CSE140 Cognitive Science Midterm 1, October, 2005 Name _________________ (2 points) Penn ID ________________ Score (please leave blank) possible actual Your name 2 True/false 14 multiple choice 6 short answer 78 __________________________________ TOTAL 100 Closed book, no calculators. You have 80 minutes. True/False (2 points each) grading scheme: 0 if incorrect, 2 if correct. 1. __F__ A Turing Machine will halt in finite time for any program. 2. __T__ A Turing Machine can simulate any modern computer. 3. __F__ The number of five word sentences is exponential in the number of words in the English language. 4. __F__ The Pineal gland is responsible for processing color. 5. __F__ Cartesian dualism is a scientific hypothesis because it is falsifiable. (please read carefully) 6. __F__ A synapse allows information flow (electrical and/or chemical) from the dendrite of one cell to the axon of another cell. 7. __T__ The blind spot is blind because there are no receptors at that point of the retina. Multiple Choice (2 points each) grading scheme – 2 points of all correct, if none correct; 1 if both right and wrong. 1. Which of the following describes a brain but not a Turing Machine? (Select all that apply.) * (a) Parallel (b) Serial (c) Polynomial (c) Exponential 2. Fill in the blanks: The ___ visual field is projected on the ___ side of the retina, which is sent to the ___ hemisphere of the brain. (a) left, left, left (b) left, right, left (c) right, left, right * (d) right, left, left 3. A lesion in which brain region(s) will affect the "what" pathway? (Select all that apply.) (a) Frontal (b) Parietal * (c) Temporal * (d) Occipital Short Answer (6 points each) grading scheme: to be determined 1. What two components are required for an agent to show intentionality? (i) beliefs (ii) desires 2. What is an "interactive proof" and how are they powerful? (i) Interactive proofs include two properties which are.. (for example) randomization by the verifier and interaction (ii) In what way is an "interactive proof" more powerful than a conventional proof? Confidence is known to grow exponentially with the number of rounds (well, as confidence it is 1 – (1/2)k). 3. Match each of the following statements to the appropriate Marr level 1) computation 2) algorithmic/representation 3) implementation (i) __2_ The brain processes visual inputs using both a "what" and a "where" pathway. (ii) __1_ A properly functioning brain analyzes sensory input to determine motion of objects. (iii) __3_ The visual signals from the retina are sent to the LGN. 4. When using Bayes rule, it is often a good idea to simply compute p(H|D) ~ P(D|H)P(H), instead of the correct P(H|D) = P(D|H)P(H)/P(D) When might one prefer to do this and why? If there are two competing hypotheses, the ratio of the hypothesis is all that matters. And it is faster because you don't have to compute P(D). 5. In order to use Bayes rule, one needs prior probabilities. Name and briefly describe two ways of obtaining priors. Lots of possible answers here. (i) ___ Availability– the ease with which people can draw examples from memory___ (ii) ____ Description length – how many combinations of the space are available ____ In general, counting, models of the world, # of combinations, etc. 6. Give the equation that defines conditional probability. P(A/B)=P(A,B)/P(B) 7. What assumption is made to transform Bayes rule to a Naive Bayes model? Bayes:P(H/D)=P(D/H)P(H)/P(D). Independence – both conditional (likelihood; P(D/H)) and for P(D). NOTE __ just conditional independence is ok. 8. Imagine a non-human primate has suffered a lesion to the temporal lobe portions of its "what" or ventral visual pathway. (i) Briefly describe a task this animal would be expected to successfully complete. A landmark discrimination study – there are two food wells in front of the animal, one to the left one to the right. A "cue" is a block that is located nearer one or the other food well, and that well has the food in it. The animal will learn to choose the well nearer the cue. (ii) Briefly describe a task this animal would not be capable of completing. An object discrimination study. Again two food wells, but this time two objects. The animal becomes familiar with one object, and the objects (one new, one known) are placed next to separate wells. The food well with the known object has food. The animal will *not* learn to choose the food well next to the known object. Leave this space blank 9. Imagine that a subject is viewing a photograph of this lecture hall. While doing so, a small region of their MT (or V5) is stimulated by an electrode (e.g., current is introduced to a small cluster of adjacent cells). What perceptual consequence do you expect, and why? This question is a bit open-ended. I assume the ipsilateral eye is closed. In this case, a region of the visual world will appear to move. The region will depend on the receptive field of the stimulated cells and the direction and velocity of the motion will depend on the directional and velocity selectivity of the cluster of cells being stimulated. Leave this space blank 10. Studies in humans have shown that the two brain hemispheres have different specializations and can operate independently. Describe one such study, indicating the brain regions involved. After a general lesion to the left hemisphere, including the IT region, hierarchical figures are perceived globally rather then locally. One way to demonstrate this is to ask patients with lesions to draw a figure in which small xs make up a square. The patient will draw the square. 11. What is Prosopagnosia? Failure to perceive faces. Leave this space blank 12. Our lab is studying a hypothetical animal species called shrdlu. Shrdlus have two mechanisms for recognizing objects visually, which we call mechanisms A and B. Shrdlus use only either A or B at a time, and mechanism A is used twice as often as mechanism B. In addition, experiments show that mechanism A makes correct identifications 95% of the time, and errors 5% of the time. Mechanism B makes correct identifications 97% of the time and errors 3% of the time. One of our shrdlus was shown an object but misidentified it. What is the probability that the prediction was produced by mechanism A? Be sure to define your terms and show your work. C: correct; ~C: incorrect; A: mechanism A; B: mechanism B P(~C/A)=.05 P(~C/B)=.03 P(A)=2/3 P(B)=1/3 What is P(A/~C)=P(~C/A)P(A)/P(~C). P(~C)=P(~C/A)P(A)+P(~C/B)P(B) P(~C/A) = .05*.67/(.05*.67+.03*.33) = .77 13. I show you a red square. (a) What priors would I use, following the number game approach, for each of the following three hypotheses (please show your work)? (i) The rule is "red objects" (ii) The rule is "squares" (iii) The rule is "red squares" (b) What is likelihood of seeing the red square under each of the following assumptions (please show your work)? (i) The rule is "red objects" (ii) The rule is "squares" (iii) The rule is "red squares" To answer the above question, we need more information. Assume that if I show you a square, it is equally likely to be of any color, and if I show you a red object, it is equally likely to be of any shape. (All red squares are, of course, red and square!) (c) Which rule am I most likely to have used, based on the data you saw (show your work)? (i) The rule is "red objects" (ii) The rule is "squares" (iii) The rule is "red squares" I assume 3 shapes and 3 colors. (a) Following the number game, there are three "categories" (hypothesis), and using the inverse of the produce of the number of and the number of elements in each category: (i) 1/(3*3)=1/9 (ii) 1/9 (iii) 1/(9*3)=1/27 (b). The likelihood is P(observed/hypothesis) (i) 1/3 (ii) 1/3 (iii) 1 (c). Because only the ratio of posteriors is important, comparing the product of the likelihood and the prior is sufficient to choose the most likely (i.e., P(D) is the same for all three posteriors). These values are all equal, 1/27. Thus all three rules are equally likely to have been used.