CMSA Quantum Matter in Mathematics and Physics: The information bottleneck: A numerical microscope for order parameters
Zohar Ringel - Hebrew University
The analysis of complex systems often hinges on our ability to extract the relevant degrees of freedom from among the many others. Recently the information bottleneck (IB), a signal processing tool, was proposed as an unbiased means for such order parameter extraction. While IB optimization was considered intractable for many years, new deep-learning-based techniques seem to solve it quite efficiently. In this talk, I'll introduce IB in the real-space renormalization context (a.k.a. RSMI), along with two recent theoretical results. One links IB optimization to the short-rangeness of coarse-grained Hamiltonians. The other provides a dictionary between the quantities extracted in IB, understood only qualitatively thus far, and relevant operators in the underlying field theory (or eigenvectors of the transfer matrix). Apart from relating field-theory and information, these results suggest that deep learning in conjunction with IB can provide useful and interpretable tools for studying complex systems.