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Sample Exam Questions
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I. Introduction
Q.
Spell out the three essential ingredients of a Sixth Generation computer.
For each of these three ingredients, give a biological and a technological example of a specific
system/subsystem employing this ingredient.
II. Neural Networks
Q. (a) Give weights and threshold for a McCulloch-Pitts neuron with inputs a, b, and c, and whose
output is c if a = 0 and b= 1, and is otherwise 0.
(b) Give weights and threshold for a McCulloch-Pitts network with inputs a and b and output ab, the
modulo 2 sum of a and b.
(c) In what follows, we view the bit-pairs ab, cd, and ef as binary numbers. Use McCulloch-Pitts neurons
to build a network that generates e where ef are the low-order bits of the numerical product of the
numbers ab and cd.
[Hint: A case by case analysis for the 4 values of cd provides one approach.]
[Simplification: For part (c), it's OK to use AND and OR gates without spelling out the weights and
thresholds.]
Q. (a) Give a McCulloch-Pitts neuron for the boolean function a<b (i.e., the neuron has 2 inputs a and b,
and gives output 1 only if a = 0 and b = 1).
(b) No single McCulloch-Pitts neuron can provide output 1 if and only if its two inputs are equal.
Provide a 2-neuron circuit that does the job.
(c) Consider two 2-bit binary numbers ab and cd.
Write an expression in terms of the 0-1 symbols a, b,
c and d, using the boolean connectives =, <, AND and v (inclusive-OR) to express the numerical relation
ab < cd.
(d) Given the above, use McCulloch-Pitts neurons to fill in
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Sample Exam Questions
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so that e = 1 when ab < cd, while f = 1 if ab = cd
Q. Recall the view of the neuron as firing whenever the membrane potential passes the threshold.
Suppose the equation describing the threshold is:
(t) = 
if 0  t  r ;
= h+e
1/(t - r)
if t > r,
where t is the time since the last spike was fired, h is the resting level for the threshold, and r is the
absolute refractory period.
Sketch the graph of (t), then derive a formula for the firing rate F(m) of the neuron if the membrane
keeps the constant value m.
Sketch the graph. Is it sigmoid?
Q. Draw and explain a neural circuit that will respond to a spot moving across a one dimensional retina
whether it moves to left or right , but will not respond to a stationary spot or to full-field illumination.
Q. List four ways to build neuron models that are more sophisticated than the leaky integrator neuron.
Q. (a) Contrast (briefly) the results of Kuffler and Hubel and Wiesel on the cat with those of Lettvin et al.
on the frog.
(b) Relate these differences to the different "ecological niches" of the animals.
(c) In at most a page describe the implications of this for technological applications of neural networks.
Q (a) Define “simple” and “complex” cells. Briefly explain the Hubel-Wiesel hierarchical model for the
wiring of simple cells and complex cells. What is the key observation on timing that led Dr. Mel to seek
an alternative model? (3 points)
(b) Contrast (briefly) the results of Kuffler and Hubel and Wiesel on the cat with those of Lettvin et al. on
the frog.
Relate these differences to the different "ecological niches" of the animals. As a Neural
Engineer, describe two applications of machine vision — showing one for which frog-like preprocessing is
better, and one for which monkey-like preprocessing is better. In each case, make clear the technological
issues that guide your choice. (4 points)
Q. Describe a neuron that serves as a Kuffler-style contrast detector.
Assume that it receives a
2-dimensional pattern of illumination that is bright for all (x,y) with x  X and dark for all (x,y) with x >
X.
Place beneath your drawing of the ERF and IRF of the cell a graph showing how the response of the
cell varies with X as X moves from left to right across the receptive fields.
Q. (a) The book presents the connection schemes which Hubel and Wiesel suggested might give rise to the
behavior of simple cortical cells.
However, in their models a very bright spot can produce the same
response as a dimmer line pattern in the receptive field. Present a more adequate model, giving a neural
network that can check that a minimal level of contrast is achieved all along the edge.
