Optimal Input Encoding For Memristor Based Reservoir Computing Charles Boutens Supervisor: Prof. dr. ir. Joni Dambre Counsellor: Prof. dr. ir. Joni Dambre Master's dissertation submitted in order to obtain the academic degree of Master of Science in Engineering Physics Department of Electronics and Information Systems Chair: Prof. dr. ir. Rik Van de Walle Faculty of Engineering and Architecture Academic year 2016-2017 Optimal Input Encoding For Memristor Based Reservoir Computing Charles Boutens Supervisor(s): Prof. dr. ir. Joni Dambre1 Abstract| One of the most promising fields of unconventional ap- With Moore's law reaching its end, alternatives to the proaches to computation might be the brain-inspired field digital computing paradigm are being investigated. These of analogue, neuromorphic computing [4]. Here, the ulti- unconventional approaches range from quantum- and opti- cal computing to promising analogue, neuromorphic imple- mate vision is to use self-organised neural networks consist- mentations. A recent approach towards computation with ing of nano-scale components with variable properties and analogue, physical systems is the emerging field of physi- erroneous behaviour, inevitable at the nano-scale. These cal reservoir computing (PRC). By considering the physical system as an excitable, dynamical medium called a reser- neuromorphic approaches require highly connected com- voir, this approach enables the exploitation of the intrinsic plex neural networks with adaptive synapse-like connec- computational power available in all physical systems. tions. Recently [5] [6] [7] interest has arisen in the function- In this work the RC approach towards computation is ap- alities of locally connected switching networks. These net- plied to networks consisting of resistive switches (RS). A densely connected atomic switch network (ASN) and a net- works consist of switches and memory components such as work build up from T iO2 memristors are used as reservoirs molecular transistors, negative differential resistances [8], in simulation. Both simulation models rely on volatile ex- memristors [6] or atomic switches [9]. tensions of Strukov's widely spread current controlled mem- ristor (CCMR) model. The dynamics of the ASN in simu- Contrary to the digital framework, in analogue com- lation are thoroughly characterized and based on these ob- puting the state of the system can take up any contin- servations two encoding schemes are proposed in order to uous value. Hence processes cannot be reliably repeated solve two reservoir benchmark tasks, memory capacity and NARMA-10 task. Experiments executed with the reservoirs with exact equivalence. Also, in the fabrication process consisting of T iO2 memristors lead to the observation of the of these analogue computation blocks, device variability failure of the RC approach in the absence of volatility of the is inevitable and thus a computational framework aiming used devices. at using these systems should account for both inter- and By comparing the simulation with the actual dynamics of the ASN, it is concluded that the CCMR model, used intra-device variability. to describe the individual atomic switches, fails at captur- This is where the RC approach towards computing with ing some of the fundamental characteristics of the device. By looking at the performance of both the ASN and the recurrent neural networks (RNN) comes into play [10] [11] T iO2 reservoir, and at similar research found in the litera- [12]. Here an artificial, randomly assembled RNN is consid- ture, it is argued that the CCMR models are unsuited for ered as a dynamical, excitable medium called the reservoir, the RC approach. Nevertheless, the real ASN devices do whose internal dynamics are untrained. The RC concept show promising reservoir properties. A voltage controlled memristor model (VCMR), already used in a memristor- relies on two key points. Firstly, the detailed nature of the based RC approach, is suggested to continue further re- reservoir is unimportant, only its overall dynamics play a search. Also, some interesting new architectures are briefly role. Secondly, RC allows for a simple training approach discussed that could increase the performance of these RS reservoirs. where only the readout layer is trained. This flexibility en- Index terms { memristor based reservoir computing, ables the RC approach to be applied to a large variety of neuromorphic computation, physical reservoir computing, dynamical systems. Swapping the RNN reservoir with a memristor models, memristor models for reservoir comput- physical system, leads to what is called physical reservoir ing. computing (PRC). PRC presents the right framework and tools to exploit the analogue computational power, intrin- I. Introduction sic to physical dynamical systems, in a robust way: i.e. Digital computation has been the standard for over half without the need to control the randomness and fluctua- a century, mainly thanks to its