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(Solved): COMPUTER SCIENCE TRIPOS Part IB - 2018 - Paper 6 2 Artificial Intelligence (SBH) Evil Robot is updat ...
COMPUTER SCIENCE TRIPOS Part IB - 2018 - Paper 6
2 Artificial Intelligence (SBH)
Evil Robot is updating his visual system. He has a single camera that produces an
n\times n matrix I of pixel values. His visual system is arranged as follows:
The input I is reduced to an m\times m matrix H(I). The elements H_(i,j) are
H_(i,j)(I)=\sigma (\sum_(k=1)^n \sum_(l=1)^n w_(k,l)^((1,j))I_(k,l)+b^((i,j)))
where \sigma is an appropriate function, and w_(k,l)^((i,j)) and b^((i,j)) are the weights and bias for
element (i,j). A single output o(H) is computed as
o(H)=\sigma (\sum_(k=1)^m \sum_(l=1)^m w_(k,l)H_(k,l)+b).I^('),y^(') E(w) where w
is a vector of all weights and biases available, derive an algorithm for computing
(delE)/(delw) for the example.
[12 marks]
(b) A modification to the system works as follows:
The mapping from I to H is replaced by an n^(')\times n^(') convolution kernel. This has
a single set of parameters v_(k,l) and c used to compute every element of H as the
weighted sum of a patch of elements in I
H_(i,j)(I)=\sigma (\sum_(k=1)^(n^(')) \sum_(l=1)^(n^(')) v_(k,l)I_(i+k-1,j+l-1)+c).
Provide a detailed description of how the algorithm derived in Part (a) must be
updated to take account of this modification.
[8 marks]