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Sample Exam Questions
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(b) Sketch the Hubel-Wiesel scheme for mapping the visual world onto visual cortex. Briefly describe it
using at least 4 key terms.
How many dimensions are mapped onto 2 by this scheme?
Discuss.
Q. (a) Define (specify the behavior - you don't have to give the wiring diagram) a simple cell in the sense
of Hubel and Wiesel and explain why its output is ambiguous.
(b)
Consider two small, overlapping regions of the receptive field, and suppose each region has
associated with it 24 simple cells cji - j = 1,2; 0  i < 24 - where the optimal stimulus for cji is an edge in
region j "pointing" in the direction 15i° (where the direction of an edge is such that it has the darker side
to its left, the brighter side to its right).
Set down "coupling coefficients" for cell c 1i and cell c2k
expressing the likelihood that they sense two portions of the same edge. This should be a function f(i k).
The exact mathematical formula is not important (you may even draw a graph) but you should
explain the general shape of the formula.
(c) Now consider a rectangle which provides a simple visual field covered by an 8x8 array of overlapping
receptive fields, each of which drives 24 simple cells of the kind described above.
Write down a
formula for the relation of these cells considrerd as a Hopfield network (you may simply use the
expression hji(R) to summarize the input received by cji from the retina).
(d) Draw a fixed retinal input which consists of a vertical edge at cell (2,2), a horizontal edge at (3,3) and a
linking corner at cell (2,3), and also draw what you think a minimum energy state of the network will
look like for this input. Explain (formally or informally) your prediction.
Q: (a) Compare the preprocessors in the frog and monkey visual systems, and relate them to the different
ecological niches of these animals.
(b) As a Neural Engineer, describe two applications of machine vision — showing one for which frog-like
preprocessing is better, and one for which monkey-like preprocessing is better. In each case, make clear
the technological issues that guide your choice.
Q. (a) Present a sketch of the neuroanatomy of Dejerine's patient who could write but not read, and
explain why indeed this person exhibited "alexia without agraphia".
(b) We have seen how feedback through the spinal cord may be used to contract an agonist that is too
long and simultaneously relax the antagonist.
Extend these ideas to draw a circuit that will, in response
to a pinprick to the sole of the left foot, simultaneously cause the left leg to flex and the right leg to extend.
Q Write a simple mathematical description for the system comprising 2 people sharing an electric blanket
with crossed controls — so person A changes the temperature of person B when trying to change his/her
own temperature. Explain why it is a positive feedback system.
Q. (a) Consider the system described by the equation
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 x.
 
.
 y
=
Sample Exam Questions
 3 5
-1 9
4
x
y
Calculate its eigenvalues and explain why it is, or is not, stable.
2(b) Now repeat the exercise for the system
 x.
  =  - 4 5  x 
 2 2 y
.
 y
Use your analysis of the eigenvalues to provide a precise description of the trajectory of the system.
Q (a) Draw the circuit diagram for our linear model of the  controller for the mass-spring muscle, and
write out the equation in state variable form.
(b)
What value of the feedback gain h will make the system undergo oscillations?
Prove your result.
Q (a) Write down the differential equation for the mass-spring model of muscle, and convert it into state
variable form.
(b) Imagine that the mass m was negative!
Discuss the stability properties of the system under this
assumption.
Q. Consider a simple feedback system governed by the delay equation
dm
dt
=
mo - m(t - T) :
(a) What is the state of this system at time t? (Write down an informal definition of state first).
(b) Complete the following graph to indicate a possible trajectory of the system.
interval T will play an important role.
Note that the time
Give an informal explanation of your graph (i.e., in English
rather than mathematics).
Q. When you "jiggle" your eyeball with your finger, the world "jiggles" too.
phenomenon of corollary discharge.
Q Draw a sketch of a "hillside" and use it to discuss three kinds of stable equilibria
Q. (a)
Consider the matrix
Relate this to the
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Sample Exam Questions
Compute the eigenvalues.
