91 research outputs found
Critical branching processes in digital memcomputing machines
Memcomputing is a novel computing paradigm that employs time non-locality
(memory) to solve combinatorial optimization problems. It can be realized in
practice by means of non-linear dynamical systems whose point attractors
represent the solutions of the original problem. It has been previously shown
that during the solution search digital memcomputing machines go through a
transient phase of avalanches (instantons) that promote dynamical long-range
order. By employing mean-field arguments we predict that the distribution of
the avalanche sizes follows a Borel distribution typical of critical branching
processes with exponent . We corroborate this analysis by solving
various random 3-SAT instances of the Boolean satisfiability problem. The
numerical results indicate a power-law distribution with exponent , in very good agreement with the mean-field analysis. This indicates
that memcomputing machines self-tune to a critical state in which avalanches
are characterized by a branching process, and that this state persists across
the majority of their evolution.Comment: 5 pages, 3 figure
Taming a non-convex landscape with dynamical long-range order: memcomputing Ising benchmarks
Recent work on quantum annealing has emphasized the role of collective
behavior in solving optimization problems. By enabling transitions of clusters
of variables, such solvers are able to navigate their state space and locate
solutions more efficiently despite having only local connections between
elements. However, collective behavior is not exclusive to quantum annealers,
and classical solvers that display collective dynamics should also possess an
advantage in navigating a non-convex landscape. Here, we give evidence that a
benchmark derived from quantum annealing studies is solvable in polynomial time
using digital memcomputing machines, which utilize a collection of dynamical
components with memory to represent the structure of the underlying
optimization problem. To illustrate the role of memory and clarify the
structure of these solvers we propose a simple model of these machines that
demonstrates the emergence of long-range order. This model, when applied to
finding the ground state of the Ising frustrated-loop benchmarks, undergoes a
transient phase of avalanches which can span the entire lattice and
demonstrates a connection between long-range behavior and their probability of
success. These results establish the advantages of computational approaches
based on collective dynamics of continuous dynamical systems
A Compact CMOS Memristor Emulator Circuit and its Applications
Conceptual memristors have recently gathered wider interest due to their
diverse application in non-von Neumann computing, machine learning,
neuromorphic computing, and chaotic circuits. We introduce a compact CMOS
circuit that emulates idealized memristor characteristics and can bridge the
gap between concepts to chip-scale realization by transcending device
challenges. The CMOS memristor circuit embodies a two-terminal variable
resistor whose resistance is controlled by the voltage applied across its
terminals. The memristor 'state' is held in a capacitor that controls the
resistor value. This work presents the design and simulation of the memristor
emulation circuit, and applies it to a memcomputing application of maze solving
using analog parallelism. Furthermore, the memristor emulator circuit can be
designed and fabricated using standard commercial CMOS technologies and opens
doors to interesting applications in neuromorphic and machine learning
circuits.Comment: Submitted to International Symposium of Circuits and Systems (ISCAS)
201
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