SAMPLE ANSWERS FOLLOW - Biological Computation Project

PSYCHOLOGY 354 MIDTERM EXAMDr. Michael R.W. DawsonOctober 22, 2009Part I: Choose any TEN of the following terms, and write a short (2-3 sentence)definition for each. The definition should indicate what the termmeans, and should also indicate why the term is important to cognitivescience. Remember, ONLY 10 DEFINITIONS are required. Each definitionis marked out of 3 points.Structure/Process DistinctionPhrase MarkerGenerative GrammarContext Free Grammar Activation Function SelectionismGraceful Degradation Symbol Text learningLinear Separability Multilayer Perceptron Computational levelPart II: Choose any ONE of the following questions, and write a short essay(3-4 pages) to answer it. Make sure that your answer is clear and concise,and also make sure that you deal with the question directly. Your answerwill be marked out of 35 points.1. What is the trilevel hypothesis, and why is it important to cognitive science.What are the implications of adopting this hypothesis in terms of the kinds oftraining that cognitive scientists should receive? What are the implications ofthis hypothesis with respect to the research practices of cognitive scientists?Illustrate your answer with relevant examples from the lectures and from thereadings.2. Given your current knowledge about cognitivism, compare and contrast cognitivescience to cognitive psychology. In what ways do they differ? In whatways are they similar? Can one be a cognitive scientist, and at the same timenot be a cognitive psychologist? Illustrate your answer with relevant examplesfrom the lectures and from the readings.3. Given your current knowledge about the nature of information processing,compare and contrast the classical and the connectionist approaches to cognitivescience. In what ways do they differ? In what ways are they similar?Does it really matter which approach we adopt when we do research in cognitivescience? Illustrate your answer with relevant examples from the lecturesand from the readings.SAMPLE ANSWERS FOLLOW

General CommentsThis midterm was written by 42 students. The average grade was 49.43marks out of 65, which is a 76.04% average. This is much higher than expected(a typical average would be closer to 71% or 72%), but not too far offthe markThe maximum mark was 62/65, and the minimum mark was 37/65.Sample Answers for Definitions1. Structure/Process Distinction: the structure/process distinction is a crucialcharacteristic of classical cognitive science. It is the claim that thesymbols that represent data are distinct from the processes that manipulatethis data. For example, in a Turing machine the structure is the symbolsthat are stored on the tickertape, while the process is the set of rulesthat are built into the machine head. The structure/process distinction iscritical because this distinction is a prototypical description of the nature ofinformation processing, and also leads classical cognitive scientists to therequirement that they explain cognition with an architecture: that is, a particularproposal about the primitive characteristics of a structure and ofprocesses. (Note: this distinction has nothing to do with the difference betweenthe implementational and the algorithmic levels of analysis.)2. Phrase Marker: a phrase marker is a complex symbol or token used torepresent the syntax of a sentence. It is a tree-like structure that makesexplicit constituent structure, parts of speech, in the linear order of words.It is created by a context free grammar, and can be manipulated by atransformational grammar. Phrase markers are important to cognitivescience because they are a prototypical example of modeling a psychologicalphenomenon using information processing, and their constituentstructure models the recursive structure of human language.3. Generative Grammar: A transformational or generative grammar is a kindof grammar proposed by Chomsky. The grammar models the mappingbetween the phonological form of sentences and the logical form of sentences.It does this by using rules to transform one phrase marker intoanother. It is important to cognitive science because it demonstrated howan infinite variety of possible sentences could be described by an informationprocessing model -- a grammar -- that consisted of a finite number ofsymbols and a finite number of rules.4. Context Free Grammar: A context free grammar is a set of rewrite rulesthat take as input sentence components and output a complete phrasemarker. For instance, an example of such a rewrite rule could be S NPVP, which says that an S node in a phrase marker can grow into two subnodes(a noun phrase and a verb phrase). By repeatedly applying a smallset of such rules, any phrase marker can be constructed. This is impor-

