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Publications

JANURARY 01/2018

Accelerating Deep Learning with Memcomputing

Restricted Boltzmann machines (RBMs) and their extensions, often called “deep-belief networks”, are very powerful neural networks that have found widespread applicability in the fields of machine learning and big data. The standard way to training these models resorts to an iterative unsupervised procedure based on Gibbs sampling, called “contrastive divergence”, and additional supervised tuning via back-propagation. However, this procedure has been shown not to follow any gradient and can lead to suboptimal solutions. In this paper, we show a very efficient alternative to contrastive divergence by means of simulations of digital memcomputing machines (DMMs). We test our approach on pattern recognition using the standard MNIST data set of hand-written numbers…

OCTOBER 23/2017

Evidence of an exponential speed-up in the solution of hard optimization problems

Optimization problems pervade essentially every scientific discipline and industry. Many such problems require finding a solution that maximizes the number of constraints satisfied. Often, these problems are particularly difficult to solve because they belong to the NP-hard class, namely algorithms that always find a solution in polynomial time are not known. Over the past decades, research has focused on developing heuristic approaches that attempt to find an approximation to the solution. However, despite numerous research efforts, in many cases even approximations to the optimal solution are hard to find, as the computational time for further refining a candidate solution grows exponentially with input size. …

AUGUST 16/2017

Topological Field Theory and Computing with Instantons

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, …

MAY 7/2017

Memcomputing Numerical Inversion With Self-Organizing Logic Gates

We propose to use digital memcomputing machines (DMMs), implemented with self-organizing logic gates (SOLGs), to solve the problem of numerical inversion. Starting from fixed-point scalar inversion, we describe the generalization to solving linear systems and matrix inversion. This method, when realized in hardware, will output the result in only one computational step. As an example, we perform simulations of the scalar case using a 5-bit logic circuit made of SOLGs, and show that the circuit successfully performs the inversion. Our method can be extended efficiently to any level of precision, since we prove that producing n-bit precision in the output …

FEBRUARY 8/2015

Polynomial-time solution of prime factorization and NP-complete problems with digital memcomputing machines

We introduce a class of digital machines, we name Digital Memcomputing Machines, (DMMs) able to solve a wide range of problems including Non-deterministic Polynomial (NP) ones with polynomial resources (in time, space, and energy). An abstract DMM with this power must satisfy a set of compatible mathematical constraints underlying its practical realization. We prove this by making a connection with the dynamical systems theory. This leads us to a set of physical constraints for poly-resource resolvability. Once the mathematical requirements have been assessed, we propose a practical scheme to solve the above class of problems based on the novel concept …

FEBRUARY 13/2015

Universal Memcomputing Machines

We introduce the notion of universal memcomputing machines (UMMs): a class of brain-inspired general-purpose computing machines based on systems with memory, whereby processing and storing of information occur on the same physical location. We analytically prove that the memory properties of UMMs endow them with universal computing power (they are Turing-complete), intrinsic parallelism, functional polymorphism, and information overhead, namely, their collective states can support exponential data compression directly in memory. We also demonstrate that a UMM has the same computational power as a nondeterministic Turing machine, namely, it can solve nondeterministic polynomial (NP)-complete problems in polynomial time. However, by virtue …