CompSci 182 / CogSci 110 / Ling 109Midterm Examination, Spring 2006Prof. Srini NarayananName: SID: Comp(Y/N): Section:1 2 3 4 5 TotalScore/501. (10 points total) Briefly justify your answers(a) (3 points) Why is Hebbian learning not a complete story for how we learn generally?(b) (3 points) How does it work biologically?(c) (2 points) What is a triangle node in connectionist modeling?(d) (2 points) Describe an implementation of a triangle node using abstract neurons with a binarythreshold activation function.1Students in the Computation option SKIP this question2. (10 points total)Consider a behavioral experiment that is being designed to test the hypothesis that processing actionwords activates brain circuits that are used for performing the action described. The task is a picture-word matching task. Each subject is presented with a picture of a motor action (kick, chew, grasp)followed by a word (an English verb). The task is to determine if the word correctly describes theaction in the picture and to press “yes” if it does and “no” if it doesn’t.The picture stimulus is on for 1 second followed by a 500 millisecond interval where a fixation cross isshown. An English verb in written form is then presented until the subject presses a button indicatingthat the verb is or is not a good description for the action depicted in the image. Reaction times forthe response are measured and used to test the hypothesis. The type of word stimulus presented fallsinto three conditions(a) matching where the word describes the action in the picture,(b) mismatch same effector where the word describes a different action than the picture but usesthe same effector (body part). An example of this condition is the pairing of the picture of walkfollowed by the word kick.(c) mismatch different effector where the picture and word do not match and use different bodyparts. An example is the pairing of the picture of walk followed by the word scratch.The pictures and words are chosen from 3 effectors (foot, hand, and mouth). At the end of the ex-periment, for each subject, their reaction times are measured and grouped into the three conditionsdescribed above for comparison: (1) matching picture and word, (2) mismatch with the same effector(3) mismatch with different effectors.(a) (4 Points) What is somatotopy? How did the Buccino et al.(2001) fMRI mirror neuron experi-ment relate the somatotopic organization of the premotor cortex to observing actions involvingdifferent body parts?(b) (4 Points) Given the various results presented in class, would you predict greater reaction timeresults for the mismatch same effector condition or the mismatch different effector condition?Explain your answer.(c) (2 points) Why did the experiment add a 500 millisecond fixation cross between the picture andthe word? (Hint: Would it have worked if the interval was 100 milliseconds?)2Students in Computational option DO this questionConsider the special Γ subclass of PDP neural networks. A Γ network has an input layer (indexed byi), a hidden layer (indexed by h) and an output layer (indexed by o). With these networks, we willuse the letter a to refer to a node’s activation. For example, aowould be the activation of a node inthe output layer. We will use toto refer to an output node’s target value. To refer to the weight of anedge between the hidden and output layer, we will use whoand for the input to hidden, wih.In a Γ network, the activation function of an output node is of the form ao= K ∗Ph(who∗ ah) andthe activation function of a hidden node is ah= K ∗Pi(wih∗ ai) where K is the same real numberfor all activation functions in the network.For Γ networks:(a) (2 Points) What is the derivative of the error function with respect to who?(b) (2 Points) Ignoring momentum and assuming a learning rate of α, show the weight update func-tion for who(c) (2 Points) What is the derivative of the error function with respect to wih?(d) (2 Points) Rewrite the activation function for an output node of a Γ net without reference to ah.(e) (2 Points) What does the result from the previous part suggest about the class of problems that Γnetworks can solve?33. (10 points total) Consider the following concepts:• clothing• to amble• a bike• the color maroon(a) (6 points) Discuss for each concept whether it is a basic-level, superordinate or subordinate cat-egory. Support your answers with relevant criteria.(b) (4 points) From the lectures and readings covered in class, what can you say about how each ofthese concepts may be embodied in the neural circuitry of the brain. Be concise in your answer.44. (10 Points total)(a) (2 Points) Why is Regier’s program an example of embodied semantics?Regier’s model was predicated on the premise that our learning and understanding of spatial-relationterms is necessarily grounded in our basic sensory-motor circuits and our interactions with the world.Specifically, the model used image schemas as the computational primitives, and learned spatial relationsas operations over them.(b) (2 Points) Specify two limitations of Regier’s program.The model can’t scale up to other linguistic domains; has no handle on grammar; can’t do languageproduction; is not provably the unique solution to the problem of learning spatial relations (i.e. it’s onlyan “existence proof”); can’t perform inference (“if x is to the right of y then y is to the left of x”); can’tlearn abstract meanings of spatial terms; and is representationally opaque (since it’s PDP).(c) (2 Points) Why is the system not able to learn the word near?The model has no primitive distance metric—and it can’t deduce distance from the other measurements.In fact, there is no notion at all of size generally.(d) (4 Points) Why does Regier’s program use implicit as opposed to explicit negative evidence?How does the program implement implicit negative evidence?Human children don’t usually get (many) explicit negatives in the course of learning words; i.e., they mayget corrected (“No, that’s not above, that’s next to”), but they aren’t simply presented with all instancesof words that don’t apply (“The block is under the couch, kiddo; not ‘next to’ or ‘above’ or ‘to the left of’or....”). So it would be cheating to supply the model with explicit negatives to all spatial-relation wordsthat don’t apply.On the other hand, Regier couldn’t simply take positive evidence of one word as