tant to cognitive science because it demonstrates the ability of a finite systemto generate a potentially infinite variety of behaviour. It is also importantbecause it is a key component of the classical account of language –this grammar is required to create the phrase markers that are laterprocessed by a transformational grammar.5. Activation Function: In a PDP network, an activation function is used toconvert the total incoming signal to a unit (its net input) into an internallevel of activity, usually between 0 and 1. There are many different activationfunctions in use in various versions of connectionism, such as thesigmoid-shaped logistic equation and the bell-shaped Gaussian equation.Activation functions are important to cognitive science because the capabilitiesof a network (that is, the kinds of problems that a particular networkcan solve) are dictated by the activation function. For example, the factthat the activation function for the output unit of a perceptron has only onethreshold is why it can only deal with linearly separable problems.6. Selectionism: In a typical instructionist theory, it is assumed that the mindor brain is a blank slate, and that the structure placed there is a consequenceof experience. Selectionism is a radical alternative to this view. Itis the theory, inspired by Jerne’s analogy with the immune system, that allrequired structure is already innately available in the brain. Rather thanbeing “written” by the environment, the environment chooses the existingstructure that it needs, making this structure more available in the brain.This theory is important to cognitive science because it offers a radical alternativeto standard theories of learning, and can lead to artificial neuralnetworks that quickly adapt to the requirements of an environment.7. Graceful Degradation: Graceful degradation refers to the situation inwhich noise is added to the input of a system and the system is still able tofunction, though not as well. In particular, the decrease in the system’sperformance should be proportional to the amount of noise in the input.For example, in PDP networks, because of the redundancy of informationin the inputs the system is able to function proportionately to the amount ofnoise headed into the system. An example of this would be in thesharks/Jets example in class, when incorrect information was provided tothe network, but the network still made a correct response even thoughthis response was weaker than when all information is correct. This is interestingto cognitive science because graceful degradation is one characteristicthat appears to be true of the brain, but not true of classical models,and therefore can be used to support connectionist. (Note: If yousimply said that it distinguished connectionism from classical models, youdidn’t get full marks – you need to relate this distinction to cognitivescience, e.g. the brain. Also, if you mixed this up with damage resistance,then you also lost marks).

8. Symbol: A symbol is a token or a sign that is used by a classical systemto represent some information or meaning. The key property of the symbolis that its shape or form can be used to identify what type of symbol itis. In turn, this identification determines what classical rules can be appliedto the symbol. Symbol of our important to cognitive science becausesymbol manipulation is the fundamental definition of informationprocessing that is used by classical cognitive science. Identifying symbols,and rules to manipulate the symbols, is central to explaining phenomenalike language and problem solving. Classical cognitive science arguesthat all of cognition can be explained by appealing to cognitive symbols,and how they are manipulated by cognitive rules. (Note: if you justsaid that a symbol was required to get a Turing machine to work, then thiswasn’t a sophisticated enough claim to get full marks – nor was it relatedenough to cognitive science in general.)9. Text learning: Text learning is a form of learning proposed by Gold inwhich a language learner is only presented grammatical examples of alanguage that is being learned (positive information). This is to be contrastedwith informant learning, in which grammatical and non-grammaticalexamples are both presented (positive and negative information). Textlearning was shown by Gold to be much less effective than informantlearning. However, understanding text learning is crucial to cognitivescience because evidence shows that when human children learn theirfirst language, they do so as text learners, not as informant learners.10. Linear Separability: A pattern space is a multidimensional space in whicheach pattern that is presented to a network can be represented as a point.Linear separability means that a single straight cut through a patternspace solves a problem by separating all of the patterns that the networkturns “on” to from all of the patterns that the network turns “off” to. For examplethe AND problem is linearly separable, but the XOR problem is not.This term is important to cognitive science because it was proven thatperceptron's could only solve problems that were linearly separable, andthis was a devastating blow to old connectionism. This is because humansare capable of solving classification problems that are not linearlyseparable, like identifying connectedness. (Note: linear separability is aproperty of a pattern space, not of a network. It is also a property of aproblem, not of the system that solves the problem – so we could easilyimagine a classical system dealing with a linearly separable pattern recognitionproblem.)11. Multilayer Perceptron: A multilayer perceptron is a prototypical networkof modern connectionism. Like the simpler perceptron, it has a set of inputunits to represent environmental inputs, and a set of output units torepresent responses to these inputs. However, it also has one or morelayers of hidden units that stand as intermediate processors, and which

