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Learning Representations with Neuromodulators

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Learning Representations with Neuromodulators Learning Representations with Neuromodulators vorgelegt von M. Sc. Rapha¨elHolca-Lamarre geb. in Montr´eal von der Fakult¨atIV { Elektrotechnik und Informatik der Technischen Universi¨atBerlin zur Erlangung des akademischen Grades Doktor der Naturwissenschaften - Dr. rer. nat. - genehmigte Dissertation Promotionsausschuss: Vorsitzender: Prof. Dr. Hennig Sprekeler Gutachter: Prof. Dr. Klaus Obermayer Gutachter: Prof. Dr. J¨orgL¨ucke Gutachterin: Prof. Dr. Shu-Chen Li Tag der wissenschaftlichen Aussprache: 30. Juni 2017 Berlin 2017 To those from whom I learned, alongside whom I went on adventures, or with whom I shared a good laugh. Acknowledgements First of all, I would like to thank my supervisors Prof. Klaus Obermayer and Prof. J¨org L¨ucke. Klaus and J¨orgprovided valuable support throughout my PhD, from the initial application for funding to the execution of the work and up until the results publication. Then come all the members of the Neural Information Processing group who I thank, among many others, for their feedback during group talks and their company over lunch breaks{especially enjoyable when sitting outside in the sun. I would also like to express my gratitude to everyone at the Bernstein Centre, both staff and students, for providing a supportive environment, in particular for the many events and courses, the financial support, and the good times, among others at the annual retreat at Schloß Tornow. And last but not least, I acknowledge the funding bodies that made this research possible, the Studientstiftung des deutschen Volkes, the Fonds de Recherche du Qu´ebec { Nature et Technologies, and the Deutsche Forschungsgemeinschaft. Abstract Neurons in the cortex and in multi-layer perceptrons (MLPs) represent inputs as pat- terns of activity. In both systems, the nature of a neural representation carries im- portant consequences and, accordingly, the mechanisms guiding representation learn- ing are of great relevance. In MLPs, the most widespread learning method is the error-backpropagation algorithm. Although functionally effective, this method bears its limitations and is also unlikely to be implemented in the cortex. On the other hand, the mechanisms orchestrating plasticity in cortical representations remain un- clear; neuromodulators appear to contribute to this process but their exact roles are largely unknown. This thesis examines the plastic effects of two neuromodulators, acetylcholine (ACh) and dopamine (DA), with the following aims: first, to gain a functional understanding of ACh and DA transmission in shaping biological representations and, second, to explore neuromodulator-inspired learning rules for MLPs. I address these questions in a Hebbian-learning neural network model. I extend the model to simulate the plastic effects and physiological release properties of ACh and DA. I then study the impact of neuromodulatory transmission on the network's representation and its performance on a classification task. In the model, ACh activation approximates the concept of attentional effort. I demonstrate that this signal redistributes neural preferences such that more neurons encode challenging or relevant stimulus classes, thereby boosting performance on these classes. DA activation in the model accompanies reward prediction errors. I show that this signal adjusts neural weights to the reward contingencies of a task, in turn enhancing class selectivity in neurons and yielding large gains in classification accu- racy. These results suggest functional roles for ACh and DA in guiding biological representation learning. Additionally, in comparison with MLPs of the same architec- ture, neuromodulator-inspired learning produces lower error rates than those originally reported on the MNIST dataset and measures up with modern state-of-the-art optimi- sation methods. A single modulatory signal also proves to successfully guide learning in multiple layers concurrently in a deep convolutional network. Neuromodulator learning requires weak supervision signals and interacts with synaptically-local weight updates, thus offering potential applications in learning with weakly labelled data or in neuro- morphic processors. vi Zusammenfassung Neuronen im Kortex und in k¨unstlichen neuronalen Netzwerken (z.B. \Multi-layer perceptrons", MPLs) repr¨asentieren Inputs als Aktivit¨atsmuster. In beiden Systemen ist die Natur des neuronalen Codes entscheidend und folglich sind die Mechanismen, die das Lernen von Repr¨asentationen beeinflussen, von großer Bedeutung. In k¨unstlichen Netzwerken ist der `error-backpropagation' Algorithmus die am weitesten verbreitete Lernmethode. Es ist unwahrscheinlich, dass diese Methode im Kortex implementiert ist, jedoch ist derzeit nicht bekannt, wie das Gehirn Repr¨asentationen lernt. Die beiden Neuromodulatoren, Acetylcholin (ACh) und Dopamin (DA), l¨osenplas- tische Ver¨anderungenin kortikalen Repr¨asentationen aus. In dieser Arbeit unter- suche ich die funktionalen Rollen, die diese beiden Modulatoren, in