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Statistical Mechanics (Tutorial) by Chandan Dasgupta

1,332 views · Published 7 February 2018 · 1:26:59 · Indexed 21 September 2026

Channel: International Centre for Theoretical Sciences · 2018 · Science & Technology

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Statistical Physics Methods in Machine Learning

DATE: 26 December 2017 to 30 December 2017
VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru
The theme of this Discussion Meeting is the analysis of distributed/networked algorithms in machine learning and theoretical computer science in the "thermodynamic" limit of large number of variables. Methods from statistical physics (eg various mean-field approaches) simplify the performance analysis of these algorithms in the limit of many variables. In particular, phase-transition like phenomena appear where the performance can undergo a discontinuous change as an underlying parameter is continuously varied. A provocative question to be explored at the meeting is whether these methods can shed theoretical light into the workings of deep networks for machine learning.

The Discussion Meeting will aim to facilitate interaction between theoretical computer scientists, statistical physicists, machine learning researchers and mathematicians interested in these questions. Examples of specific topics to be covered include (but are not limited to) problems such as phase transitions in optimization and learning algorithms, matrix approximation, mixing in large networks, sub-linear time algorithms, learning theory and non convex optimization. The meeting will allow structured and and unstructured interactions among the participants around the main theme.

 

*Participation is by invitation only.

CONTACT US: [email protected]

PROGRAM LINK: https://www.icts.res.in/discussion-meeting/SPMML2017

Table of Contents (powered by https://videoken.com)
0:00:00 Start 
0:00:11 Tutorial on Statistical Physics
0:02:08 Equilibrium Statistical Physics 
0:05:15 Thermodynamic (equilibrium) average:
0:07:46 Canonical Ensemble: p(n) = expl-H(n)/T]
0:10:38 Entropy S = 
0:15:43 Connections with constraint satisfaction problems
0:19:12 Local minima of the Hamiltonian play an important role in the dynamics of the system.
0:22:17 Canonical Ensemble: p(n) = expl-H(n)/T] T: Absolute temperature
0:24:48 Simulated Annealing
0:26:37 Phase Transitions
0:28:09 First-order Phase Transitions
0:31:22 Spontaneous Symmetry Breaking
0:33:20 Symmetries of the Hamiltonian 
0:35:59 The Ferromagnetic Ising Model
0:36:54 Exact solution in two dimensions (Onsager)
0:38:41 Ising Hamiltonian: H = - Jijojoj - ho; For h=0,
0:39:35 Typically, (order-disorder) phase transitions occur due to a competition between energy and entropy.
0:40:54 This is possible only in the thermodynamic limit
0:52:01 Mean Field Theory
1:01:03 Mean field theory is exact for systems with infinite range interactions
1:05:27 Disordered Systems
1:06:05 H is different in different parts of the system The system is not translationally invariant
1:09:38 Spin Glasses 
1:10:33 Frustration
1:13:29 Edwards -Anderson Model
1:15:25 Spin Glass Phase 
1:19:17 Thouless-Anderson-Palmer Equations
1:21:40 TAP Equations (contd.)
1:22:22 Q&A

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