Abstract
The neural network enables efficient solutions for Nondeterministic Polynomial-time (NP) hard problems, which are challenging for conventional von Neumann computing. The hardware implementation, i.e., neuromorphic computing, aspires to enhance this efficiency by custom hardware. Particularly, NP hard graphical constraint optimization problems are solved by a network of stochastic binary neurons to form a Boltzmann Machine (BM). The implementation of stochastic neurons in hardware is a major challenge. In this work, we demonstrate that the high to low resistance switching (set) process of a PrxCa1−xMnO3 (PCMO) based RRAM (Resistive Random Access Memory) is probabilistic. Additionally, the voltage-dependent probability distribution approximates a sigmoid function with 1.35%–3.5% error. Such a sigmoid function is required for a BM. Thus, the Analog Approximate Sigmoid (AAS) stochastic neuron is proposed to solve the maximum cut—an NP hard problem. It is compared with Digital Precision-controlled Sigmoid (DPS) implementation using (a) pure CMOS design and (b) hybrid (RRAM integrated with CMOS). The AAS design solves the problem with 98% accuracy, which is comparable with the DPS design but with 10× area and 4× energy advantage. Thus, ASIC neuro-processors based on novel analog neuromorphic devices based BM are promising for efficiently solving large scale NP hard optimization problems.
Highlights
The conventional von Neumann computer based on deterministic CMOS logic implementation has been extremely successful in implementing sequential algorithms using clearly demarcated processing and memory units.1,2 there are many important problems such as graphical constraint optimization, factorization, and other Nondeterministic Polynomial-time (NP)-hard problems which do not have a polynomial time algorithm to find globally optimal solutions
We present a stochastic neuron based on PCMO RRAM for a Boltzmann Machine (BM) to solve an NP hard problem, i.e., Maximum Cut
We study stochastic neuron design for the BM to solve classic NP hard problems, which are of great theoretical interest and with a wide range of practical applications
Summary
The conventional von Neumann computer based on deterministic CMOS logic implementation has been extremely successful in implementing sequential algorithms using clearly demarcated processing and memory units. there are many important problems such as graphical constraint optimization, factorization, and other Nondeterministic Polynomial-time (NP)-hard problems which do not have a polynomial time algorithm to find globally optimal solutions. The switching resistance ratio was poor and stochasticity (without an external magnetic field support) was experimentally observed for only low temperatures (T ∼ 130 K) and very high current densities [100× > than PCMO RRAM (Resistive Random Access Memory)] Another general-purpose weight storage element and stochastic neuron model was proposed using a TiO2 memristor.. Low barrier magnets have been proposed for stochastic switching in a 1T/1M arrangement.33–35 These devices have very stringent fabrication constraints of near-critical thickness magnetization layer or circular magnets for an absence of preferential magnetic orientation which are a challenge for nanoscale production and often require noise amplification inverters at the output.
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