Non smooth implicit differentiation
| Quand ? |
Le 04/04/2023, de 14:00 à 15:00 |
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| Participants |
Tony Silveti-Falls |
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Speaker: Tony Silveti-Falls (CentraleSupélec/University of Paris-Saclay)
Title: Non smooth implicit differentiation
Abstract: In view of training increasingly complex learning architectures, we establish a non-
smooth implicit function theorem with an operational calculus. Our result applies
to most practical problems (i.e., definable problems) provided that a nonsmooth
form of the classical invertibility condition is fulfilled. This approach allows for
formal subdifferentiation: for instance, replacing derivatives by Clarke Jacobians
in the usual differentiation formulas is fully justified for a wide class of nonsmooth
problems. Moreover this calculus is entirely compatible with algorithmic differen-
tiation (e.g., backpropagation). We provide several applications such as training
deep equilibrium networks, training neural nets with conic optimization layers, or
hyperparameter-tuning for nonsmooth Lasso-type models. To show the sharpness
of our assumptions, we present numerical experiments showcasing the extremely
pathological gradient dynamics one can encounter when applying implicit algo-
rithmic differentiation without any hypothesis.
More information: https://tonysf.github.io/