方程，平衡概率密度函数（PDF），自相关函数，加性与乘性噪声 [3学时]

  (3) Euler-Maruyama方法，强收敛与弱收敛，Milstein方法，Feynman-Kac公式 [3学时]

  (4) 数据同化，参数估计 [3学时]

  (5) 采样方法，包括MCMC类型与基于Score的类型。 相关证明包括：耦合方法（Coupling Method）、Langevin Monte Carlo（LMC）收敛性、一般MCMC方法、Girsanov定理 [3学时]

  (6) 带有平均场极限的相互作用粒子系统，相关示例包括：集合Kalman方法、神经网络极限、Transformer模型以及其他全局优化求解器 [3学时]

课程叁?

• 课程名称：Nonlinear Dynamics and Applications

• 授课老师：Miguel A.F. Sanjuán，Universidad Rey Juan Carlos, Madrid, Spain，Royal Academy of Sciences of Spain

• 授课时间：2025/7/21-2025/7/25,  2025/7/28-2025/8/1,  9:00-11:00

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• 教学内容：

• The goal of the course on Nonlinear Dynamics and Applications is to introduce and describe chaotic phenomena as well as fundamental concepts of complex systems theory in physical systems. The course aims to provide a general overview of nonlinear dynamical systems and their applications across various scientific and technological fields. Special attention will be given to presenting concepts clearly, fostering students’ appreciation for the dynamic perspective this discipline offers, and highlighting its connection to real-world applications.

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  As chaos theory deals with complex dynamics in simple systems, numerical studies have played a central role in the development of Nonlinear Dynamics and remain a key tool in learning. Therefore, numerical explorations will be essential throughout the course. A defining feature of this course is the visualization of nonlinear and chaotic physical phenomena using various multimedia tools.
  
  Objectives: This course aims to:
  ?  Introduce the basic concepts of Nonlinear Dynamics, Chaos Theory, and Complex Systems
  ?  Present examples of dynamical systems applied in basic sciences and engineering
  ?  Show how scientific computing can solve and analyze real-world problems
  ?  Provide a broad overview of many compelling problems from an interdisciplinary perspective
  ?  Visualize chaotic and nonlinear physical phenomena through simulations
  
  Duration: 20 hours over 2 weeks
  
  Methodology:
  The specific methodology for this course includes:
  ?  Classroom presentation of theoretical foundations
  ?  Key concept demonstrations through computer-based numerical simulations
  ?  Use of the software packages DYNAMICS and CHAOS FOR JAVA, tailored to dynamical systems

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• 教学大纲：

• 1. Introduction to Nonlinear Dynamics, Chaos Theory, and Complexity
  ?  Introduction and course overview
  ?  Basic notions of dynamical systems: dynamics, chaos, fractals, and complex systems
  ?  Historical approach to nonlinear dynamics
  
  2. One-Dimensional Discrete Dynamical Systems
  ?  Discrete dynamical systems: maps or iterations
  ?  Fixed points: analytical and graphical methods
  ?  A simple one-dimensional map: the logistic map
  ?  Bifurcations and chaos in the logistic map
  ?  Feigenbaum bifurcation diagrams
  
  3. Two-Dimensional Discrete Dynamical Systems
  ?  Modeling natural phenomena
  ?  Classification of fixed points
  ?  Linear and nonlinear maps
  ?  Stable and unstable manifolds
  ?  Basins of attraction and their boundaries
  ?  Dynamics of the bouncing ball
  
  4. Continuous Dynamical Systems Theory
  ?  Discrete vs. continuous dynamical systems
  ?  The logistic differential equation and mass-spring oscillating system
  ?  One-dimensional continuous dynamical systems
  ?  Continuous systems in the plane: phase space methods, Poincaré section
  ?  Some numerical methods for solving ODEs
  ?  Applications in ecology: the Lotka-Volterra system
  
  5. Bifurcations and Stability
  ?  Basic notion of bifurcation
  ?  Saddle-node bifurcation
  ?  Transcritical bifurcation
  ?  Pitchfork bifurcation
  ?  Examples of applications in science and engineering
  
  6. Chaotic Dynamical Systems
  ?  Chaos in discrete systems: the Hénon chaotic attractor
  ?  Examples of chaotic attractors in discrete and continuous systems
  ?  The Lorenz system, the R?ssler system, and Chua's electronic circuit
  ?  Notion of Lyapunov exponent and chaos
  ?  Numerical computation of the maximal Lyapunov exponent
  
  7. Fractals and Fractal Dimension
  ?  The Cantor set
  ?  Examples of fractals
  ?  Fractal dimension and methods for calculating it
  ?  Fractals in dynamical systems: fractal structures and chaotic dynamics
  ?  Algorithms for constructing fractals
  
  8. Hamiltonian Chaos
  ?  Introduction, motivations, and examples: the frictionless mass-spring system
  ?  Hamilton's equations and properties of Hamiltonian systems
  ?  The conservative pendulum
  ?  Area-preserving discrete maps
  ?  The Chirikov standard map
  ?  Physical examples: chaotic scattering
  
  9. Introduction to Nonlinear Time Series
  ?  Introduction to time series
  ?  Nonlinear dynamics and data analysis
  ?  Methods to detect chaos in time series
  ?  Application examples
  
  10. Introduction to Complexity
  ?  Basic concepts in complex systems
  ?  Complexity and interdisciplinarity
  ?  Emergence, nonlinear dynamics, and complexity
  ?  Some illustrative examples
   