(b)
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Is the matrix stable?
Consider the dynamic system
What is its equilibrium point?
Q.
Draw the block diagram for the linear mass-spring model of the  system.
Write down the differential equation for this system, and express it in state variable form.
Demonstrate whether or not the equilibrium of this system will differ if a disturbing mass m is added.
Q. (a) Derive the force u(xe) that yields the equilibrium length xe starting from the basic formula
d2x/dt2 = mg - u - k(x-xo) - b.dx/dt
(b) What is the formula for how the linear feedback model of the  system changes its equilibrium
position when the mass changes?
(c) Discuss the formula in (b).
What other "tricks" does the nervous system use to improve muscle
control beyond the use of positional feedback from the muscle spindles?
Q Formalize Didday's prey-selector model as follows: Let si, 1 i n, be the input "foodness" signals, let
ui(t), 1 i n, be the membrane potentials of the "relative foodness" units, and let S i(t), 1 i n, be the
membrane potentials of the "sameness" cells.
We will study the linearized dynamics of the network as
given by
Si(t) =  ijuj(t)
dui(t)/dt = -ui(t) + si - c Si(t) - h
for suitable time constant  and constants c and h.
(a) Provide a closed form for the equilibrium value of ui(t) for given sj. [Hint: First provide an answer
that depends on  j uj, and then provide a closed form for  j uj.]
(b) Draw the equivalent circuit with one inhibitory neuron. What are the excitatory and inhibitory
weights that make this circuit equivalent to the one given above? Why?
III. Schemas
Q Briefly summarize three of McCulloch's main contributions to brain theory, and show how they
motivate a short list of organizational principles for the study of brain and neural networks.
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Sample Exam Questions
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Q Distinguish LTM from STM and relate this distinction to our vocabulary of schemas.
Q: (a) Make a simple drawing of some "scene" you would like interacting schemas to interpret, and for
which at least one schema must have multiple instances during the interpretation. Briefly describe the
interpretation process for that scene so as to explain why multiple schema instances are needed, and to
explain the idea of competition and cooperation between schemas/schema instances.
(b) List 3 of the main differences between the TMB2 and the Rumelhart et al. approaches to schemas.
Pick one of these differences and either argue for the superiority of one approach, or offer your ideas for a
new alternative.
Q. (a) Provide a semi-formal account (i.e., using a mix of English and programming language that
combines clarity with precision) to spell out explicitly how the lexicon knowledge source is invoked, and
how it acts, in HEARSAY.
You may feel free to make up those details which fill in gaps in the text but
which you feel are "in the spirit" of that exposition.
(b) Now explain how you would replace serial activation of the lexicon by distributed activity of a whole
population of "word schemas."
Q. (a) Recreate the drawing showing Nauta's view of the evolution of the mammalian brain, indicating
the basic functions of the spinal cord, how these are modified and what is added by the brainstem, and
similarly for the neocortex.
(b) Outline the main points in the view of layered robot control offered by Rodney Brooks.
(c) Explain to what extent Nauta's evolutionary view can be seen as an example of Brooks' perspective,
and to what extent it and/or schema theory suggest a different viewpoint .
Q. (a) Explain the phrase "action-oriented perception"
(b) In reaching to grasp a ball, the hand preshapes before reaching the ball. Draw the coordinated
control program (schema assemblage) for this task, distinguishing pathways for transfer of data from
pathways for schema activation. Explain why this strategy may be relevant for control of the next
generation of robots.
(c) In Section 5.3, we looked at the hand movement of a patient with hemianesthesia following a parietal
lesion. Describe her behavior in reaching for a ball when her hand is not visible to her for the first half of
the trajectory. Spell out the implications of this for the perceptual and motor schemas that appear in
your answer to part (b).
Q. (a) Explain the problems that HEARSAY would face in deciding whether an ambiguous input was
"pomp and circumstance" or "pompous circus dance".
To do this, indicate the phoneme level
hypotheses that this input might generate, and show how one or more knowledge sources could be
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Sample Exam Questions
applied to yield the interpretation.
