# Global minimization via classical tunneling assisted by collective force field formation

arXiv: https://arxiv.org/abs/2102.03385 · HTML: https://mlsanity.com/paper/2102.03385/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Feb 2021.

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

- [Self-Organising Memristive Networks as Physical Learning Systems](https://mlsanity.com/paper/2509.00747/) (2025)
- [How to Train Your Resistive Network: Generalized Equilibrium Propagation and Analytical Learning](https://mlsanity.com/paper/2602.03546/) (2026)

## Abstract (arXiv)

Simple dynamical models can produce intricate behaviors in large networks. These behaviors can often be observed in a wide variety of physical systems captured by the network of interactions. Here we describe a phenomenon where the increase of dimensions self-consistently generates a force field due to dynamical instabilities. This can be understood as an unstable ("rumbling") tunneling mechanism between minima in an effective potential. We dub this collective and nonperturbative effect a "Lyapunov force" which steers the system towards the global minimum of the potential function, even if the full system has a constellation of equilibrium points growing exponentially with the system size. The system we study has a simple mapping to a flow network, equivalent to current-driven memristors. The mechanism is appealing for its physical relevance in nanoscale physics, and to possible applications in optimization, novel Monte Carlo schemes and machine learning.