EE 378 B : Syllabus

Here is a rough syllabus (precise schedule will depend on the progress in class, and suggestions/feedback are welcome).

1. The p-spin model and tensor PCA

   1. Introduction

   2. Replica method and replica symmetric calculation

   3. One-step replica symmetry breaking

   4. The expected number of critical points

2. synchronization and the Sherrington-Kirkpatrick model

   1. Introduction

   2. Replica symmetric calculation and its inconsistency

   3. Full replica symmetry breaking and its interpretation

   4. Random overlap structures and the variational principle

   5. Ultrametricity

3. The Hopfield model of associative memories

   1. Replica solution

   2. Intepretation and algorithms

4. The cavity method

   1. Introduction

   2. Connection with message passing algorithms

5. Depending on time/interest might treat some of the followig

   1. High-dimensional regression

   2. Sparse PCA and the hidden submatrix problem

   3. Models on sparse graphs

   4. The stochastick block model

   5. Random -satisfiability