Connections to the output units:

1

• Connections to the output units
• D Wij h rµ diµ Vjµ
• where diµ ziµ - lt Siµ gt
• lt Siµ gt tanh ( b hiµ )
• For rest of the units use back propagation to
  adjust weights.
• For continuous reward
• D Wij h rµ (rµ Siµ - lt Siµ gt
• (1- rµ )-Siµ - lt Siµ gt) Vjµ

2
Unsupervised Hebbian Learning

• Outputs continuous-valued or binary (not winner
  takes all)
• Vectors z
  are picked
• from an
  underlying
• 
  distribution Prob(z).
• Net
  measures how
• close an
  input z fits distribution. V how probable z
  is.
• V S Wj zj wT x z zT x w component
• of z along the w direction

v
w1
wN
z1
z2
zN
j
3

• Ojas Learning rule
• D Wi h V(z i V wi)
• Output V is the component of z along the w
  direction.
• Let C lt z x z T gt , Cij lt z i z jgt average
  over input distribution P(z )
• w approaches the eigenvector of C with
  eigenvalue lmax (the biggest of eigenvalues).
• Ozas rule chooses w
• w 1
• W lies in maximal eigenvector direction of C
• W lies in direction which maximizes ltV2gt

4
Principal Component Analysis

• Find set of M orthogonal vectors accounting for
  as much as possible of datas variance.
• Ojas rule
• D Wij h Vi (z j S Vk wkj)
• Sangers learning rule
• D Wij h Vi (z j S Vk wkj)

v1
v2
vM
M ltlt N
Vi S wij z j wiT x z z T x wi
z 1
z 2
zN
j
N
k1
i
k1