Hopfield Network - 3 Neurons
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Hopfield Network Formulas
1. Weight formula (Hebbian Learning):
J
ij
=
1
/
N
Σ
P
μ=1
p
i
μ
· p
j
μ
(i ≠ j)
J
ii
= 0 (no self-connection)
2. Local field:
h
i
=
Σ
j≠i
J
ij
· s
j
3. Decision rule (asynchronous update):
s
i
(t+1)
= sign(h
i
) =
{
+1
if h
i
≥ 0
{
−1
if h
i
< 0
4. Energy function:
E
= −
1
/
2
Σ
i
Σ
j≠i
J
ij
· s
i
· s
j
(For 3 neurons: E = −(J
AB
·s
A
·s
B
+ J
AC
·s
A
·s
C
+ J
BC
·s
B
·s
C
))
5. Properties:
• Energy always decreases or stays constant
• The network converges to a fixed point (local minimum)
• Stored patterns are attractors