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UID:0-1131@lptms.universite-paris-saclay.fr
DTSTART;TZID=Europe/Paris:20260612T160000
DTEND;TZID=Europe/Paris:20260612T173000
DTSTAMP:20260604T163645Z
URL:http://www.lptms.universite-paris-saclay.fr/seminars/mlpp-seminar-g-mo
 ngillo/
SUMMARY:MLP@P seminar: Gianluigi Mongillo\, Institut de la vision (Paris) -
  Salle des séminaires du FAST et du LPTMS\, bâtiment Pascal n°530 - 12 
 Juin 26 16:00
DESCRIPTION:Gianluigi Mongillo (Institut de la vision\, Paris)\nOn the rela
 tionship between equilibria and dynamics in large\, random neuronal networ
 ks\n&nbsp\;\n\nSeminar of the Series MLP@P (Machine Learning Physics @ Pla
 teau)\, joint with LISN and IPhT.\nWhere: LPTMS\, Salle des Séminaires (1
 ° étage)\n\nModel neuronal networks provide a phenomenological descripti
 on of brain activity and serve as a primary tool for interpreting experime
 ntal observations in Neuroscience. Specifically\, random networks exhibiti
 ng chaotic dynamics represent a standard framework for modeling the spatio
 temporal irregularity observed in cortical activity. However\, fundamental
  questions remain unanswered regarding what controls the geometry and dime
 nsionality of the chaotic attractor. Here\, we attempt to predict qualitat
 ive and quantitative features of the dynamics by investigating its equilib
 ria and their stability. In the chaotic regime\, a large number of equilib
 ria are present. They are all saddles with an extensive\, but fractionally
  small\, number of unstable directions. Despite the network's connectivity
  being completely random\, the equilibria are strongly correlated and\, as
  a result\, they occupy a relatively small region in the phase space. The 
 attractor is located within this region. Because of this geometric organiz
 ation\, quantitative properties of the equilibria provide natural bounds o
 n the network's dynamics. In particular\, the fraction of positive Lyapuno
 v exponents\, and therefore the attractor dimension\, is fundamentally con
 strained by the fractional dimension of the unstable manifold of the typic
 al equilibria. This explains why the chaotic dynamics in these models can 
 be described by a fractionally small number of collective modes. However\,
  because the attractor dimension is extensive\, data-driven geometric meth
 ods and system identification techniques for reconstructing the dynamics f
 rom purely observational data are fundamentally limited. We argue that the
  study of the dynamics must instead rely on ergodic theory by focusing on 
 invariant measures that robustly capture the system's macroscopic properti
 es.
CATEGORIES:MLP@P
LOCATION:Salle des séminaires du FAST et du LPTMS\, bâtiment Pascal n°53
 0\, rue André Riviere\, Orsay\, 91405\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=rue André Riviere\, Orsay\
 , 91405\, France;X-APPLE-RADIUS=100;X-TITLE=Salle des séminaires du FAST 
 et du LPTMS\, bâtiment Pascal n°530:geo:0,0
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TZID:Europe/Paris
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DTSTART:20260329T030000
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