神经网络的统计力学课程优惠上线！
导语
课程介绍
课程介绍
第 28 讲：随机矩阵之非厄米篇：索普林斯基遇见麦克斯韦
课程负责人
课程负责人
加入课程，开始学习
加入课程，开始学习
为了庆祝课程完整上线1年，让更多的人体验学习课程的优质内容，我们特做出如下优惠方案：
1. 价格调整为49元；
2. 同时对于2个月内（2024年4月15日-至今）购买本课程的用户，将返还价值200元的积分到账户，可以用户消费（不可提现）；
3. 加入「AI by Complexity」读书会的成员，开放4个月课程学习权限（2024年7月-10月）。
课程链接：https://campus.swarma.org/course/4543?from=wechat
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第三步：扫码添加助教微信，入群本课程可开发票。
核心参考书籍
核心参考书籍
书籍目录（详版）：
Chapter 1: IntroductionChapter 2: Spin Glass Models and Cavity Method
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2.1 Multi-spin Interaction Models
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2.2 Cavity Method
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2.3 From Cavity Method to Message Passing Algorithms
Chapter 3: Variational Mean-Field Theory and Belief Propagation
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3.1 Variational Method
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3.2 Variational Free Energy
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3.3 Mean-Field Inverse Ising Problem
Chapter 4: Monte Carlo Simulation Methods
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4.1 Monte Carlo Method
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4.2 Importance Sampling
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4.3 Markov Chain Sampling
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4.4 Monte Carlo Simulations in Statistical Physics
Chapter 5: High-Temperature Expansion
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5.1 Statistical Physics Setting
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5.2 High-Temperature Expansion
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5.3 Properties of the TAP Equation
Chapter 6: Nishimori Line
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6.1 Model Setting
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6.2 Exact Result for Internal Energy
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6.3 Proof of No RSB Effects on the Nishimori Line
Chapter 7: Random Energy Model
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7.1 Model Setting
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7.2 Phase Diagram
Chapter 8: Statistical Mechanical Theory of Hopfield Model
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8.1 Hopfield Model
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8.2 Replica Method
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8.3 Phase Diagram
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8.4 Hopfield Model with Arbitrary Hebbian Length
Chapter 9: Replica Symmetry and Replica Symmetry Breaking
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9.1 Generalized Free Energy and Complexity of States
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9.2 Applications to Constraint Satisfaction Problems
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9.3 More Steps of Replica Symmetry Breaking
Chapter 10: Statistical Mechanics of Restricted Boltzmann Machine
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10.1 Boltzmann Machine
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10.2 Restricted Boltzmann Machine
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10.3 Free Energy Calculation
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10.4 Thermodynamic Quantities Related to Learning
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10.5 Stability Analysis
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10.6 Variational Mean-Field Theory for Training Binary RBMs
Chapter 11: Simplest Model of Unsupervised Learning with Binary
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11.1 Model Setting
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11.2 Derivation of sMP and AMP Equations
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11.3 Replica Computation
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11.4 Phase Transitions
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11.5 Measuring the Temperature of Dataset
Chapter 12: Inherent-Symmetry Breaking in Unsupervised Learning
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12.1 Model Setting
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12.2 Phase Diagram
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12.3 Hyper-Parameters Inference
Chapter 13: Mean-Field Theory of Ising Perceptron
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13.1 Ising Perceptron model
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13.2 Message-Passing-Based Learning
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13.3 Replica Analysis
Chapter 14: Mean-Field Model of Multi-layered Perceptron
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14.1 Random Active Path Model
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14.2 Mean-Field Training Algorithms
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14.3 Spike and Slab Model
Chapter 15: Mean-Field Theory of Dimension Reduction in Neural Networks
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15.1 Mean-Field Model
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15.2 Linear Dimensionality and Correlation Strength
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15.3 Dimension Reduction with Correlated Synapses
Chapter 16: Chaos Theory of Random Recurrent Neural Networks
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16.1 Spiking and Rate Models
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16.2 Dynamical Mean-Field Theory
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16.3 Lyapunov Exponent and Chaos
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16.4 Excitation-Inhibition Balance Theory
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16.5 Training Recurrent Neural Networks
Chapter 17: Statistical Mechanics of Random Matrices
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17.1 Spectral Density
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17.2 Replica Method and Semi-circle Law
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17.3 Cavity Approach and Marchenko
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17.4 Spectral Densities of Random Asymmetric Matrices
Chapter 18: Perspectives
AI By Complexity读书会招募中
集智俱乐部联合加利福尼亚大学圣迭戈分校助理教授尤亦庄、北京师范大学副教授刘宇、北京师范大学系统科学学院在读博士张章、牟牧云和在读硕士杨明哲、清华大学在读博士田洋共同发起「AI By Complexity」读书会，探究如何度量复杂系统的“好坏”？如何理解复杂系统的机制？这些理解是否可以启发我们设计更好的AI模型？在本质上帮助我们设计更好的AI系统。读书会于6月10日开始，每周一晚上20:00-22:00举办。欢迎从事相关领域研究、对AI+Complexity感兴趣的朋友们报名读书会交流！
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