Feb 15, 2021

 

Global minimization via classical tunneling assisted by collective force field formation

Francesco Caravelli, Forrest C. Sheldon, Fabio L. Traversa

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.

View arXiv version  →

• All Tags Absence of periodic orbits in digital memcomputing machines with solutions Accelerating Deep Learning with Memcomputing Aircraft Loading Optimization: MemComputing the 5th Airbus Problem Coupled oscillator networks for von Neumann and non von Neumann computing Digital Memcomputing: from Logic to Dynamics to Topology Directed percolation and numerical stability of simulations of digital memcomputing machines Dynamic computing random access memory: A brain-inspired computing paradigm with memelements Efficient solution of Boolean satisfiability problems with digital memcomputing Evidence of an exponential speed-up in the solution of hard optimization problems Global minimization via classical tunneling assisted by collective force field formation Instantons in Self-Organizing Logic Gates MemComputing Integer Linear Programming Memcomputing Numerical Inversion With Self-Organizing Logic Gates Memcomputing: Leveraging memory and physics to compute efficiently Mode-Assisted Unsupervised Learning of Restricted Boltzmann Machines On the Universality of Memcomputing Machines Polynomial-time solution of prime factorization and NP-complete problems with digital memcomputing machines Stress-testing memcomputing on hard combinatorial optimization problems Taming a non-convex landscape with dynamical long-range order: memcomputing the Ising spin-glass Topological Field Theory and Computing with Instantons