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How could a speaker "push" the process in one direction or the
other? (3 points)
(b) Summarize and compare your knowledge of HEARSAY and VISIONS: for each special feature of
HEARSAY or VISIONS, either provide the corresponding feature of the other system (and briefly discuss
the relationship) or discuss why there is no corresponding feature in this case.
(1 point for each
"important" feature, up to a maximum of 4.)
Q. (a)
Explain some of the tasks and subtasks for a service robot whose job it is to deliver drugs from
the pharmacy in the basement of a hospital to nurses at the bedsides in many different rooms of the
hospital.
Provide several drawings of receptors, effectors, schemas and neural networks for a system
that could do this job. (4 points)
(b) Discuss the receptors, effectors, schemas and neural networks using the vocabulary of cooperative
computation, perceptual robotics, and learning.
In particular, explain the concept of hybrid
reactive/deliberative robotic architectures and relate your design to this notion. (3 points)
Q. (a) Consider the problem of fitting a smooth curve in the (x,y) plane which passes near to a given set of
data points (xi ,zi ), (xi ,zi ), ..., (xi ,zi ). More precisely, we are given a set of n x-values x1, x2, ..., xn
1
1
2
2
m
m
and must choose corresponding y-values y1, y2, ..., ynwhich minimizes the following sum:
n-1
(yi+1 - yi) 2

i=1
m
+
(yj - zj) 2
j=1
Design a Hopfield network that will find a local minimum for this function.
Q. (a) Consider an input-free network with N neurons with binary activity si and threshold i, 1 ≤ i ≤
N, and weights wij from neuron j to neuron i. Define the "energy" of this network. State and prove
conditions under which the dynamics moves the state to an equilibrium in which the energy is a local
minimum.
(b) Consider a network consisting of 2 neurons, where each neuron has threshold 0.5 and a single input,
from the other neuron, of weight 1.
What is the sequence of states exhibited, following the
McCulloch-Pitts (synchronous) dynamics, when the network starts with neuron 1 in state 1 and neuron 2
in state 0?
Spell out how to reconcile this with the result in part (a), specifying the relevant sequences in
this case.
Q. The following picture illustrated a book review in The Economist of October 10 1987 of a book about
John Sculley who went from PepsiCo to Apple Computer.
(a) The picture is "inconsistent."
Describe the problems that a "normal" vision system might have with
this picture.
[The picture was a drawing of a Macintosh computer being opened like a can of Pepsi.]
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Sample Exam Questions
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(b) Outline what special properties must be added to a vision system to let it "understand" pictures of
this kind.
(c) Outline the schema networks required to interpret this picture. (Use between 7 and 10 schemas in
your answer.
Include appropriate hierarchical relations.
Your answer to (b) must provide the
mechanism to recognize an "object" for which there is no stored schema.)
Q This question refers to an imaginative drawing from a Kleinwort Benson ad in The Economist
emphasizing that the international stock market combines London, New York and Tokyo.
[A copy of
this picture followed.]
A. What low-level vision routines would be appropriate for processing the image?
(Colour is out!)
Do not describe how the routines work, but be precise about what data they make available to
interpretation routines.
Briefly relate these routines to the following items: sky, cloud, roof, chinese
character, and vehicle.
B(a)
Complete as much as possible of the following semantic net:
Bb In the picture, I can recognize which building is the London Stock Exchange, but I have no idea
whether any of the oriental buildings is an actual building in the Tokyo financial district.
(i) Rewrite the above sentence rigorously, inserting such qualifiers as "drawing of" and "representation
of".
(ii) What does the above say about the structure of human knowledge?
we access knowledge at different levels of specialization?
In particular, how do you think
Use the terms "data-driven" and
"knowledge-driven in your answer.
(c) Discuss briefly the schemas involved in recognizing the oriental buildings in this picture.
(d)
Discuss briefly the schemas involved in recognizing the sky in this picture.
