# On the coercivity condition in the learning of interacting particle systems

arXiv: https://arxiv.org/abs/2011.10480 · HTML: https://mlsanity.com/paper/2011.10480/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Nov 2020.

## Built on by (most cited first, 2 of 2)

- [Identifiability of interaction kernels in mean-field equations of interacting particles](https://mlsanity.com/paper/2106.05565/) (2021)
- [Minimax Rates for Learning Pairwise Interactions in Attention-Style Models](https://mlsanity.com/paper/2510.11789/) (2025)

## Abstract (arXiv)

In the learning of systems of interacting particles or agents, coercivity condition ensures identifiability of the interaction functions, providing the foundation of learning by nonparametric regression. The coercivity condition is equivalent to the strictly positive definiteness of an integral kernel arising in the learning. We show that for a class of interaction functions such that the system is ergodic, the integral kernel is strictly positive definite, and hence the coercivity condition holds true.