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Updated: Sep 28, 2025
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Setting Limits on Supersymmetry Using Simplified Models
Published on: November 15, 2013
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Gaussian Information Bottleneck and the Non-Perturbative Renormalization Group.
Adam G Kline1, Stephanie E Palmer2
1Department of Physics, The University of Chicago, Chicago IL 60637.
New Journal of Physics
|April 4, 2022
Summary
The renormalization group (RG) and information bottleneck (IB) are formally equivalent. This equivalence allows IB to impose large-scale structures, like biological function, onto RG procedures for complex systems.
Area of Science:
- Theoretical Physics
- Computational Neuroscience
- Machine Learning
Background:
- Renormalization Group (RG) techniques analyze collective behavior in many-body systems.
- Information Bottleneck (IB) is a dimensionality-reduction framework used in complex systems, optimizing signal compression while preserving relevance.
- Previous work suggests a link between RG and IB through neural network discovery.
Purpose of the Study:
- To investigate the formal equivalence between Renormalization Group (RG) and Information Bottleneck (IB) frameworks.
- To explore the application of IB in discovering and interpreting emergent low-dimensional structures in complex systems.
- To determine if IB can guide or impose structure on RG procedures.
Main Methods:
- Formal mapping between soft-cutoff non-perturbative RG techniques and IB using non-deterministic coarsening maps.
- Focusing on Gaussian statistics (GIB) for exact, closed-form solutions in IB.
- Analyzing the semigroup structure of GIB and identifying the associated RG cutoff scheme.
Main Results:
- A formal equivalence is established between a class of RG techniques and the IB framework.
- Gaussian IB (GIB) exhibits a semigroup structure, ensuring successive transformations remain optimal.
- The RG cutoff scheme can be identified within the GIB framework.
Conclusions:
- The study demonstrates a formal equivalence between RG and IB, unifying two distinct theoretical approaches.
- Information Bottleneck (IB) can be utilized to impose 'large scale' structures, such as biological function, onto RG procedures.
- This finding opens new avenues for applying RG concepts in fields like biology and computer science through the lens of IB.
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