are capable of detecting complex features present in the inputs. It is thesehidden units that give the multilayer perceptron its exceptional power: tobe an arbitrary pattern classifier, a universal function approximators, or tobe equivalent in power to a universal Turing machine. The discovery oflearning rules capable of training such powerful networks have led to theemergence of the connectionist alternative to classical cognitive science.12. Computational level: At the computational level of analysis, a cognitivescientist is concerned with answering the question “What informationprocessing problem is being solved by a system?”. Usually, to answer thisquestion involves some sort of formal analysis using mathematics or logic,because the answer requires creating a proof about the abilities or inabilitiesof a system. The computational level is important because it can beused to highlight limitations of information processing systems. For example,Minsky and Papert’s proof that perceptrons could not learn todetect connectedness demonstrated a fatal limitation in that kind of neuralnetwork, and was a computational level analysis.Sample Answers for Essay Questions1. What is the tri-level hypothesis, and why is it important to cognitivescience. What are the implications of adopting this hypothesis interms of the kinds of training that cognitive scientists should receive?What are the implications of this hypothesis with respect tothe research practices of cognitive scientists? Illustrate your answerwith relevant examples from the lectures and from the readings.The sample answer below was given 35/35. I especially liked the reflectionsabout the eventual utility (or futility) of the information processing hypothesis. Ithink it is too early to be making this kind of argument, because to do it properly itneeds to be informed about embodied cognitive science, but it demonstrates a lotof depth of thinking about course material. Indeed, this is one of the best essayanswers that I have seen in several years of teaching this course! Well done!!This answer was 752 words, written as 3¼ single spaced pagesCognitive science has been a scholarly movement, relatively recent in the historyof science, that has facilitated an interdisciplinary approach to the study of thehuman phenomena of thought. Fundamental to cognitive science is a sharedassumption that cognition is information processing. In addition to this, the informationprocessing hypothesis, cognitive scientists, generally speaking, agreethat questions about cognition should be addressed by three levels of inquiry.According to the tri-level hypothesis, cognition should be understood on a computational,algorithmic, and implementational level for it to have any valid and relevantstance as an addition to human knowledge. While it has been argued thatthe tri-level hypothesis and the information processing hypothesis full facilitate aninterdisciplinary, and therefore more complete (implicitly) understanding of cogni-

tion, I would suggest that it still limits our understanding of human mental functions.First, let me briefly describe the tri-level hypothesis in more detail. As statedabove, it involves three levels of inquiry. First, the computational level addressesquestions concerning what information processing problem is being solved. Fora cognitive scientist, this involves formulating questions about cognition into logicalor mathematical methods. For example, asking about the informationprocessing problem of language learning is done by making it into a mathematicallyprovable statement. At the algorithmic level, questions are asked about thesteps that the information processor carries out in order to solve the problem.For cognitive scientists, these steps usually take the form of algorithms, heuristics,or any other rule-governed or logical method for converting input data intoproper output. Lastly, the implementational level deals with questions about theactual, bodily, physical properties of the information processor that enables it tocarry out cognition. For the human this is generally believed to be the brain.The tri-level hypothesis determines how cognitive scientists think about cognition,and consequently the questions they ask, the assumptions they make, what isdetermined as a plausible discovery, etc. It also frames why cognitive science isinterdisciplinary. Because this hypothesis necessitates agreement between thelevels, disciplines that usually focus on one level will have to communicate andshare their findings with other disciplines in order to create theories that stand upto these demands. However, this does not invoke the notions that different disciplinesshould focus on only one level, with the unifying name cognitive scienceas just an ???? term uniting distinct factions. Rather, a cognitive scientist, asopposed to a purely psychologically trained academic, would have to be trainedin all relevant areas of the multiple disciplines that help illuminate all three levelsof the hypothesis. Therefore, he or she would have to be trained in the findingsof multiple disciplines that conform to the information processing hypothesis.The information processing hypothesis completely defines the parameters of assumptionsmade by the scientist, whereas the tri-level hypothesis categorizes levelsof meaning when it comes to investigation. By adopting the informationprocessing hypothesis, cognitive scientists were hoping to put the mind back intoscientific inquiry as the ??? where symbols are manipulated to create meaning.Any investigation carried forth from here then has its language constrained. Totalk only of information processing, the storing, receiving, transmitting, and transformingof symbols (information).My problem arises when the findings of cognitive science are compared to thelived experience of the cognitive being. Computers cannot be asked how theyare or how they think. It is the human’s unique capability for self-reflection thatprecedes the “scientific” investigation of reality, which usually culminates in categorizinguniversal truths.

