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SUMMARY:Active Paths and Effective Stochastic Dynamics in Small Neural Net
 works
DTSTART;VALUE=DATE-TIME:20260414T225700Z
DTEND;VALUE=DATE-TIME:20260414T230400Z
DTSTAMP;VALUE=DATE-TIME:20260408T063412Z
UID:indico-contribution-344@fisindico.uniandes.edu.co
DESCRIPTION:Speakers: Cristian Pena ()\nThis project proposes to study a s
 mall neural network trained on a simple supervised learning task from a pe
 rspective inspired by statistical mechanics. The central idea is to identi
 fy the active paths connecting the input and output layers\, analyze how t
 hey contribute to the represented function before and after training\, and
  investigate whether their collective behavior admits an effective macrosc
 opic description. To do this\, the network output will be decomposed into 
 contributions associated with active paths\, and several collective observ
 ables will be introduced\, including the number of active paths\, the dist
 ribution of their effective contributions\, and their temporal evolution d
 uring learning. Using multiple random initializations and training traject
 ories under stochastic gradient descent\, the project will examine whether
  the evolution of the learned output can be approximated by an effective s
 tochastic differential equation of the form $df_t(x)=A_t(x)\,dt + B_t(x)\,
 dW_t$\, where $A_t(x)$ represents an average learning drift and $B_t(x)$ a
  fluctuation term induced by the stochastic nature of training. The main g
 oal is to explore whether active paths can be interpreted as mesoscopic va
 riables linking the microscopic dynamics of the weights with the macroscop
 ic evolution of the learned function\, providing a more structured descrip
 tion of supervised learning.\n\nhttps://fisindico.uniandes.edu.co/event/23
 /contributions/344/
LOCATION:Universidad Nacional Edificio 564
URL:https://fisindico.uniandes.edu.co/event/23/contributions/344/
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