Koch-Janusz & Ringel: Mutual information, neural networks and the renormalization group
Journal Club 16.09.21
Claudia Merger
"Job" of RG: Keep important degrees of freedom (DOFs), integrate out the rest
"Job" of RG: Keep important degrees of freedom (DOFs), integrate out the rest
Difficulty: Which DOFs are important?
"Job" of RG: Keep important degrees of freedom (DOFs), integrate out the rest
Difficulty: Which DOFs are important?
Idea: Let a neural network (NN) find the answer for you
RSMI algorithm
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RSMI algorithm
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Application to Ising model
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Application to dimer model
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Discussion
RSMI algorithm
RSMI algorithm
maximize
RSMI algorithm
maximize
RSMI algorithm
Variant of "Information Bottleneck method"
3 restricted Boltzmann machines:
2 trained with contrastive divergence algorithm, learn and
3 restricted Boltzmann machines:
2 trained with contrastive divergence algorithm, learn and
Third learns
3 restricted Boltzmann machines:
2 trained with contrastive divergence algorithm, learn and
Third learns
using
3 restricted Boltzmann machines:
2 trained with contrastive divergence algorithm, learn and
Third learns
using
to maximize
Then: Sample from
and iterate the whole procedure
Application to Ising model
Application to Ising model
Application to Ising model
= Kardanoff
Block-spin
Application to Dimer model
Discussion
- RSMI algorithm maximizes mutual information btw. input and hidden DOFs
- Without prior knowledge, learns to perform RG coarse graining in two examples
- Claim: Can be used to find relevant DOFs in cases where they are unknown
Mutual information
Goal: Train on
have: ,
Train:
use:
Estimating temperature
deck
By merger
deck
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