Algorithmic (Semi-)Conjugacy via Koopman Operator Theory
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Abstract (arXiv)
Iterative algorithms are of utmost importance in decision and control. With an ever growing number of algorithms being developed, distributed, and proprietarized, there is a similarly growing need for methods that can provide classification and comparison. By viewing iterative algorithms as discrete-time dynamical systems, we leverage Koopman operator theory to identify (semi-)conjugacies between algorithms using their spectral properties. This provides a general framework with which to classify and compare algorithms.
Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). First posted on arXiv 14 Sep 2022.
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Citing papers per year: 2022: 2; 2023: 2; 2024: 0; 2025: 3.
7 papers.
- 2022A Recursively Recurrent Neural Network (R2N2) Architecture for Learning Iterative Algorithmscited by 8
- 2022QuACK: Accelerating Gradient-Based Quantum Optimization with Koopman Operator Learningcited by 7
- 2023Identifying Equivalent Training Dynamicscited by 7
- 2025A Spectral-Grassmann Wasserstein metric for operator representations of dynamical systemscited by 2
- 2023Koopman Learning with Episodic Memorycited by 0
- 2025Characterizing Nonlinear Dynamics via Smooth Prototype Equivalencescited by 0
- 2025Fast dynamical similarity analysiscited by 0
- 2025Fast dynamical similarity analysis28 Nov 2025
- 2025A Spectral-Grassmann Wasserstein metric for operator representations of dynamical systems29 Sep 2025
- 2025Characterizing Nonlinear Dynamics via Smooth Prototype Equivalences13 Mar 2025
- 2023Koopman Learning with Episodic Memory21 Nov 2023
- 2023Identifying Equivalent Training Dynamics17 Feb 2023
- 2022A Recursively Recurrent Neural Network (R2N2) Architecture for Learning Iterative Algorithms22 Nov 2022
- 2022QuACK: Accelerating Gradient-Based Quantum Optimization with Koopman Operator Learning2 Nov 2022