  Seminars on different applications

  1. Nonlinear Dynamics, Chaos Theory and Complex Systems: A historical perspective
  2. Symphony of the uncertainty (不确定) in three movements
  3. Physics and Dynamics of Cancer: Tumor and Immune Cell Interactions
  4. New Advances in Measuring the Unpredictability of Physical Systems: Basin Entropy and Wada Basins
  5. Exploring Noisy Hamiltonian Dynamics
  6. Partial Control and Beyond: Forcing Escapes and Controlling Chaotic Transients with the Safety Function
  7. Binary Black Hole Shadows: Chaos in General Relativity
  8. Artificial Intelligence, Prediction and Understanding: The Role of Dynamical Systems
  9. Chaos and the Three-Body Problem
  10. An Overview on Contributions to Nonlinear Dynamics, Chaos and Complex Systems

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• Bibliography
  Main References
  1. K.T. Alligood, T.D. Sauer, J.A. Yorke – Chaos: An Introduction to Dynamical Systems, Springer, 1997.
  2. S.H. Strogatz – Nonlinear Dynamics and Chaos, Addison-Wesley, 1994.
  3. D. Kaplan, L. Glass – Understanding Nonlinear Dynamics, Springer, 1995.
  4. S. Wiggins – Ordinary Differential Equations: A Dynamical Point of View, World Scientific, 2023.
  5. J.C. Sprott – Chaos and Time-Series Analysis, Oxford University Press, 2003.
  6. H.-O. Peitgen, H. Jürgens, D. Saupe – Chaos and Fractals, Springer, 1992.
  7. Peter Erdi – Complexity Explained, Springer, 2007.
  
  Other References of Interest
  1. S. Lynch – Dynamical Systems with Applications using MAPLE, Birkh?user, 2001.
  2. E.A. Jackson – Perspectives of Nonlinear Dynamics (Vols. 1 & 2), Cambridge University Press, 1991.
  3. R. Clark Robinson – An Introduction to Dynamical Systems: Continuous and Discrete, Pearson/Prentice Hall, 2004.
  4. T. Kapitaniak – Chaos for Engineers, Springer, 1998.
  5. G.W. Flake – The Computational Beauty of Nature, MIT Press, 2001.
  6. E. Ott – Chaos in Dynamical Systems, Cambridge University Press, 1993.
  7. T. Tél, M. Gruiz – Chaotic Dynamics, Cambridge University Press, 2006.
  
  Algorithms, Software, and Fractals
  1. H.E. Nusse, J.A. Yorke – Dynamics: Numerical Explorations, 2nd Ed., Springer, 1997.
  2. H.-O. Peitgen, D. Saupe (eds.) – The Science of Fractal Images, Springer, 1988.
  3. T.S. Parker, L.O. Chua – Practical Numerical Algorithms for Chaotic Systems, Springer, 1989.
  4. B. West, S. Strogatz, J.M. McDill, J. Cantwell – Interactive Differential Equations, Addison-Wesley, 1997.
  
  Various Applications
  1. P. Ball – The Self-Made Tapestry: Pattern Formation in Nature, Oxford University Press, 1999.
  2. F.C. Moon – Chaotic and Fractal Dynamics: An Introduction for Applied Scientists and Engineers, Wiley, 1992.
  3. H. Goldstein, C. Poole, J. Safko – Classical Mechanics (3rd ed.), Addison-Wesley, 2002. (Chapter 11 on chaos)
  
  Complexity
  1. Melanie Mitchell – Complexity: A Guided Tour, Oxford University Press, 2009.
   

   

课程四

• 课程名称：计算数学中的量子算法

• 授课老师：安冬，北京大学

• 授课时间：2025/7/21-2025/7/25,  2025/7/28-2025/8/1,  14:00-16:00

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• 教学内容：

• 量子计算是基于量子力学原理进行计算的新型模式，有望革命性地改变科学计算，突破经典计算的算力瓶颈。本课程旨在介绍量子算法的数理基础，及其在计算数学重要问题中的应用。在本课程中，我们将从量子算法的基本概念和性质开始，逐步介绍量子算法的主要思想、基本线性代数运算的量子算法、以及重要的量子算法基元，随后介绍针对大规模线性方程组、微分方程组、特征值问题、矩阵函数等问题的量子算法，并分析它们的计算复杂度。

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• 教学大纲：

• (1) 量子算法基础：量子力学的基本原理、量子算法的基本概念
• (2) 量子数值线性代数基础：矩阵块编码、Hadamard测试、线性酉组合
• (3) 量子算法基元：量子Fourier变换、量子搜索算法、量子振幅估计与放大算法、量子相位估计算法
• (4) 线性方程组的量子算法：Harrow-Hassidim-Lloyd算法、基于线性酉组合的算法
• (5) 微分方程的量子算法：量子欧拉法、量子多步法、基于线性酉组合的算法
• (6) 矩阵函数的量子算法：量子化、量子信号处理、量子奇异值变换算法、矩阵函数量子算法的应用
• (7) 特征值问题的量子算法：绝热量子计算

课程五

• 课程名称：大模型的优化理论和算法

• 授课老师：孙若愚，香港中文大学(深圳)

• 授课时间：2025/7/28-2025/8/1,  14:00-17:00

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• 教学内容：

• 本课程系统讲解基础大模型（large foundation models）的优化理论和算法。将从收敛速度、全局优化等理论视角出发，介绍大模型训练中的优化理论和算法技巧。本课程涵盖反向传播、随机梯度下降、正则化、自适应优化算法、二阶优化算法、全局几何图景、高效监督微调等内容，帮助学员了解和掌握大模型高效训练和微调的主要理论和算法。

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• 教学大纲：

• （1）大规模优化的基础理论和算法；
  （2）神经网络的训练稳定性和正则化技术；
  （3）自适应优化算法和理论；
  （4）神经网络全局优化的几何图景；
  （5）大模型优化的扩展法则；
  （6）大模型的高效监督微调算法；
  （7）大模型的遗忘和连续学习算法。