Symmetries and phase diagrams with real-space mutual information neural estimation

@article{Gkmen2021SymmetriesAP,
  title={Symmetries and phase diagrams with real-space mutual information neural estimation},
  author={Doruk Efe G{\"o}kmen and Zohar Ringel and Sebastian D. Huber and Maciej Koch-Janusz},
  journal={Physical Review E},
  year={2021}
}
Doruk Efe Gökmen, Zohar Ringel, Sebastian D. Huber, and Maciej Koch-Janusz 3, 4 Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel Department of Physics, University of Zurich, 8057 Zurich, Switzerland James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA (Dated: October 19, 2021) 
3 Citations
Relevance in the Renormalization Group and in Information Theory
TLDR
It is shown analytically that for statistical physical systems described by a field theory the relevant degrees of freedom found using IB compression indeed correspond to operators with the lowest scaling dimensions, which provides a dictionary connecting two distinct theoretical toolboxes, and an example of constructively incorporating physical interpretability in applications of deep learning in physics.
An Information-Theoretic Framework for Optimal Design: Analysis of Protocols for Estimating Soft Tissue Parameters in Biaxial Experiments
TLDR
A new framework for optimal design based on the information-theoretic measures of mutual information, conditional mutual information and their combination is proposed and is tested on the analysis of protocols in a biaxial experiment of soft tissues for the estimation of hyperelastic constitutive model parameters.
Statistical Physics through the Lens of Real-Space Mutual Information.
TLDR
An algorithm employing state-of-the-art results in machine-learning-based estimation of information-theoretic quantities is presented, and this advance is used to develop a new paradigm in identifying the most relevant operators describing properties of the system.

References

SHOWING 1-10 OF 63 REFERENCES
Mutual information, neural networks and the renormalization group
TLDR
This work demonstrates a machine-learning algorithm capable of identifying the relevant degrees of freedom of a system and executing RG steps iteratively without any prior knowledge about the system, and applies the algorithm to classical statistical physics problems in one and two dimensions.
Optimal Renormalization Group Transformation from Information Theory
TLDR
This work investigates analytically the RG coarse-graining procedure and the renormalized Hamiltonian, which the RSMI algorithm defines, and shows that a perfect RSMI coarse- graining generically does not increase the range of a short-ranged Hamiltonian in any dimension.
Relevance in the Renormalization Group and in Information Theory
TLDR
It is shown analytically that for statistical physical systems described by a field theory the relevant degrees of freedom found using IB compression indeed correspond to operators with the lowest scaling dimensions, which provides a dictionary connecting two distinct theoretical toolboxes, and an example of constructively incorporating physical interpretability in applications of deep learning in physics.
Machine learning for quantum matter
ABSTRACT Quantum matter, the research field studying phases of matter whose properties are intrinsically quantum mechanical, draws from areas as diverse as hard condensed matter physics, materials
Regularity properties and pathologies of position-space renormalization-group transformations: Scope and limitations of Gibbsian theory
We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Our main
Information theoretic aspects of the two-dimensional Ising model.
  • H. LauP. Grassberger
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2013
TLDR
It is conjecture that such logarithmic divergence happens generically for any one-dimensional subset of sites at any two-dimensional second-order phase transition in the square lattice Ising model.
Area laws in quantum systems: mutual information and correlations.
TLDR
This Letter shows that the holographic principle not only emerges in the search for new Planck-scale laws but also in lattice models of classical and quantum physics: the information contained in part of a system in thermal equilibrium obeys an area law.
Correlations and confinement in nonplanar two-dimensional dimer models
TLDR
It is found that, in the presence of longer dimers preserving the bipartite graph structure, algebraic correlations persist, and the leading decay of dimer correlations remains 1/r^2, although the logarithmic peaks present in the dimer structure factor of the nearest-neighbour model vanish.
On Variational Bounds of Mutual Information
TLDR
This work introduces a continuum of lower bounds that encompasses previous bounds and flexibly trades off bias and variance and demonstrates the effectiveness of these new bounds for estimation and representation learning.
Estimating mutual information.
TLDR
Two classes of improved estimators for mutual information M(X,Y), from samples of random points distributed according to some joint probability density mu(x,y), based on entropy estimates from k -nearest neighbor distances are presented.
...
...