MACHINE LEARNING TECHNIQUES - LASA
MACHINE LEARNING TECHNIQUES - LASA
MACHINE LEARNING TECHNIQUES - LASA
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133<br />
6.5 Willshaw net<br />
David Willshaw developed one of the simplest associative memory in 1967.<br />
Figure 6-8: The Willshaw Network - Learning phase<br />
The update rule follows:<br />
⎧⎧1 if h = 1<br />
Δ wij = δ( xi ⋅ yi<br />
) δ( h)<br />
=⎨⎨ (6.17)<br />
⎩⎩ 0 otherwise<br />
The retrieval rule follows:<br />
⎛⎛<br />
⎞⎞<br />
⎧⎧1 if h ≥ 0<br />
yj = ϑ⎜⎜<br />
wij ⋅xi<br />
− w w = h =⎨⎨<br />
⎝⎝ i ⎠⎠ ⎩⎩0 otherwise<br />
∑ 0⎟⎟<br />
0<br />
1 ϑ( )<br />
(6.18)<br />
Such a network suffers from two major drawbacks: the memory quickly fills up; the network<br />
cannot learn patterns with overlapping inputs.<br />
One can show that the total number of patterns that can be stored in such a network is:<br />
⎛⎛ MIN MOUT<br />
ρ = 1−⎜⎜1− ⋅<br />
⎝⎝ NIN<br />
NOUT<br />
⎞⎞<br />
⎟⎟<br />
⎠⎠<br />
(6.19)<br />
with N<br />
IN<br />
input lines , M<br />
IN<br />
the nm of input bits set to 1, NOUT<br />
output lines<br />
M the nm of output bits set to 1.<br />
OUT<br />
and<br />
A more generic learning rule for such associative net is the Hebbian rule, which we will see next.<br />
© A.G.Billard 2004 – Last Update March 2011
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