Contrastive divergence for memristor-based restricted Boltzmann machine

Abstract

Restricted Boltzmann machines and deep belief networks have been shown to perform effectively in many applications such as supervised and unsupervised learning, dimensionality reduction and feature learning. Implementing networks, which use contrastive divergence as the learning algorithm on neuromorphic hardware, can be beneficial for real-time hardware interfacing, power efficient hardware and scalability. Neuromorphic hardware which uses memristors as synapses is one of the most promising areas to achieve the above-mentioned goals. This paper presents a restricted Boltzmann machine which uses a two memristor model to emulate synaptic weights and achieves learning using contrastive divergence.

Introduction

Memristors have initiated a new direction for the advancement of neuromorphic and analog applications. Biologically inspired computation is appealing and recently many methods have been researched extensively. Artificial neural network, being one of them, has been getting more attention due to deep learning and its hardware implementation in neuromorphic devices. The pioneering work (Snider, 2007) presented neural networks using memristors as synapses which emphasized easily manufactured and large scale devices. Demonstration of an associative memory using memristors was first presented in Pershin and Di Ventra (2010) while in Pershin and Ventra (2014) use of memcapacitors as synapses with integrate and fire neurons is presented. In many later works, memristors have been employed to implement synapses in neural networks (Thomas, 2013, Indiveri et al., 2013). Spike-Timing-Dependent-Plasticity (STDP) using memristors as synapses which can be used to emulate the auditory system is discussed in Serrano-Gotarredona et al. (2013). Memristors have also been used in image processing to detect edges (Prodromakis and Toumazou, 2010).

Restricted Boltzmann machine (RBM) used in deep networks has shown promising results in general, while the best results were achieved within the image classification problem (Larochelle and Bengio, 2008). RBMs in deep networks are trained in an unsupervised fashion using contrastive divergence (CD) as a learning algorithm. Since training large-scale RBMs is time consuming, some fast hardware implementations have been suggested in the literature e.g. FPGA-based RBM implementations have been suggested in Ly and Chow (2010), Kim et al. (2010) and recently in Kim et al. (2014). RBM with continuous valued neurons called Continuous RBM has VLSI implementation suggested in Chen et al. (2006). An implementation of RBM using digital synapses has been presented in Merolla et al. (2011), but no such implementation of RBMs exists for memristor based synapses.

This paper presents an approach to implementing CD in one layer of RBM which uses memristors as weight edges (synapse). Conductance of memristors is used to emulate a positive real number storage memory, which can be read and written using digital pulses. Furthermore, given that the conductance of an electronic device cannot be negative, a mechanism needs to be developed so that memristors can store negative real numbers as well. Additionally, since memristors are very noisy devices, it is important to use a realistic model of memristor with noise to better understand how learning behavior is affected under such conditions. This work presents such a mechanism, which makes little adjustments to RBMs and CD to keep the architecture simple resulting in an extensible system.

This paper is organized as follows. Section 2 introduces the background of the RBM followed by description of CD, and the resistive random-access memory (RRAM) memristors. Section 3 describes in detail the proposed RBM architecture and CD for memristor-based RBM. Section 4 presents the simulation setup and the obtained results. Finally, Section 5 concludes the paper.