DEGREE PROJECT IN TECHNOLOGY, FIRST CYCLE, 15 CREDITS STOCKHOLM, SWEDEN 2018 The (perhaps) causal brain A comparison of attractor neural networks using temporally symmetric and antisymmetric synaptic rules. LEO LINDÉN KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ENGINEERING SCIENCES EXAMENSARBETE INOM TEKNIK, GRUNDNIVÅ, 15 HP STOCKHOLM, SVERIGE 2018 Den (möjligtvis) kausala hjärnan En jämförelse mellan associativa neurala nätverk med kausalitets- eller korrelationsbaserade synaptiska modeller LEO LINDÉN KTH SKOLAN FÖR TEKNIKVETENSKAP The (perhaps) causal brain A comparison of attractor neural networks using temporally symmetric and antisymmetric synaptic rules Leo Lind´en 2018 Abstract The associative memory of the brain is thought to be well modelled by attractor neural networks. A sort of artificial neural network that may store memories and has the ability to associate them with distorted input. The memories may be stored in the system by changing the connecting weights depending on the activity pattern in the network, a process known as synaptic plasticity. There are several different theories of the conditions required for the strength of synaptic connection increase or decrease and which one of these that is the most likely is still an open issue. Many recent studies of the associative memory have used a model that only take correlated activity between neurons into account (BCPNN), but there is some experimental support for another one in which the exact timing of pre- and postsynaptic activity plays a role (STDP). There is, however, no conclusive evidence for either one and this study will, therefore, investigate the differences in an attractor neural network model using the two different rules for synaptic plasticity. In this study two simple attractor neural networks with 64 neurons were created, each using either STDP or BCPNN as a model for synaptic plasticity. Forcing the system into several states corresponding to different memories the connecting weights between the neurons changed. By stimulating the network with partial memory patterns its ability to recall memories remain stable could be tested. In several aspects, the system using STDP was found to perform better than BCPNN, and it is possible to conclude that the former synaptic rule was the better choice in this specific case. To draw any conclusions regarding which of STDP or BCPNN is more prob- able as a model for the synaptic plasticity in the brain more detailed studies would have to be undertaken. Preferably utilising more advanced and biologi- cally realistic models. 1 Sammanfattning Hj¨arnansf¨orm˚agatill associativt minne anses kunna modelleras med hj¨alpas- sociativa neurala n¨atverk. Ett slags konstgjort neuralt n¨atverk som kan lagra minnen och har f¨orm˚aganatt associera dessa med f¨orvr¨angdaexempel. Min- nena kan lagras i systemet genom att ¨andraanslutningsvikterna beroende p˚a aktivitetsm¨onstreti n¨atverket, en process som kallas synaptisk plasticitet. Det finns flera olika teorier om villkoren f¨oratt styrkan hos synaptiska anslutningar ska ¨oka eller minska, och vilken av dessa som ¨armest sannolika ¨arfortfarande en ¨oppen fr˚aga.Flertalet studier av det associativa minnet har anv¨ant en mod- ell som enbart tar h¨ansyn till korrelerad aktivitet mellan neuroner (BCPNN). Det finns dock ett visst experimentellt st¨odf¨oren annan modell, d¨arden exakta tidpunkten f¨orpre- och postsynaptisk aktivitet spelar en st¨orreroll (STDP). D˚a det inte finns n˚agra avg¨orande bevis f¨oratt n˚agonav dessa modeller skulle vara n¨armareverkligheten ¨anden andra kommer denna studie att unders¨oka skill- naderna mellan associativa neurala n¨atverksmodell som anv¨andersig av dessa olika teorier f¨orsynaptisk plasticitet. I denna studie skapades tv˚aenkla associativa neurala n¨atverk med 64 neu- roner, vardera med antingen STDP eller BCPNN som modell f¨orsynaptisk plasticitet. Genom att systemet tvingades in i flera olika tillst˚and,motsvarande olika minnen ¨andrasde anslutande vikterna mellan neuronerna. Genom att senare stimulera n¨atverken med partiella minnesm¨onsterkunde deras f¨orm˚aga att ˚aterkalla minnen, samt deras stabilitet testas. I flera avseenden visade sig STDP fungera b¨attre¨anBCPNN, och det ¨arm¨ojligtatt dra slutsatsen att den tidigare av dessa synaptiska regler ¨ardet b¨attrevalet i detta specifika fall. F¨oratt dra n˚agraslutsatser om vilken av STDP eller BCPNN som ¨arden mest sannolika modellen f¨orsynaptisk plasticitet i hj¨arnan, skulle mer detaljer- ade studier beh¨ova genomf¨oras. F¨orb¨attreresultat b¨ordessa anv¨andasig av mer avancerade och biologiskt realistiska modeller. 2 Contents 1 Introduction 5 2 Background 7 2.1 Associatve memory . 7 2.2 Neurons . 7 2.2.1 Action Potential . 8 2.2.2 Hodgkin-Huxley model . 9 2.2.3 Integrate and fire model . 11 2.3 Synapses . 11 2.3.1 Synaptic plasticity . 12 2.3.2 Spike-timing-dependent plasticity . 12 2.3.3 Bayesian Confidence Propogation . 12 2.4 Attractor networks . 13 2.5 Hopfield Network . 14 2.6 Related Work . 