# Predicting AI Agent Behavior through Approximation of the Perron-Frobenius Operator

arXiv: https://arxiv.org/abs/2406.02723 · HTML: https://mlsanity.com/paper/2406.02723/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 18 references that are in the map.
- First posted on arXiv 4 Jun 2024.

## Builds on (most cited first, 10 of 10)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [A Tutorial on Kernel Density Estimation and Recent Advances](https://mlsanity.com/paper/1704.03924/) (2017)
- [Generic bounds on the approximation error for physics-informed (and) operator learning](https://mlsanity.com/paper/2205.11393/) (2022)
- [Koopman Operator Dynamical Models: Learning, Analysis and Control](https://mlsanity.com/paper/2102.02522/) (2021)
- [Reachability Analysis of Neural Feedback Loops](https://mlsanity.com/paper/2108.04140/) (2021)
- [Learning Density Distribution of Reachable States for Autonomous Systems](https://mlsanity.com/paper/2109.06728/) (2021)
- [Reachability Analysis of Neural Network Control Systems](https://mlsanity.com/paper/2301.12100/) (2023)
- [Deep Learning with Kernels through RKHM and the Perron-Frobenius Operator](https://mlsanity.com/paper/2305.13588/) (2023)
- [Learning Transfer Operators by Kernel Density Estimation](https://mlsanity.com/paper/2210.03124/) (2022)

## Abstract (arXiv)

Predicting the behavior of AI-driven agents is particularly challenging without a preexisting model. In our paper, we address this by treating AI agents as nonlinear dynamical systems and adopting a probabilistic perspective to predict their statistical behavior using the Perron-Frobenius (PF) operator. We formulate the approximation of the PF operator as an entropy minimization problem, which can be solved by leveraging the Markovian property of the operator and decomposing its spectrum. Our data-driven methodology simultaneously approximates the PF operator to perform prediction of the evolution of the agents and also predicts the terminal probability density of AI agents, such as robotic systems and generative models. We demonstrate the effectiveness of our prediction model through extensive experiments on practical systems driven by AI algorithms.