Bolte, Jérôme, Le, Tam
, Pauwels, Edouard
and Silveti-Falls, Antonio
(2022)
Nonsmooth implicit differentiation for machine learning and optimization.
In: NIPS'21: 35th International Conference on Neural Information Processing Systems, 6-14 décembre 2021, En ligne.
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Abstract
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) |
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Language: | English |
Date: | March 2022 |
Subjects: | B- ECONOMIE ET FINANCE |
Divisions: | TSE-R (Toulouse) |
Site: | UT1 |
Date Deposited: | 23 Apr 2024 13:48 |
Last Modified: | 27 Feb 2025 13:41 |
OAI Identifier: | oai:tse-fr.eu:126837 |
URI: | https://publications.ut-capitole.fr/id/eprint/45098 |
Available Versions of this Item
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Nonsmooth Implicit Differentiation for Machine Learning and Optimization. (deposited 22 Mar 2022 09:44)
- Differentiating Nonsmooth Solutions to Parametric Monotone Inclusion Problems. (deposited 12 Feb 2025 08:43)
- Nonsmooth implicit differentiation for machine learning and optimization. (deposited 23 Apr 2024 13:48) [Currently Displayed]