# Algorithmic (Semi-)Conjugacy via Koopman Operator Theory

arXiv: https://arxiv.org/abs/2209.06374 · HTML: https://mlsanity.com/paper/2209.06374/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Sep 2022.

## Built on by (most cited first, 8 of 8)

- [Identifying Equivalent Training Dynamics](https://mlsanity.com/paper/2302.09160/) (2023)
- [A Recursively Recurrent Neural Network (R2N2) Architecture for Learning Iterative Algorithms](https://mlsanity.com/paper/2211.12386/) (2022)
- [QuACK: Accelerating Gradient-Based Quantum Optimization with Koopman Operator Learning](https://mlsanity.com/paper/2211.01365/) (2022)
- [A Spectral-Grassmann Wasserstein metric for operator representations of dynamical systems](https://mlsanity.com/paper/2509.24920/) (2025)
- [Koopman Learning with Episodic Memory](https://mlsanity.com/paper/2311.12615/) (2023)
- [Characterizing Nonlinear Dynamics via Smooth Prototype Equivalences](https://mlsanity.com/paper/2503.10336/) (2025)
- [Fast dynamical similarity analysis](https://mlsanity.com/paper/2511.22828/) (2025)
- [Interpreting Reinforcement Learning Model Behavior via Koopman with Control](https://mlsanity.com/paper/2603.19968/) (2026)

## 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.