Cognitive science seems to be a discipline confused, in that it thinks by studyingconcepts that they create to represent non-originally defined happenings in reality,that they are getting answers about this human phenomenon. Any constraint,whether it be information processing or mind, is a human desire to make senseof this, fallible to the context in which it is used and formed.If I have gone in a tangent, I apologize. The main concern I am addressing issimilar to Bruner’s problem with information processing. The essence of whatwas originally this human “thing” is lost by defining it with respect to the tri-levelhypothesis because, according to the lecture, the tri-level hypothesis is tied to theinformation processing hypothesis. Therefore, computational questions are definedwithin the limes of the assumptions made that information processing is agiven. Therefore, when talking about language, as an example, everything outsideof the formal, mathematical definitions is left undiscovered, because of howquestions and answers are framed according to the tri-level hypothesis.2. Given your current knowledge about cognitivism, compare and contrastcognitive science to cognitive psychology. In what ways dothey differ? In what ways are they similar? Can one be a cognitivescientist, and at the same time not be a cognitive psychologist? Illustrateyour answer with relevant examples from the lectures andfrom the readings.To my amazement, no one answered this question. Remember the lecture andthe chapter on the difference between cognitive science and psychology? Whywouldn’t you expect this difference to also be true when we talk of “cognitive psychology”instead of “psychology” in general?3. Given your current knowledge about the nature of informationprocessing, compare and contrast the classical and the connectionistapproaches to cognitive science. In what ways do they differ? Inwhat ways are they similar? Does it really matter which approach weadopt when we do research in cognitive science? Illustrate your answerwith relevant examples from the lectures and from the readings.I liked this answer’s approach, which was to actually use the tri-level hypothesisto organize the answer, instead of just saying that the tri-level hypothesis appliesto both approaches. The ‘proof’ of equivalence at the computational level is alsonicely put, and surprising. This answer was one of 2 that received 35/35 forquestion 3. This answer was 699 words, written as 3 full single-spaced pages.This essay will explore classical and connectionist approaches to cognitivescience. I will explore how they differ and where they are similar through the le-

vels in the tri-level hypothesis. I begin at the tip, that is, with the computationallevel.At the computational level, a cognitive science researcher asks “What type of informationprocessing problem is being solved?” and attempts to specify, formally,what the problem is. At this level, both approaches are actually equivalent interms of what problems they can solve. It is easy to see this when one learnsthat a connectionist network can implement logical operators (e.g., OR, AND)and this provides the possibility to simulate a Turing machine or other serialcomputer. Computers are von Neumann machines (Turing machines with RAM)and as we saw in class, with the Jets/Sharks example, serial computers can simulateconnectionist networks, since that is exactly what we saw happening.At the algorithmic level the two approaches diverge substantially. Under theclassical approach, one would more or less explicitly program the specific stepsrequired to solve a problem. This is easy to understand since the calculationsare easy to see by the cognitive scientist. On the other hand, it is difficult tosolve ill posed problems in this way. An ill posed problem has multiple possiblesolutions but only one correct one (like a crossword row or visual perception).In contrast to the classical approach, the connectionist network is able to betterhandle ill posed problems, but because of how the networks are trained (ratherthan programmed), it is difficult to communicate what exactly is being done. Thenetwork looks like a “pile of goo”. This has actually been used to criticize connectionistnetworks, but a) connectionists have ways of explaining the networksand b) this does not make any difference in terms of power.Before proceeding to the implementational level, I want to mention one way thatthe two approaches can differ methodologically. In contrast to the traditional,classical “top down” strategy, whereby one works from the computational leveldown to the algorithmic to the implementational level, connectionist researchershave used a ‘synthetic’ approach which is directed upwards. One uses a connectionistnetwork to study the higher level phenomenon that emerges. One example,form class, is the classical solution to Piaget’s balance scale problem.The old approach was a decision tree that was produced from the top down, buta connectionist network was used to solve the problem in a much cleaner way(according to the graphs).At the implementational level the approaches also differ substantially. One reasonis that connectionist systems compute in parallel in a distributed fashion, unlikethe serial processing of the classical approach. This, I think, gives connectionistnetworks an advantage. They are able to process faster due to their distributedprocessors, they are able to perform relatively well when a unit is damaged,and incomplete or incorrect input is accommodated by the distributed natureof the processors. In contrast, a classical processor is brittle in the sensethat it ceases to perform if at all damaged and cannot directly handle incomplete

or damaged input. Classical processors are also slower in general because theydo not compute things in parallel (although I just noticed that I repeated myselfhere).Connectionist networks also have the advantage of being more biologicallyplausible since the distributed sorts of processing found in them are similar tothat of the brain. They are also more biologically plausible since they degradegracefully and are resistant to damage, as above.I think it does really matter which approach is adopted by the researcher. This isbecause, while in principle they are equivalent, they offer different approachesand methodological tools for understanding cognition. These differing methodologicalconsiderations affect what questions are asked, and how problems can beapproached. I view the approaches as complementary and non-competing, butthese methodological pros and cons can inform which approach is best for a givenproblem, and so I think generally the research problem should inform the researcherof what approach to employ rather than trying to determine the best approachin general and then trying to solve the problem with that approach, whateverit is.