Sep 11, 2016

Topological Field Theory and Computing with Instantons

Fabio Lorenzo Traversa, Massimiliano Di Ventra, Igor V. Ovchinnikov

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It is well known that dynamical systems may be employed as computing machines. However, not all dynamical systems offer particular advantages compared to the standard paradigm of computation, in regard to efficiency and scalability. Recently, it was suggested that a new type of machines, named digital –hence scalable– memcomputing machines (DMMs), that employ non-linear dynamical systems with memory, can solve complex Boolean problems efficiently. This result was derived using functional analysis without, however, providing a clear understanding of which physical features make DMMs such an efficient computational tool. Here, we show, using recently proposed topological field theory of dynamical systems…

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• 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