QLS Seminar via Zoom - 2 March 2021 at 15.00 CET

[QLS]

Dear All,

on Tuesday, 2 March at 15.00 CET, Francesco Camilli, Universita' di 
Bologna, will give a seminar titled:

*"*The deep Boltzmann machine on the Nishimori line"

Abstract: In this talk I will address the direct problem of the deep 
(restricted) Boltzmann machine (DBM) in the form of a multi-partite 
spin-glass model. Multi-partite models emerge as a natural 
generalization of mean field models where the permutation symmetry among 
the spins is weakened and preserved only inside each partition of the 
system. These models were studied both in deterministic and disordered 
settings and in general their solution requires a technical convexity 
assumption on the interactions that does not hold for the DBM. This 
feature makes it a challenging problem. Indeed, the DBM is still 
unsolved for centered interactions. On the contrary, in my talk I will 
show how to exactly and rigorously compute its thermodynamic limit on 
the Nishimori line, a particular subregion of the phase space where 
replica symmetry is proved to hold. As I will try to explain, besides 
its interest in Statistical Mechanics the Nishimori line also provides a 
bridge between disordered systems and Statistical Inference. Finally, I 
will discuss how the geometry of the model, especially the relative 
sizes of the layers, can influence the phase transition. This is 
expected to provide some insight on the optimal shape of a deep 
architecture in order to have a non trivial spontaneous magnetization.

https://zoom.us/j/475819702 <https://zoom.us/j/475819702>

Meeting ID: 475-819-702

If you haven't registered for previous QLS webinars, please contact 
qls at ictp.it to obtain the PASSWORD for this zoom meeting.

Barbara Valassi for QLS Section