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SUMMARY:Marissa Masden (University of Puget Sound)
DTSTART:20250331T020000Z
DTEND:20250331T030000Z
DTSTAMP:20260415T175940Z
UID:TropicalmathandML/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Tropicalmath
 andML/8/">Sign Sequence Combinatorics for Topological Measures of ReLU neu
 ral networks</a>\nby Marissa Masden (University of Puget Sound) as part of
  Tropical mathematics and machine learning\n\n\nAbstract\nA (ReLU) neural 
 network is a type of piecewise linear (PL) function F which induces a cano
 nical polyhedral subdivision\, $\\mathcal C(F)$\, on its input space (Grig
 sby and Lindsey\, 2022). This class of function is commonly used in modern
  machine learning applications. Following a brief introduction to these fu
 nctions and a topological perspective on data classification\, we will the
 n discuss how ReLU networks induce a polyhedral complex on their input spa
 ce which arises from hyperplane arrangements. The face poset of this polyh
 edral complex (for a given ReLU neural network) is entirely determined by 
 combinatorial "sign sequence" information about the vertices of the comple
 x. We will explore how combinatorial properties of the face poset of this 
 polyhedral subdivision may be used to compute topological properties of a 
 given ReLU function such as its level set topology\, critical points\, and
  (most recently) a discrete gradient vector field agreeing with the functi
 on\, among other useful measures\, and demonstrate how this may be used to
  understand ReLU neural networks as a class of functions.\n
LOCATION:https://researchseminars.org/talk/TropicalmathandML/8/
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