Computational Neuroscience and Cognitive Modelling

A Student′s Introduction to Methods and Procedures

Britt Anderson, Author

• Publisher: SAGE Publications Ltd
• Year: 2014
• Print ISBN: 9781446249307, 9781446249291
• eBook ISBN: 9781446297360
• Edition: 1
• Topic: Psychology
• Subtopic: Research & Methodology in Psychology
• Index: Psychology

"For the neuroscientist or psychologist who cringes at the sight of mathematical formulae and whose eyes glaze over at terms like differential equations, linear algebra, vectors, matrices, Bayes' rule, and Boolean logic, this book just might be the therapy needed."

- Anjan Chatterjee, Professor of Neurology, University of Pennsylvania


"Anderson provides a gentle introduction to computational aspects of psychological science, managing to respect the reader's intelligence while also being completely unintimidating. Using carefully-selected computational demonstrations, he guides students through a wide array of important approaches and tools, with little in the way of prerequisites...I recommend it with enthusiasm."
- Asohan Amarasingham, The City University of New York


This unique, self-contained and accessible textbook provides an introduction to computational modelling neuroscience accessible to readers with little or no background in computing or mathematics. Organized into thematic sections, the book spans from modelling integrate and firing neurons to playing the game Rock, Paper, Scissors in ACT-R. This non-technical guide shows how basic knowledge and modern computers can be combined for interesting simulations, progressing from early exercises utilizing spreadsheets, to simple programs in Python. Key Features include:

• Interleaved chapters that show how traditional computing constructs are simply disguised versions of the spread sheet methods.
• Mathematical facts and notation needed to understand the modelling methods are presented at their most basic and are interleaved with biographical and historical notes for contex.
• Numerous worked examples to demonstrate the themes and procedures of cognitive modelling.

 An excellent text for postgraduate students taking courses in research methods, computational neuroscience, computational modelling, cognitive science and neuroscience. It will be especially valuable to psychology students.

Chapter 1

An Introduction to the Ideas and Scope of Computational Methods in Psychology

Objectives

After reading this chapter you should be able to:

• understand the goals of computational modeling for psychology and neuroscience;

• describe the limits of computational models;

• describe the role played by computers in the growth of computational modeling; and

• describe how the success of a model can be evaluated.

1.1 Overview

My overall objective in this chapter is to introduce some of the motivations for using computational models in psychology and to suggest some of the limitations. It is often easier to sharpen one’s thinking on these points if there is some form of dialogue. If you do not have the chance to discuss these ideas with someone else, you might first read one of a number of recent position papers (e.g., McClelland, 2009; McClelland et al., 2010; Griffiths et al., 2010) and try to come to your own personal opinion of their correctness. Try to form your own answers to the following questions:

• Why bother modelling at all?

• Can we make a brain? Should we try? Should we care? Is this important for computational psychology?

• What role should biological plausibility play in neural and psychological models?

• Do you need a computer to create a computational model?

• How do you evaluate a model?

• What is the importance of a model’s assumptions?

1.2 Why Model?

One answer to this question might be because you believe that modelling is something that the brain itself engages in. By modelling you are trying to reproduce or discover the architecture of thought.

Mental models as a basis for cognition have their roots in the writings of Craik (1952). A more contemporary proponent for mental models as models of cognition is Johnson-Laird(e.g., Johnson-Laird, Byrne, & Schaeken, 1992). Just as a small mechanical model can be used to predict the oscillations of high and low tides, perhaps in our brains (or our minds) we have some small simulacra that reproduce the functional organization of our world. To model cognition then is to model our models of our world (Chapter 21 looks at one modelling platform for building mental models).

Modelling does not have to be justified so directly. Models can be viewed as simplified versions of complex phenomena. The phenomena may be too complex for us to directly grapple with, but by abstracting away some of the complications we can achieve a core set of features that we think are important to the phenomena of interest. This reduced, simpler set provides a more tractable basis for us to see how the pieces fit together and to understand better the causal relations.