extreme robustness against tions of the system. The physical system is considered as a noise and variability. However, with the continuous de- reservoir that maps the input via its own intrinsic dynam- mand for more computational power and the slowing down ics onto a high dimensional feature space. These features of Moores law [1] [2], alternatives to the silicon based com- are read out by measuring the system's state and are sub- putational methods are being developed and researchers sequently combined in a trained way (using any standard are reconsidering the field of unconventional computing regression technique) to produce the desired output. PRC which stayed on the sideline of their Turing machine broth- has been demonstrated in various physical systems, both ers for many years [3]. experimentally and in simulations, ranging from a bucket of water in [13], morphological [14], to very promising pho- 1Department of Electronics and Information Systems, Ghent Uni- tonics implementations [15] [16] [17] [18] [19]. In the light of versity neuromorphic computing, the RC approach has also been applied to networks consisting of nano-scale switching ele- in Figure 1. Here w corresponds to the width of the doped ments based on memristive junctions [20] [21] [22] [23] [24]. region. The total resistance of the memristor device is de- With the advancements in material sciences, self- termined by two variable resistors connected in series. RON assembled networks of memristive devices at the nano-scale and ROF F denote the resistance of the memristor in both have been produced, forming very promising candidates limit cases where w = D and w = 0 respectively. Ohm's in the search for synthetic synapses for the fabrication law leads to the following port equation (1): of neuromorphic systems. These devices exhibit similar properties present in biological neurons, such as hystere- v(t) = RON x + ROF F (1 − x) i(t): (1) sis, short-term and long-term-placticity (STP, LTP), long- where x = w 2 [0; 1]. Applying a bias v across the device term depression etc [6] [5]. One very promising implemen- D will cause the charged dopants to drift towards the undoped tation is a highly interconnected atomic switch network region and hence move the boundary between both regions (ASN) [7] [5] [22] [9]. In the ASN, the individual atomic [27]. Here, the simplest case of ohmic electronic conduc- switches are composed of a AgjAg SjAg metal-insulator- 2 tion and linear ionic drift in a uniform field is considered, metal (MIM) interface, where the switching process is gov- leading to the following state equation: erned mostly by a combination of two phenomena: the formation/annihilation of a conductive metal filament to- dx µR = ON i(t); (2) gether with a bias induced phase transition in the insulator dt D2 layer of the MIM junction. A multi-electrode-array (MEA) for the state variable x. Here µ denotes the average ion is being overgrown by a complex structure of densely con- mobility. The coupled equations 1, 2 take the normal form nected silver nanowires, the ASN. The electrodes on the for a current controlled memristor [28]. This CCMR model MEA can serve both as a source or readout. This densely is used as basis for both the T iO memristor and the ASN connected network structure gives rise to new interesting 2 models in [26] and [22] respectively. properties unseen in single AgjAg SjAg atomic switches. It 2 A simulation model for the ASN has been developed in has been reported[5] that the ASNs show signs of an oper- MATLAB [22]. The CCMR model, introduced above, is ational regime near the "edge of chaos", where the network used as a starting point to describe the behavior of a single exhibits avalanche dynamics, criticality and power law scal- atomic switch. The port equation 1 remains unchanged ing of temporal metastability. More over, the ASN shows with w 2 [0;D], now representing the length of the Ag distributed, continuous network activity caused by the in- nano filament. If w = 0 there is no conducting filament, terplay between filament formation and dissolution across corresponding with a resistance R . For w = D the the whole network. A voltage drop due to the formation of OF F filament is fully formed, the switch is in the ON state, a filament in the network instigates the filament's thermo- R . Next a new state equation is introduced for w: dynamical instability and hence its corresponding decay. ON The second memristive device under investigation is the T iO2 memristor created by HP [25]. This device consists dw(t) Ron = [µv i(t)] Ω(w(t)) − τ (w(t) − D) + η(t); (3) of a thin T iO2 film sandwiched between two platinum elec- dt D trodes. The T iO2 layer consists of a highly conductive + channel (T iO2−x), due to positively charged oxygen va- where µv represents the ionic mobility of Ag and Ω(w) = 2 cancies, and a very narrow insulating T iO2 barrier near [w (D−w)=D ] is a window function, modelling the nonlin- the positive electrode.