Non-Euclidean Monotone Operator Theory with Applications to Recurrent Neural Networks
- Resource Type
- Conference
- Authors
- Davydov, Alexander; Jafarpour, Saber; Proskurnikov, Anton V.; Bullo, Francesco
- Source
- 2022 IEEE 61st Conference on Decision and Control (CDC) Decision and Control (CDC), 2022 IEEE 61st Conference on. :6332-6337 Dec, 2022
- Subject
- Robotics and Control Systems
Casting
Analytical models
Recurrent neural networks
Machine learning
Aerospace electronics
Control systems
Robustness
- Language
- ISSN
- 2576-2370
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.