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UID:512b8037863a38dd1f3be7aed3bc27e5
CATEGORIES:Colloquia
CREATED:20250210T133705
SUMMARY:Explicit construction of global minimizers and the interpretability problem in Deep Learning
LOCATION:HILL 705
DESCRIPTION:<p>In this talk, we present some recent results aimed at the rigorous mathe
 matical understanding of how and why supervised learning works. We point ou
 t genericness conditions related to reachability of zero loss minimization,
  in underparametrized versus overparametrized Deep Learning (DL) networks. 
 For underparametrized DL networks, we explicitly construct global, zero los
 s cost minimizers for sufficiently clustered data. In addition, we derive e
 ffective equations governing the cumulative biases and weights, and show th
 at gradient descent corresponds to a dynamical process in the input layer, 
 whereby clusters of data are progressively reduced in complexity ("truncate
 d") at an exponential rate that increases with the number of data points th
 at have already been truncated. For overparametrized DL networks, we prove 
 that the gradient descent flow is homotopy equivalent to a geometrically ad
 apted flow that induces a (constrained) Euclidean gradient flow in output s
 pace. If a certain rank condition holds, the latter is, upon reparametrizat
 ion of the time variable, equivalent to simple linear interpolation. This i
 n turn implies zero loss minimization and the phenomenon known as “Neural C
 ollapse”. Moreover, we derive zero loss guarantees, and construct explicit 
 global minimizers for overparametrized deep networks, given generic trainin
 g data. The work presented includes collaborations with Patricia Munoz Ewal
 d and Andrew G. Moore (UT Austin).</p>
CONTACT:Thomas Chen (UT Austin) 
DTSTAMP:20260828T081115
DTSTART;TZID=America/New_York:20250312T154500
DTEND;TZID=America/New_York:20250312T164500
SEQUENCE:0
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