COMPUTER SCIENCE TRIPOS Part IB – 2018 – Paper 6
Artificial Intelligence (SBH)
Evil Robot is updating his visual system. He has a single camera that produces an
n × n matrix I of pixel values. His visual system is arranged as follows:
I
n
n
m
m
o
H
The input I is reduced to an m × m matrix H(I). The elements Hi,j are
Hi,j (I) = σ
Xn
k=1
Xn
l=1
w
(i,j)
k,l Ik,l + b
(i,j)
!
where σ is an appropriate function, and w
(i,j)
k,l and b
(i,j) are the weights and bias for
element (i, j). A single output o(H) is computed as
o(H) = σ
Xm
k=1
Xm
l=1
wk,lHk,l + b
!
.
(a) If Evil Robot has a training example (I
0
, y0
) and is using an error E(w) where w
is a vector of all weights and biases available, derive an algorithm for computing
∂E
∂w
for the example. [12 marks]
(b) A modification to the system works as follows:
o
H
m
m
I
n
n
The mapping from I to H is replaced by an n
0 × n
0
convolution kernel. This has
a single set of parameters vk,l and c used to compute every element of H as the
weighted sum of a patch of elements in I
Hi,j (I) = σ
nX0
k=1
nX0
l=1
vk,lIi+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]