Q. The picture below is a view of the city of Kobe in Japan, published in the November 4, 1989 issue of the
Economist, in which a statue of a nude woman is in the foreground.
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Sample Exam Questions
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(a) In the spirit of Section 5.2, briefly describe a set of schemas for recognizing people, buildings, and
traffic lights.
(b) Discuss how segmentation and salience might cause attention to focus on one part of the scene rather
than another.
(c) Give a scenario to show how the system might first instantiate a "woman schema" yet converge on an
interpretation that instead posts a "statue" hypothesis.
Q. (a)
Compare constraint satisfaction algorithms and HEARSAY.
List the major similarities and
differences.
(b) List 3 ingredients in making HEARSAY "more neural." In each case, evaluate the success of the
approach.
(c) Compare and contrast HEARSAY and the VISIONS system.
Q. Describe your perceptual and motor strategies in safely crossing a street.
Then translate this into a
set of figures detailing the perceptual and motor schemas involved and how they are combined into
schema assemblages/coordinated control programs.
Make sure that you include enough information to
explain the circumstances in which you start, stop, speed up, and slow down.
For simplicity, assume
that you walk in a straight line, and that only the speed of walking, not the actual placing of your feet,
need be included in the model.
IV. Vision
Q
What are the constraints in the Dev model of stereopsis?
Explain how Dev's network may be
considered as a constraint satisfaction network.
Q. Sketch the visual systems of frog (Read part (c) first!) and human.
(b) Discuss how the optic chiasm in the human provides a basis for binocular depth perception but that in
frog does not.
(c) Add a new brain region called nucleus isthmi to the frog figure you drew in part (a), with a reciprocal
connection between the nucleus isthmi on each side and the tectum on that same side.
Then invent a
new pathway or pathways starting at nucleus isthmi which could provide a basis for binocular depth
perception.
Q (a)
Explain your solution.
Describe how disparity and accomodation provide complementary information for depth
perception.
(b) Sketch how House exploited this in his Cue Interaction Model.
(c) Explain how the shortcomings of the MATCH algorithm for optic flow may be used to build edge
detectors.
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(d) Spell out the main similarities and differences between stereopsis and optic flow.
Q
List 5 different cues for determining the depth of objects in a scene, then describe how these might be
orchestrated so that the strengths of one can remedy the weakness of the other.
Q. You are challenged to build a Sixth Generation vision system for a household robot.
(a)
What low-level vision would you give it?
relevance of "sensor fusion."
What other sensors would you give it?
Where would you use neural nets?
Discuss the
What other processing would be
appropriate?
(b) Now discuss high-level vision.
Start by listing three tasks you want the robot to accomplish.
Then for each task, present a set of visual schemas and motor schemas that will accomplish the task.
Explain how all the schemas you have described are to be integrated.
Continue on the back of the
sheet for full credit.
Q. Discuss the contribution of each of the following to our subject matter:
(a) McCulloch and Pitts (there are 3 papers they contributed together)
(b) Hartline and Ratliff
(c) Richard Gregory
(d) From your reading of the notes, pick 2 other researchers whose work you consider important and
briefly describe their contributions.
(To avoid embarassment, do not use USC faculty in your answer
to this question.)
Q.(a) What does the Dev stereopsis model add to the Didday prey-selector model?
(b) What are the main similarities and differences between the Dev model and the MATCH algorithm for
optic flow?
(c) Indicate how you would couple the Dev and MATCH algorithms (possibly with other systems) to
provide improved performance.
Discuss how the links you have shown will improve system
performance. Discuss possible flaws in your system design.
Q. For the purpose of this exercise, we will not distinguish between depth, disparity and focal length,
viewing them all as calibrated by a common variable d.
(a) Write equations for going from a "world" described by a function k(x,d) — which is 1 if there is a
significant feature in direction x at distance d and 0 otherwise — to the initial "disparity detection
function" s(x,d).
(b) Write the NSL equations for the Dev model of stereo "ghost removal." (Generic constants may be
used, rather than specific values.)
