Bolte, Jérôme, Le, Tam, Pauwels, Edouard and Silveti-Falls, Antonio (2022) Nonsmooth implicit dmifferentiation for machine learning and optimization. In: Advances in Neural Information Processing Systems, 13 décembre 2021, En ligne.

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Identification Number : 10.48550/arXiv.2106.04350


In view of training increasingly complex learning architectures, we establish a nonsmooth 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 differentiation (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 algorithmic differentiation without any hypothesis.

Item Type: Conference or Workshop Item (Paper)
Language: English
Date: March 2022
Divisions: TSE-R (Toulouse)
Site: UT1
Date Deposited: 23 Apr 2024 13:48
Last Modified: 23 Apr 2024 13:48
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