神经网络的统计力学(英文版)(精)/人工智能科学与技术丛书

1 Introduction References 2 Spin Glass Models and Cavity Method 2.1 Multi-spin Interaction Models 2.2 Cavity Method 2.3 From Cavity Method to Message Passing Algorithms References 3 Variational Mean-Field Theory and Belief Propagation 3.1 Variational Method 3.2 Variational Free Energy 3.2.1 Mean-Field Approximation 3.2.2 Bethe Approximation 3.2.3 From the Bethe to Naive Mean-Field Approximation 3.3 Mean-Field Inverse Ising Problem References 4 Monte Carlo Simulation Methods 4.1 Monte Carlo Method 4.2 Importance Sampling 4.3 Markov Chain Sampling 4.4 Monte Carlo Simulations in Statistical Physics 4.4.1 Metropolis Algorithm 4.4.2 Parallel Tempering Monte Carlo References 5 High-Temperature Expansion 5.1 Statistical Physics Seting 5.2 High-Temperature Expansion 5.3 Properties of the TAP Equation References 6 Nishimori Line 6.1 Model Setting 6.2 Exact Result for Internal Energy 6.3 Proof of No RSB Effects on the Nishimori Line References 7 Random Energy Model 7.1 Model Setting 7.2 Phase Diagram References 8 Statistical Mechanical Theory of Hopfield Model 8.1 Hopfield Model 8.2 Replica Method 8.2.1 Replica-Symmetric Ansatz 8.2.2 Zero-Temperature Limit 8.3 Phase Diagram 8.4 Hopfield Model with Arbitrary Hebbian Length 8.4.1 Computation of the Disorder-Averaged Free Energy 8.4.2 Derivation of Saddle-Point Equations 8.4.3 Computation Transformation to Solve the SDE 8.4.4 Zero-Te mperature Limit References 9 Replica Symmetry and Replica Symmetry Breaking