Final Flashcards
How do you find the length of a vector z?
sqrt(z1^2 +z2^2 + z3^2β¦)
What is the length of a normalized vector?
1
When does a scalar flip the direction of a vector?
Only when it is negative
How do you find the dot product of a1 and b1
πββ πβ=π_1 π_1+π_2 π_2+β¦+π_π π_π
What is the dot product of a vector multiplied with itself?
The magnitude of the vector squared
In other words, the cosine angle is the __ _____ of two normalized vectors
In other words, the cosine angle is the dot product of two normalized vectors
When does linear independence occur?
If the only way to zero a vector sum is to zero every single individual vector, then these individual vectors are linearly independent
If a set of vectors are _______ to each other, then they are linearly independent
If a set of vectors are orthogonal to each other, then they are linearly independent
What is the maximum number of linearly independent vectors possible in a 3 dimension space
3
When does order matter in vector operations?
Order is important unless both operands are vectors with dimensions 2 x 2 or greater
What is the product of vector g * f transpose
(β(&π[1]π[1],π[1]π[2],β¦,π[1]π[π]
;π[2]π[1],π[2]π[2],β¦,π[2]π[π]β¦;π[π]π[1],π[π]π[2]
,β¦,π[π]π[π]))_(πΓπ)
π΄π₯β=ππ₯β
In the equation above A is called a ______. And L is called a ______.
In the equation above A is called a eigen vector. And L is called a eigen value
What is distinctive about eigenvectors?
In a matrix operation with another vector, the only way they can change that vectorβs direction is to reverse it.
What is Hebbβs rule?
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 Aβs efficiency as one of the cells firing B, is increased
What are three generalizations of Hebbβs rule?
- 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
What is the mathematical formula for Hebbβs rule?
Ξπ΄βΞπΞπ
What are three traits of a feed-forward network?
- Connection is always in the direction of input to output
- No backward connections
- No lateral connections
What proportion of connections are modified during back propagation?
All of them
What is propagated back during back propagation?
error messages
How many unique legitimate solutions are there to the traveling salesman problem?
if n = # of cities; (n-1)!/2
How many solutions with the shortest path are there to the traveling salesman problem if we do not care about direction?
2n
what are mach bands and what causes them?
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
What are the two central assumptions of a lateral inhibition?
- The brighter the stimulus, the stronger the response will be.
- The more a cell fires, the more it will inhibit its neighbors
What is the evolutionary utility of lateral inhibition?
Enhance edges of the world
Since boundaries of objects provide so much information about their shapes
Alternative hypothesis for why lateral inhibition exists?
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
How is energy calculated in a neural network?
cost = error^2
Describe in one word how a boltzmann machine allows βa skierβ to escape a local minimum
annealing
What is the relative probability of some weights updating a Boltzmann machine?
exp(-E2/T) / exp(-E1/T)
What is the chance weights will update if E2 < E1 and T is very high and what does this say about the networkβs behavior?
Around 50/50; It means the network has a lot of chance to climb out a local minimum
What did Geman & Geman (1984) prove?
So long as the T cools down sufficiently slowly,
then the global minimum is guaranteed to be found with probability one
What is the equation for temperature that guarantees a global minimum for energy will found?
T(k) > c/log(1+k) where c is a constant k is the number of full weight sweeps
What equation is usually used to find T(k) and why use that instead of T(k) = c/log(1+k)?
T(k) = T0 exp(-k/n)
In a quantum computer, these bits are replaced by _______ (the qubit) of both 0 and 1 (probability in quantum mechanics)
In a quantum computer, these bits are replaced by βsuperpositionβ (the qubit) of both 0 and 1 (probability in quantum mechanics)
By putting a set of βentangledβ qubits into a suitably tuned magnetic field, the optimal solution to an __________ problem can be found in one shot.
By putting a set of βentangledβ qubits into a suitably tuned magnetic field, the optimal solution to an NP-complete problem can be found in one shot.
How do you turn a lateral inhibition network into winner take all?
High inhibition coefficient
High length
Set self inhibition to 0