(c) Choosing some suitable "blur" function, write equations for going from k(x,d) to the initial
"accommodation function" a(x,d).
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(d) Draw a diagram for House's Cue Interaction model, and write out the NSL code that describes it.
Q. (a) Describe the basic scheme of DeYoe and VanEssen for low-level vision in the brain.
two different perceptual systems these feed?
What are the
What challenges does all this set for the concept of
"dynamic linkage"?
(b) Briefly characterize the roles of somatosensory, parietal, motor and various premotor areas in the
control of reaching and grasping.
Within each grouping, you need not recall the names of specific
cortical areas, but you should be able to indicate the roles that the subsystems play in distributed control.
(c) Draw Dev's stereo model, showing how the diagram of (b) enters as a subsystem.
constraints in the Dev model of stereopsis?
What are the
Explain how Dev's network may be considered as a
constraint satisfaction network.
Q. (a) Suppose we are given two frames F1 and F2 with each frame 100x100, and that F1 has features at
coordinates (xi,yi) for i = 1, ..., 25 while F2 has features (x' i,y'i') for i = 1, ..., 28 . Give three reasons why
there might be more features in Frame 2 than in Frame 1. (3 points)
(b) Suppose that at iteration k, the MATCH algorithm has yielded vector (r i,si) for i = 1, ..., 25 as the
current estimate of the displacement of feature i of F1 in F2.
Explain the MATCH algorithm informally
(what are the two consistency conditions?) and then write down a precise formula for how the estimates
will be updated to yield the values (ri(k+1),si(k+1)) on the next iteration. (3 points)
(c) The MATCH algorithm is not a neural network. What is it? Try to put it into the framework given
by Poggio, T., Torre, V., and Koch, C., 1985, Computational vision and regularization theory, Nature,
317:314-319. (4 points)
V. Motor Control
Q What are the three main models for generating rhythmic movements?
Show with an explicit diagram how each model can be wired up to control alternating flexor and extensor
bursts, and discuss explicitly what cellular mechanisms are required for the system to work.
Q. Here is a simple model of a half-center oscillator (cf. Section 6.1):
connected as shown:
There are two cells symmetrically
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Sample Exam Questions
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a) Suppose each neuron is described by a leaky integrator equation:
dui
= - ui + w .h(ui-1) + si.
dt
Suppose w < 0, and h is the step function (h(u) = 0 if u  0, h(u) = 1 if u > 0). What are the possible
dui
equilibria of the system, i.e., states in which each
= 0 ?
[Hint: consider the sign of each ui,
dt
and be explicit about the constraints placed on the size of the si for each equilibrium to exist.]
In particular, what equilibria are possible if s1 = s2 = s > 0 ?
b) Now to model the half-center oscillator, we need the output of a cell to decline while it is active and
also to exhibit post-inhibitory rebound, so we replace h(ui) with a new quantity xi.h(ui) where xi has the
property that it gets smaller during periods in which h(ui) >0, while it gets bigger during periods in
which h(ui)  0.
For example, we could use
dxi
dt
= sgn[-h(ui)] xi
where sgn[x] = 1 if x 0, but is 0 if x < 0.
(i) Write an equations for how xi(t) changes from xi(0) > 0 if cell i is active from time 0 to time T.
(ii) Do the same for a period of quiescence.
(iii) Now start the system in a state with cell 1 active and cell 2 quiescent. Prove that u 2 must eventually
become positive. Does the system oscillate.
{Full marks for showing a case in which oscillations do
arise. But this is a rich system, and you can win extra points by exploring further aspects of its behavior.
Does the system oscillate for every choice of s, , and w? Does the period of the oscillation depend on
the initial condition? Any other interesting observations?]
{General hint for this exercise. (biii) is meant to be challenging. Read through the mathematical proofs
in Section 4.4 to increase your repertoire of techniques for this problem.}
Q(a) Make a large drawing of the Robinson circuit for saccadic eye control.