This justification raises the question of how simple is too simple. How do we really know which features are unnecessary complications and which are core features? What are the criteria for making such a judgment? And doesn’t this put us on the road to reductionism, where we reduce, ultimately, all the laws of thought to the models of particle physics? Would an explanation at that level, even if accurate, gain us a deeper understanding of human psychology?

1.3 Can We Make a Brain?

The trivial answer is that yes, we can make brains; and every parent has done so. A parent’s actions lead to a new brain with all the attendant complexities and capacities. It is done with no insight into the process. We achieve no greater understanding. Therefore, we can argue that building a brain per se is not guaranteed to improve our understanding of the rules and procedures regulating human thought.

This example is not trivial. The tools of neuroscience are giving us an increasing understanding of neurons and their constituents. We know the make-up of many ion channels down to the level of genes and post-translational modifications. If we knew the position of every molecule in the brain, would we learn anything about how the brain as a whole functions? This can be restated as a question about whether we believe the brain and the mind to be merely the sum of their parts.

There are scientists pursuing this route to modelling the brain. The Blue Brain Project at the Ecole Polytechnique Federale Lausanne announces exactly these intentions on its website*:¹

Reconstructing the brain piece by piece and building a virtual brain in a supercomputer – these are some of the goals of the Blue Brain Project. The virtual brain will be an exceptional tool giving neuroscientists a new understanding of the brain and a better understanding of neurological diseases.

Do you share this conclusion?

A challenge to this approach claims that an understanding of the brain requires a consideration of scale. A sand dune is made up of individual grains of sand just as the brain is made up of individual neurons, but no amount of study of individual sand grains can explain the behavior of sand dunes. The behavior of a dune requires a large number of sand grains to interact. Is the same true of the brain?

Discussion: Are Psychological Concepts Experimentally Accessible?

We often use computational methods because something is experimentally inaccessible. This can be due to size or complexity or because, by its very nature, it is inaccessible to direct experimental manipulation. Do you agree that cognitive processes are inaccessible to direct experimentation? For example, can one directly manipulate working memory? And how does your answer to that question effect your position on the value of computational modeling?

1.4 Computational Models as Experiments

Another reason commonly given for using computational approaches in brain research is that they offer practical efficiencies. Generally, it is easier to run a computer program over and over again with minor variations than it is to repeat a behavioral task on numerous pools of subjects. In some cases it may not be possible to repeat behavioral investigations. Patient HM,² perhaps the most psychologically studied person of all time, had his problems as the result of surgery that will never be done again. The only way to repeat HM’s lesion is by modelling.

Under what circumstances is the quest for experimental efficiency justifiable as the basis for computational modelling? Some authors suggest that it is sufficient that computational models enable exploration. We have an idea on some topic, and before doing more focused, expensive, or time-consuming research we can “play” with our computer model to decide if further experiments are warranted, and which ones we should do first. But doesn’t this presume we have more confidence in the model than we should? Isn’t there a danger that a poorly chosen model could direct us in the wrong direction or lead us not to explore lines of research that we should? How do we monitor the use of exploratory modelling to make sure these outcomes do not occur?

Since computational models do not sacrifice animal participants or take the time of humans, they are touted as more ethical. Some studies involving conflict are not ethical in human research, but we can create a computer model of hundreds or thousands of little warriors and let them battle for territory as a way of exploring ideas about social conflict (see Chapter 22 for one modelling platform that can be used for this type of research).

Can we generalize from such data though? How do we validate hypotheses gained in this way?

Coherence and Concreteness

Words are subtle, and may mean different things to different people at different times. They may even mean something different to the same person at different times. Have you ever read something you wrote and wondered, “What was I thinking?” Models typically involve translating our ideas from words into formulas or computer programs. A by-product of this reformulation is a concreteness and clarity that may be lacking from our most careful phrasings. Even if a model does not say anything “new” or make novel predictions, this clarity can aid communication and improve reproducibility.

Modularity and Simplification

One attraction to modelling cognitive phenomena is that one can pull out a piece of a larger process and focus on it alone. This is justified, in part, by asserting that cognition is modular. The same rationale can be applied to modelling the “basal ganglia” as an isolated, functionally defined construct. Is this justification persuasive? Is cognition simply the result of isolated processes summed up? If we defined each of the important cognitive modules could we study them in isolation and by “gluing” them together understand the brain?

