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UID:20260602T200406EDT-8952wmvVLL@132.216.98.100
DTSTAMP:20260603T000406Z
DESCRIPTION:Title: On the TAP equations and the local magnetization of the 
 Sherrington-Kirkpatrick (SK) mode.\n\nAbstract: The TAP equations for the 
 Sherrington-Kirkpatrick model are a set of high-dimensional\, nonlinear\, 
 fixed-point equations of the local magnetization. In the seminal work [Com
 m. Math. Phys.\, 325(1):333-366\, 2014]\, Bolthausen introduced an iterati
 ve scheme that produces an asymptotic solution to the TAP equations if the
  model lies below the Almeida-Thouless transition line (“high temperature 
 regime”). However\, it was unclear if this asymptotic solution coincides w
 ith the local magnetization. In this talk\, I will introduce a new iterati
 ve scheme\, motivated by the cavity equations of the SK model\, and show t
 hat the new scheme is asymptotically the same as the so-called Approximate
  Message Passing (AMP) algorithm\, a generalization of Bolthausen's iterat
 ion\, that has been popularly adapted in compressed sensing\, Bayesian inf
 erences\, etc. Based on this\, we confirm that our cavity iteration (and h
 ence Bolthausen's iteration) converges to the local magnetization as long 
 as the overlap is locally uniformly concentrated. If time permits\, I will
  also briefly discuss the TAP equations in the low temperature regime. The
  talk is based on joint works with Wei-Kuo Chen (University of Minnesota).
 \n\nZoom link: https://mcgill.zoom.us/j/89737173009?pwd=UzlwZkVPK0RnYXk4VG
 M2aXo4V3Q2QT09\n\n \n
DTSTART:20230119T163000Z
DTEND:20230119T173000Z
LOCATION:Room 1214\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Si Tang (Lehigh)
URL:/mathstat/channels/event/si-tang-lehigh-344934
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