We provide a novel transcription of monotone operator theory to the non-Euclidean finite-dimensional spaces ℓ 1 and ℓ ∞ . We first establish properties of mappings which are monotone with respect to the non-Euclidean norms ℓ 1 or ℓ ∞ . In analogy with their Euclidean counterparts, mappings which are monotone with respect to a non-Euclidean norm are amenable to numerous algorithms for computing their zeros. We demonstrate that several classic iterative methods for computing zeros of monotone operators are directly applicable in the non-Euclidean framework. We present a case-study in the equilibrium computation of recurrent neural networks and demonstrate that casting the computation as a suitable operator splitting problem improves convergence rates.
Non-Euclidean Monotone Operator Theory with Applications to Recurrent Neural Networks / Davydov, Alexander; Jafarpour, Saber; Proskurnikov, Anton V.; Bullo, Francesco. - ELETTRONICO. - (2022), pp. 6332-6337. (Intervento presentato al convegno 2022 IEEE 61st Conference on Decision and Control (CDC) tenutosi a Cancun, Mexico nel 06-09 December 2022) [10.1109/CDC51059.2022.9993197].
Non-Euclidean Monotone Operator Theory with Applications to Recurrent Neural Networks
Proskurnikov, Anton V.;Bullo, Francesco
2022
Abstract
We provide a novel transcription of monotone operator theory to the non-Euclidean finite-dimensional spaces ℓ 1 and ℓ ∞ . We first establish properties of mappings which are monotone with respect to the non-Euclidean norms ℓ 1 or ℓ ∞ . In analogy with their Euclidean counterparts, mappings which are monotone with respect to a non-Euclidean norm are amenable to numerous algorithms for computing their zeros. We demonstrate that several classic iterative methods for computing zeros of monotone operators are directly applicable in the non-Euclidean framework. We present a case-study in the equilibrium computation of recurrent neural networks and demonstrate that casting the computation as a suitable operator splitting problem improves convergence rates.File | Dimensione | Formato | |
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https://hdl.handle.net/11583/2974559