(b) Now consider a target which jumps from position p1 to then p2 and finally to p3 as in the
following graph.
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Sample Exam Questions
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Draw a corresponding graph for each of the components in your control diagram.
Q. (a) Draw the simple neural net diagram of the van Gisbergen et al. model of the control of eye
saccades.
(b) For the purpose of this exercise, assume that motoneuron firing MN(t) is simply the sum of its two
inputs, B(t) from the burster and T(t) from the tonic neuron. Assume also that motoneuron firing and
eyeball angle (t) are linked by the differential equation:
.
  (t)  = - (t) + MN(t)
Our verbal discussion of the model speaks as if, during a saccade (when the output of the burster takes
some large value B), the eyeball turns at some constant rate.
Present your assumptions on the constants
involved that make this approximately true, and provide a formula for that constant rate.
(c) The Neural Integrator is a key component of this diagram.
Explain in English how its input and
output are interpreted, and how the integrator functions. Then write down an integral equation for its
operation and prove that the integrator meets the specification you have given.
Q.
In Section 2.3, we saw the basic story of excitatory and inhibitory transmitters acting on a
millisecond timescale to move membrane potential toward or away from threshold, respectively.
This
question samples your knowledge of other synaptic mechanisms.
(a) Draw a basic diagram for a half-center oscillator and explain how it works, taking care to make
explicit the synaptic (and related cellular) mechanisms involved.
3(b) Explain the synaptic mechanisms that Kandel postulates to be responsible for short-term habituation
in Aplysia.
Q. We have studied a simple ring circuit which can control the contracting of El, Ab, Ad, and De
(Elevator, Abductor, Adductor, Depressor) muscles to yield locomotion.
(a) Draw a picture of the leg showing each muscle in relation to forward motion; and give the sequence of
muscle (co)contractions for one cycle of stepping.
(b) Give a circuit to yield this sequence.
Design it to prevent the ON signal from triggering a new pulse
in the control loop if one is already circulating there, and to ensure that the OFF signal does not take
effect until the foot is on the ground.
Q. (a) Recreate the diagram for van Gisbergen et al.'s basic unilateral control circuit for saccadic eye
movement. Indicate excitatory and inhibitory connections. Give the names/roles of each neuron in the
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Sample Exam Questions
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circuit. For cell B (the EBN) in the circuit, give an explicit mathematical description of how it responds to
its three inputs.
(b) Indicate, by adding dashed lines to the above circuit, how the contralateral IBN fits in.
the text - I explained it in class.)
(This is not in
Explain how this yields an appropriate effect upon the neural
integrator.
Q(a) Copy out the diagram for van Gisbergen et al.'s basic unilateral control circuit for saccadic eye
movement. Indicate excitatory and inhibitory connections. Give the names/roles of each neuron in the
circuit. Indicate, by adding dashed lines to the above circuit, how the contralateral IBN fits in. Explain
below how this yields an appropriate effect upon the neural integrator. (4 points)
(b) Contrast the above model with the Pitts-McCulloch model. Explain one important way in which
their model behaves less realistically than van Gisbergen et al.’s model (at the functional level, not in terms
of neural correlates). . Explain which important anatomical concept central to their model is missing in van
Gisbergen et al.’s model. Cite a paper that addresses this omission, describing the solution it offers in a
sentence or two. (3 points)
Q. Draw a coordinated control program for reaching toward, and forming a precision grip on (using pad
opposition), a small object.
Make explicit the role of vision and touch. Show what parameters are
passed between the various schemas (perceptual and planning schemas, and schemas for control of arm
and hand). A diagram showing the preshape may be helpful in defining these parameters.
Q. (a)
In Section 6.3 we discussed the "many motor systems" and considered a complex figure of brain
regions which we related to grasping and reaching.
