What do the linear dependencies mean?
a3 P3 = a1 P1 + a2 P2
Please give examples. And what do the operators or predicates = and + mean in
the above context?
Kindly advise.
~PM
Date: Sat, 13 Jun 2015 12:52:21 +0800
Subject: [agi] distributive representation and linear dependence
From: [email protected]
To: [email protected]
Have a question...
These days more and more people are interested in deep learning, where
distributive representations may be relevant.
In a distributive representation many units are shared to represent individual
concepts. In my mind I visualize the concepts as a partition of the vector
space:
There is also the "principle of superposition" that says that 2 concepts can
share the same vector space representation via vector addition.
But here comes a problem: if we have 3 propositions, say P1 = yesterday
rained P2 = Obama is president of US P3 = the moon is made of cheeseand
if there exists a linear dependence among them, say: a3 P3 = a1 P1 + a2
P2where a1, a2, a3 are scalars, that seems to create a relation between
apparently unrelated sentences, and would lead to error.
So it seems that the principle of superposition cannot hold with distributive
representations unless the dimension of the vector space is bigger than the
number of concepts / propositions / objects that need to be represented.
Maybe my understanding above is incorrect? What's the problem here...?
--
YKY
"The ultimate goal of mathematics is to eliminate any need for intelligent
thought" -- Alfred North Whitehead
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