15 3 Method 17 3.1 Nest . 17 3.2 Spiking Hopfield Network . 17 3.2.1 Network . 17 3.2.2 Synaptic models . 17 3.3 Memory . 18 3.3.1 Learning . 19 3.3.2 Recall . 20 4 Result 21 4.1 Differences during training . 21 4.2 Distribution of weights . 22 4.3 Completion of partial stimuli. 24 4.4 Ability to remain active . 26 5 Discussion 27 5.1 Recall and stability . 27 5.2 Connections . 27 3 5.3 Problems, improvements and future work . 28 5.4 Etical and Societal Aspects . 29 5.5 Conclusion . 29 4 Chapter 1 Introduction Raym´ony Cajal pioneered modern neuroscience in the early parts of the 20th century when he investigated the small-scale structure of the nervous system. He made hundreds of drawings of its most vital component, the neuron, and received the 1906 Nobel Prize in Physiology and Medicine for his effort (Purves et al. 2012, p. 5). It was already clear that he was breaking new ground, but little might he has known about the vast implications his inquiries into this incredibly complex system | that gives rise to every part of our experience of the world around us | would have for the modern society. The possibility for us to understand, and even recreate the workings of the brain has created a lasting imprint in contemporary culture with works as "I robot" by Isaac Asimov, but also captured the imagination of myriads of scientists and engineers over the last century. There are many paths to investigate the brain; it may be by studying be- haviour, observing it with different technologies such as MRI, or by the meth- ods of computational neuroscience. By creating models of parts of the nervous system we may manipulate them, change parameters or add and remove com- ponents to mimic observed phenomena and thereby gain insight into what is causing the behaviour we can see, and how. One part of the brain's cognitive ability that vital to function well in the environment is the ability to associate. To recognise things from only partial information and to be able to remember them at all. In 1982 the American scientist John Joseph Hopfield designed an artificial neural network with the ability to store memories and to associate them with similar input (Hopfield 1982). This original network consists of several binary units that might be either on or of and all updating to new states at once (Gerstner, Kistler, et al. 2014, Chapter 17.2), useful but far from the biological reality of the brain and its dynamically spiking neurons. This type of network has since been extended to more likely and more elaborate versions, introducing models of actual neutrons | albeit often simplified | and synaptic connections. At the simpler end of the scale, the units and connections in the Hopfield network are replaced by spiking neurons and synapses,(W¨arnberg 2014) while others go into much more detail, 5 (Amit and Brunel 1997; Lundqvist, Rehn, et al. 2006; Lundqvist, Herman, and Anders Lansner 2011; Tully, Henning, and Anders Lansner 2014; Fiebig and Lansner 2017). Recreating the architecture and modularity of the cortex, an area in the brain where the memory is thought to reside (Lundqvist, Rehn, et al. 2006) may give even more insight. Given the same stimuli, the behaviour of single neutrons are largely similar, and the ability for the brain to adapt to and learn other behaviours largely depends on the synaptic connections in between them (Gerstner, Kistler, et al. 2014, Chapter 19). Depending on the activity patterns in the brain a synapse connecting two neurons may either strengthen or weaken in a process known as plasticity according to a principle postulated by Donald Hebb in 1949 (Hebb 1949), summarised merely as \Neurons that fire together wire together". This Hebb's rule may be implemented in a variety of ways, some taking the relative timing of the neuronal activity into account, such as Spike-Timing-Dependent Plasticity (Markram, Gerstner, and Sj¨ostr¨om2012), and others merely caring about a correlation, e.g. Bayesian Confidence Propagation (BCPNN) (Anders Lansner and Ekeberg 1989; Sandberg et al. 2002; Tully, Henning, and Anders Lansner 2014; Fiebig and Lansner 2017). One of the parameters that may be tweaked in associative neural networks is the type of synaptic connections used, and if this gives rise to different behaviour, it may provide insight in what is most likely to be present in real networks in the brain. Most recent studies investigating spiking attractor neural networks as models for memory have used the BCPNN approach (Fiebig and Lansner 2017; Tully, Henning, and Anders Lansner 2014; Sandberg et al. 2002) and it remains unclear whether Bayesian plasticity produces different results than would spike-timing-dependent plasticity. As there is no conclusive evidence regarding the temporal aspect of synaptic plasticity (Schulz 2010) this study will investigate how the type of memory model utilised in recent experiments (Fiebig and Lansner 2017) compare when used with BCPNN (a temporally symmmetric model) and STDP (a temporally assymetric model).