Quote:
Originally Posted by MaciekLeks
That's the point. This part is crucial: "the proof let the choice for the value of depends on the value of ". The only certain correlation is . How do we know (definition, theorem, lemma,...) that works the same as ? IMHO it cannot be drawn from the , (where not all coefficients are zeros).

I'm not sure if this is the point you are talking about
: Here is my understanding:
If the perceptron hypothesis set can shatter the data set
then:
If for every
that
then there exists such a
that satisfies
for every
that
. In other words, we first have
for every
that
, then we
must be able to find a
that satisfies the equation
if the perceptron hypothesis set can shatter the data set.