Bezug auf die Verbesserung sensorischer Repr¨asentationen, haben. Dabei stehen zwei Ziele im Vorder- grund: Zum einen, soll ein funktionales Verst¨andnisder von ACh und DA ausgel¨osten Plastizit¨atin der Biologie geschaffen werden. Zum anderen, sollen Lernregeln f¨urMPLs erforscht werden, welche von Neuromodulatoren inspiriert sind. Ich behandle diese Fragen mithilfe eines neuronalen Netzwerkmodells, welches auf Hebb'schen Lernregeln basiert. Dazu simuliere ich ACh und DA als Modulatoren der Lernrate des Netzwerkes und best¨atigedadurch, dass dieses Modell bekannte Plastizit¨atseffekteaus der Biologie reproduziert. Danach simuliere ich die physiologischen Eigenschaften der Aussch¨uttung von ACh und DA und quantifiziere deren Auswirkung mithilfe einer Klassifikationsauf- gabe. Im Modell folgt die Ausch¨uttungvon ACh den Anforderungen der Aufgabe und der Motivation, als N¨aherungdes Konzepts des Aufmerksamkeitsaufwandes (`attentional effort’). Ich zeige, dass dieses Signal neuronale Pr¨aferenzderart umverteilt, dass mehr Neuronen herausfordernde oder relevante Stimulusklassen kodieren, was die Klassifika- tion dieser Klassen deutlich verbessert. Ich gehe daher davon aus, dass ACh diese Rolle in der Biologie ausf¨ullt.DA Ausch¨uttung wird im Modell von Belohnungsvorhersage- fehlern (`reward prediction errors') hervorgerufen. Dieses Signal verbessert neuronale Selektivit¨at,was wiederum zu einer Steigerung der Klassifikationsgenauigkeit f¨uhrt.Ich vermute daher, dass die DA-induzierte Plastizit¨atin senorischen Kortexarialen diese Funktion ¨ubernimmt. Angewandt auf den MNIST Datensatz zeigt DA-basiertes Ler- nen eine sehr gute Leistung, die vergleichbar mit modernen Optimisierungsmethoden in MLPs ist. Diese aussichtsreichen Ergebnisse motivieren weitere Forschungen auf dem Gebiet des neuromodulatorisch-inspirierten Lernens als Modell in der Biologie sowie f¨urpraktische Anwendungen. vii Contents Abstract vi Zusammenfassung vii List of Figures xii List of Abbreviations xiii List of Variables xiv List of Parameters xv 1 Introduction 1 1.1 The Brain's Shadow Theatre . 1 1.2 Biological Neural Representations . 2 1.3 Artificial Neural Representations . 3 1.4 Contributions of this Work . 4 1.5 Thesis Outline . 5 2 Sensory Representations in the Cortex 8 2.1 Overview . 8 2.2 Development of Representations . 8 2.2.1 Genetic Program . 9 2.2.2 Experience-dependent Development . 9 2.3 Modifications in Sensory Representations . 10 2.3.1 Sensory Deprivation . 10 2.3.2 Altered Sensory Experience . 11 2.3.3 Perceptual Learning . 11 2.3.4 Classical Conditioning . 12 2.3.5 Cortical Stimulation . 12 2.3.6 Neuromodulation . 12 2.4 Acetylcholine . 13 2.4.1 ACh and Attentional Demand . 14 2.4.2 Plastic Effects on Sensory Representations . 14 2.5 Dopamine . 16 2.5.1 DA and Reward Processing . 17 2.5.2 Plastic Effects on Sensory Representations . 18 2.6 Summary . 18 viii 3 Representation Learning in ANNs 21 3.1 Overview . 21 3.2 Learning Rules in Neural Networks . 21 3.2.1 Hebbian Learning . 22 3.2.2 Error-correcting Rules . 24 3.3 Neural Network Model . 27 3.3.1 Learning Mechanisms . 27 3.3.2 Interpretation as Maximum Likelihood Estimation . 31 3.3.3 Hierarchical Model for Classification . 32 3.3.4 Supplementary Methods . 34 3.4 Models of the Neuromodulators . 35 3.4.1 Modifications in Representations . 35 3.4.2 Models of ACh and DA . 36 3.4.3 Relation to Previous Models . 38 3.5 Summary . 38 4 Model of Acetylcholine 41 4.1 Overview . 41 4.2 Classification Performance as Proxy of Task Demand . 42 4.2.1 Model Description . 42 4.2.2 Results . 43 4.3 Alternate Models of Task Demand . 46 4.3.1 Classification Confidence . 46 4.3.2 Inferred Stimulus Class and Stimulus-Wise Confidence . 48 4.3.3 Results . 49 4.4 Signal of Stimulus Relevance . 51 4.4.1 Non-uniform Stimulus Relevance . 51 4.4.2 Non-uniform Stimulus Distribution . 52 4.5 Additional Effects on Learning . 54 4.5.1 Network Size . 54 4.5.2 Label Availability . 55 4.6 Discussion . 56 4.7 Summary . 57 5 Model of Dopamine 59 5.1 Overview . 59 5.2 Greedy Model . 60 5.2.1 Model Description . 60 5.2.2 Results . 61 5.3 Explorative Model . 65 5.3.1 Methods of Exploration . 66 5.3.2 Model Description . 68 5.3.3 Results . 69 5.4 Expectations as Reward Predictions . 72 5.4.1 Model Description . 73 5.4.2 Results . 74 5.5 Model Comparison . 75 5.5.1 Greedy versus Explorative . 75 ix Learning with Neuromodulators 5.5.2 Discrete versus Continuous Reward Predictions . 77 5.5.3 Comparison with Acetylcholine . 80 5.5.4 Comparison with Error-backpropagation . 81 5.6 Discussion . 85 5.6.1 Relationship to Biology . 85 5.6.2 Relationship to Machine learning . 86 5.7 Summary . 87 6 Deep Convolutional Model 89 6.1 Overview . 89 6.2 Convolutional Network Model . 90 6.2.1 Model Description . 90 6.2.2 Receptive Field Reconstruction . 93 6.3 Hebbian Learning . 94 6.3.1 Results . 94 6.4 Dopamine in Greedy Model . 95 6.4.1 Model Description . 95 6.4.2 Results . 96 6.4.3 Additional Effects on Learning . 97 6.5 Dopamine in Explorative Model . 100 6.5.1 Model Description . 100 6.5.2 Results . 101 6.5.3 Additional Effects on Learning . 102 6.6 Discussion . 103 6.7 Summary .
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