Final

Question 1

How do you find the length of a vector z?

Answer 1

sqrt(z1^2 +z2^2 + z3^2…)

Question 2

What is the length of a normalized vector?

Answer 2

1

Question 3

When does a scalar flip the direction of a vector?

Answer 3

Only when it is negative

Question 4

How do you find the dot product of a1 and b1

Answer 4

𝑎⃗⋅𝑏⃗=𝑎_1 𝑏_1+𝑎_2 𝑏_2+…+𝑎_𝑛 𝑏_𝑛

Question 5

What is the dot product of a vector multiplied with itself?

Answer 5

The magnitude of the vector squared

Question 6

In other words, the cosine angle is the __ _____ of two normalized vectors

Answer 6

In other words, the cosine angle is the dot product of two normalized vectors

Question 7

When does linear independence occur?

Answer 7

If the only way to zero a vector sum is to zero every single individual vector, then these individual vectors are linearly independent

Question 8

If a set of vectors are _______ to each other, then they are linearly independent

Answer 8

If a set of vectors are orthogonal to each other, then they are linearly independent

Question 9

What is the maximum number of linearly independent vectors possible in a 3 dimension space

Answer 9

3

Question 10

When does order matter in vector operations?

Answer 10

Order is important unless both operands are vectors with dimensions 2 x 2 or greater

Question 11

What is the product of vector g * f transpose

Answer 11

(█(&𝑔[1]𝑓[1],𝑔[1]𝑓[2],…,𝑔[1]𝑓[𝑛]
;𝑔[2]𝑓[1],𝑔[2]𝑓[2],…,𝑔[2]𝑓[𝑛]…;𝑔[𝑛]𝑓[1],𝑔[𝑛]𝑓[2]
,…,𝑔[𝑛]𝑓[𝑛]))_(𝑛×𝑛)

Question 12

𝐴𝑥⃗=𝜆𝑥⃗

In the equation above A is called a ______. And L is called a ______.

Answer 12

In the equation above A is called a eigen vector. And L is called a eigen value

Question 13

What is distinctive about eigenvectors?

Answer 13

In a matrix operation with another vector, the only way they can change that vector’s direction is to reverse it.

Question 14

What is Hebb’s rule?

Answer 14

When an axon of cell A is near enough to excite a cell B and repeatedly or persistently takes part in firing it, some growth process or metabolic change takes place in one or both cells such that A’s efficiency as one of the cells firing B, is increased

Question 15

What are three generalizations of Hebb’s rule?

Answer 15

• If excitation of A leads to excitation of B
• Then the connection between A and B is strengthened
• So that in the future, excitation of A will more easily excite B

Question 16

What is the mathematical formula for Hebb’s rule?

Answer 16

Δ𝐴∝Δ𝑓Δ𝑔

Question 17

What are three traits of a feed-forward network?

Answer 17

• Connection is always in the direction of input to output
• No backward connections
• No lateral connections

Question 18

What proportion of connections are modified during back propagation?

Answer 18

All of them

Question 19

What is propagated back during back propagation?

Answer 19

error messages

Question 20

How many unique legitimate solutions are there to the traveling salesman problem?

Answer 20

if n = # of cities; (n-1)!/2

Question 21

How many solutions with the shortest path are there to the traveling salesman problem if we do not care about direction?

Answer 21

2n

Question 22

what are mach bands and what causes them?

Answer 22

Mach bands are an optical illusion that exaggerates the contrast between alternating bands of slightly different shades of gray. They demonstrate lateral inhibition in the visual system

Question 23

What are the two central assumptions of a lateral inhibition?

Answer 23

• The brighter the stimulus, the stronger the response will be.
• The more a cell fires, the more it will inhibit its neighbors

Question 24

What is the evolutionary utility of lateral inhibition?

Answer 24

Enhance edges of the world

Since boundaries of objects provide so much information about their shapes

Question 25

Alternative hypothesis for why lateral inhibition exists?

Answer 25

It is a good idea for a system to transmit only the difference signal relative to the previous one This is sufficient Difference signal can be more efficiently coded because of a larger range for its neural representation

Question 26

How is energy calculated in a neural network?

Answer 26

cost = error^2

Question 27

Describe in one word how a boltzmann machine allows "a skier" to escape a local minimum

Answer 27

annealing

Question 28

What is the relative probability of some weights updating a Boltzmann machine?

Answer 28

exp(-E2/T) / exp(-E1/T)

Question 29

What is the chance weights will update if E2 < E1 and T is very high and what does this say about the network's behavior?

Answer 29

Around 50/50; It means the network has a lot of chance to climb out a local minimum

Question 30

What did Geman & Geman (1984) prove?

Answer 30

So long as the T cools down sufficiently slowly, | then the global minimum is guaranteed to be found with probability one

Question 31

What is the equation for temperature that guarantees a global minimum for energy will found?

Answer 31

T(k) > c/log(1+k) where c is a constant k is the number of full weight sweeps

Question 32

What equation is usually used to find T(k) and why use that instead of T(k) = c/log(1+k)?

Answer 32

T(k) = T0 exp(-k/n)

Question 33

In a quantum computer, these bits are replaced by _______ (the qubit) of both 0 and 1 (probability in quantum mechanics)

Answer 33

In a quantum computer, these bits are replaced by “superposition” (the qubit) of both 0 and 1 (probability in quantum mechanics)

Question 34

By putting a set of “entangled” qubits into a suitably tuned magnetic field, the optimal solution to an __________ problem can be found in one shot.

Answer 34

By putting a set of “entangled” qubits into a suitably tuned magnetic field, the optimal solution to an NP-complete problem can be found in one shot.

Question 35

How do you turn a lateral inhibition network into winner take all?

Answer 35

High inhibition coefficient High length Set self inhibition to 0