# Generalization as a robust performance property of learning-enabled dynamical systems

arXiv: https://arxiv.org/abs/2608.30431 · HTML: https://mlsanity.com/paper/2608.30431/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 26 references that are in the map.
- First posted on arXiv 31 Aug 2026.

## Builds on (most cited first, 14 of 14)

- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [Analysis and Design of Optimization Algorithms via Integral Quadratic Constraints](https://mlsanity.com/paper/1408.3595/) (2014)
- [Stability and Generalization of Learning Algorithms that Converge to Global Optima](https://mlsanity.com/paper/1710.08402/) (2017)
- [Generalization Bounds of SGLD for Non-convex Learning: Two Theoretical Viewpoints](https://mlsanity.com/paper/1707.05947/) (2017)
- [Stability and Convergence Trade-off of Iterative Optimization Algorithms](https://mlsanity.com/paper/1804.01619/) (2018)
- [Train simultaneously, generalize better: Stability of gradient-based minimax learners](https://mlsanity.com/paper/2010.12561/) (2020)
- [Algorithmic Instabilities of Accelerated Gradient Descent](https://mlsanity.com/paper/2102.02167/) (2021)
- [Reliably-stabilizing piecewise-affine neural network controllers](https://mlsanity.com/paper/2111.07183/) (2021)
- [Instability, Computational Efficiency and Statistical Accuracy](https://mlsanity.com/paper/2005.11411/) (2020)
- [Dissipativity and Integral Quadratic Constraints, Tailored computational robustness tests for complex interconnections](https://mlsanity.com/paper/2105.07401/) (2021)
- [The Analysis of Optimization Algorithms, A Dissipativity Approach](https://mlsanity.com/paper/2205.14264/) (2022)
- [Concentration inequalities for semidefinite least squares based on data](https://mlsanity.com/paper/2509.13166/) (2025)
- [Finite-sample guarantees for data-driven forward-backward operator methods](https://mlsanity.com/paper/2512.19172/) (2025)
- [A Unified Lyapunov-IQC Framework for Uniform Stability of Smooth Quadratic First-Order Accelerated Optimizers](https://mlsanity.com/paper/2605.08488/) (2026)

## Abstract (arXiv)

By focusing on algorithmic stability as a means of establishing out-of-sample bounds, we provide a system-theoretic interpretation of generalization in learning-enabled dynamical systems arising in data-driven optimization and feedback control approximation. Given two neighboring datasets, we specifically model sample replacement as an exogenous disturbance acting on a sensitivity system, while the incremental behavior of the data-dependent operator is encoded through an integral quadratic constraint. By relying on dissipativity arguments, we establish a matrix inequality-based certificate and a uniform stability bound that separates the one-sample sensitivity of the learned operator, and an algorithm-dependent dynamical gain. The latter can then be optimized, offering a tractable tool for certifying and comparing generalization capabilities of learning dynamics. We show that our results recover classical ones for gradient descent, apply naturally to momentum-based methods such as heavy-ball and Nesterov acceleration, and extend to data-driven control.