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SUMMARY:Domain-theoretic Semantics for Dynamical Systems: From Analog Comp
 uters to Neural Networks - Levin Hornischer
DTSTART:20241107T150000Z
DTEND:20241107T160000Z
UID:TALK224221@talks.cam.ac.uk
CONTACT:Matthew Colbrook
DESCRIPTION:Despite great empirical success\, we are still lacking a theor
 y of modern artificial intelligence. In particular\, we are missing an int
 erpretation of the 'sub-symbolic' computation performed by neural networks
 . For digital computation\, this problem was solved by semantics: the math
 ematical description of the meaning of program code. In this paper\, we wo
 rk toward an analogous semantics for neural networks and other forms of 'n
 on-symbolic' computation like analog computers—which all can be regarded
  as dynamical systems. To do so\, we first summarize the three semantics f
 or digital computation (operational\, denotational\, logical)\, and then d
 evelop their counterparts for non-symbolic computation (dynamical systems\
 , domains\, and modal logic). The key idea is to represent the dynamics of
  non-symbolic computation as a limit of finite symbolic approximations\, w
 hich are given by interpretable observations. In an implementation\, we th
 us illustrate the training dynamics of a neural network in a standard mach
 ine learning task.
LOCATION:Centre for Mathematical Sciences\, MR14
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