# A Note on Analyzing the Stability of Oscillator Ising Machines

arXiv: https://arxiv.org/abs/2310.09322 · HTML: https://mlsanity.com/paper/2310.09322/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Oct 2023.

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

- [Learning at the Speed of Physics: Equilibrium Propagation on Oscillator Ising Machines](https://mlsanity.com/paper/2510.12934/) (2025)
- [Different Paths, Same Destination: Designing New Physics-Inspired Dynamical Systems with Engineered Stability to Minimize the Ising Hamiltonian](https://mlsanity.com/paper/2504.06280/) (2025)

## Abstract (arXiv)

The rich non-linear dynamics of the coupled oscillators (under second harmonic injection) can be leveraged to solve computationally hard problems in combinatorial optimization such as finding the ground state of the Ising Hamiltonian. While prior work on the stability of the so-called Oscillator Ising Machines (OIMs) has used the linearization method, in this letter, we present a complementary method to analyze stability using the second order derivative test of the energy / cost function. We establish the equivalence between the two methods, thus augmenting the tool kit for the design and implementation of OIMs.