Can you think of a school of psychology that concerned itself with emergent properties, a psychological school that emphasized that wholes were more than the sum of their parts? What do you think this school would have felt about computational modelling in psychology?

In complex environments it is often the embedding of elements in an environment that is necessary for observing a desired effect. A common example is the role of raindrops and rainbows. Water droplets are essential for the production of rainbows, but the study of rainbows cannot be reduced to the study of water droplets. It cannot even be reduced to collections of raindrops. One could have a complex modular model of water and its coalescence into drops, and still not have rainbows. If one wired a water droplet model to a sunlight model, would the models then have rainbows? Or would there need to be an observing visual apparatus (i.e., a person)? A name for phenomena that only appear in the large or from interactions is emergent; these are phenomena, like the sand dune, that cannot be understood from their individual pieces alone.

Models for Exploring the Implications of Ideas

One of the fathers of connectionism as an approach to modelling in psychology (Chapters 11 and 13 introduce two types of simple neural networks), James McClelland (2009), has emphasized two main purposes behind his own work. He states that he seeks to simplify complex phenomena, and that he wants to investigate the implications of ideas.

Implications

A justification for models as a route to implications rests on the assertion that models are more transparent than behavioral experiments. Computational models are suggested to be more transparent because they require greater specificity, and because they do exactly what you tell them to do (even if you did not realize what you were telling them at the time, a “logic bug”).

As modellers, we specify the rules and the players. There is no ambiguity. This gives us an opportunity to demonstrate the sufficiency of our ideas. Models do not have to be biologically realistic to provide sufficiency proofs. If I assert that variation in light intensity across facial photographs contains information sufficient for identification, it is enough for me to build a program that can do it, even if I use methods that are inherently biologically implausible. My model represents an existence proof. While it does not show that people actually recognize faces from light intensity, it proves that they could. Note that this argument is one way. While a successful program shows that luminance information is sufficient for identification, we cannot draw a similarly strong conclusion from a failed program. We can only conclude that that program was inadequate, not that no program could ever be designed to do the same.

Typically, though, we have higher aspirations than simply stating our ideas clearly or providing existence proofs. We want to advance our understanding of the phenomena in question; we want to travel beyond where our ability to forecast can take us. When we specify a computational model we want to be able to ask, “What if?” In order for our models to be computationally tractable, and to permit us to still be able to follow what is going on, we can usually only implement simplified models. This brings us back to the questions considered above. Is our simplified model too simple? Can we make inferences about more complex systems from simpler ones? If the only circumstances in which we can take advantage of model concreteness for investigating model implications are those situations where we have had to simplify, reduce, or modularize the situation, do we ever really achieve this advantage? One criticism of studying cognition by computational simulation is that our simplifications are arbitrary. In the process of simplifying, paradoxically, we lose our transparency.

1.5 Do Models Need to Be Biologically Plausible?

When we review neural networks (Chapters 11 and 13), we will see that modellers often draw inspiration from biology, but how close do models need to be to biology in order to be useful? Back-propagation is a tool used in neural networks This error correction method relies on propagating the error signal from the end of a computation back to earlier nodes in the chain. It is not obvious that neurons in our brains have the requisite wiring or methods necessary to propagate errors backwards. Therefore, what can we conclude from a computational model that uses the backpropagation error correction algorithm?

“There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy.”

One response is philosophical. This response claims that it is just too early in our research program to presume that our knowledge of biological mechanisms is sufficient to reject any possible account. Just because we do not know now of any way for real neurons to backpropagate an error signal does not mean that we will not know it next week, or the week after. This justification gives renewed vigor to the use of models as exploration and for examining the implications of ideas. If something turns out to be very u...

Table of contents

• Cover Page
• Half Title
• Title
• Copyright
• Contents
• Preface
• 1 Introduction
• I Modelling Neurons
• II Neural Networks
• III Probability and Psychological Models
• IV Cognitive Modelling as Logic and Rules
• Notes
• References
• Index