You were instructed to study the ideas of the
diagram, rather than remember all the anatomical terminology. In the same spirit, try to diagram the
regions that the brain might employ in playing a game of tennis. (4 points)
(b) Pick five pairs of regions in the above diagram. For each pair, say something interesting about the
neural traffic between them. For at least two pairs, discuss the type of learning that might be employed
in tuning them. Discuss the credit assignment problem. (6 points)
VI. Adaptation, Learning, and Memory
Q. (a) Use an account of the Sutton-Barto Landmark Learning System to make clear the distinction
between hill-climbing in the "physical" space, and hill-climbing in weight-space.
(b) Write out (i) the Sutton-Barto synaptic adjustment rule, (ii) a formal expression for Hebb's learning
rule, and (iii) the Perceptron error-correction rule, and offer an explicit comparison of the three rules.
Arbib: CS 564
Sample Exam Questions
15
Q. (a) Write a precise set of formulae to implement the "run and twiddle" rule for hill-climbing, given
that the last step was in direction d(t) and the change in payoff was [z(t) - z(t-1)].
[Hint: Use a
random number generator.]
(b) Draw the network to control the landmark-learning hill-climbing bug; write down the equations for
changing the weights wij; and write out the motivation for these equations.
(c)
The text gives an informal description of Samuel's solution to the credit assignment problem.
Spell out as fully as you can how you would formalize his procedure.
Write out a justification for your
approach using the concept "hill climbing in weight space."
Q Write out formulas for the three main learning rules for synaptic adjustment studied in this course.
Q. (a) Summarize the back-propagation learning rule, and give the idea (not the mathematical details) of
its derivation.
(b) To what extent is this a biological learning rule?
Compare it with the Hebb rules and Perceptron
rules in this respect.
(c) After training a back-propagation network to recognize curvature from shading, it was found that
some hidden units seemed trained to be oriented edge detectors.
First explain why this is surprising,
then indicate why, on second thoughts, it might make sense.
Q. (a) Give the inductive definition of i for back propagation in a layered loop-free network.
(b) Whether or not you got the above formulas correct, you should be able to reproduce the informal
motivation for these rules. Do so here.
(c) Discuss the problems of an infant learning to reach for a ball; and explain how they might be
addressed by Rumelhart's MM/MP scheme.
(What are MM and MP?)
Q. This question tests your mastery of the material on formation of retino-tectal connections.
(a) Briefly contrast the method for connecting (one-dimensional) retina and tectum that you used in your
NSL assignment with EITHER the Willshaw-von der Malsburg OR the Kohonen approach to this
problem.
(b) Explain why the first method yields an almost unique pattern of retino-tectal connections, while the
second does not.
What stratagem must be used in the second case to favor a particular such pattern?
Q. (a) Give a formal specification of the Perceptron error-correction rule and state (without proof) the
Perceptron Convergence Theorem.
(b) Explain what advantages backpropagation has over a simple Perceptron.
(c) Explain what disadvantages backpropagation has compared to a simple Perceptron. Use the term
"gradient descent" in an informative way in your answer.
Arbib: CS 564
Sample Exam Questions
16
Q. (a) List 4 ways in which non-adaptive neural networks can play an important role in technology, and
4 ways in which adaptive networks can play such a role:
(b) Which of your non-adaptive networks do you consider most interesting? Explain why.
Then give
a diagram and explain how it works.
(c) Which of your adaptive networks do you consider most interesting? Explain why. Then give a
diagram and explain how it works.
Q. (a) Define the terms "simple perceptron" and "linearly separable" and spell out and explain the relation
between them (2 points)
(b) The following discrimination cannot be performed by a simple perceptron:
x
x
x
x
x
x
x
x
x
x
x
x
x
x x
x
x
o
oo
x
x
o o
oo
o
x
x
x
x
oo
x
x o
x
x
o o
x x
x
x
x
x x
x x x
x
x
x
x
x
x
Explain why (1 point):
By drawing carefully on the diagram, indicate the design of a set of hidden units and an output unit that
will enable the output unit to fire for input x but not for output o (3 points).
(c)
Spell out the difference between supervised and unsupervised learning, and for each give an
important example of a technological application. (4 points)