AI, neural nets & generalization

Ok, so I can get neural nets to converge to solve a training set perfectly, but when I put other values, it always gives weird as fuck answers. In other words, my neural nets don't generalize (which is the point of AI), even if the training set is fuckhuge. How do I make them generalize? Some site on the internet told me to make the net smaller, but that just causes it to not even be able to solve the training set and become stuck on a local (nonzero) minimum.

I don't see how neural nets are any better than just making a program that creates random programs and changes them slightly until the result is appropriate, they don't generalize jack shit, it's the same as just returning
if(input==challenge1)return answer1;
if(input==challenge2)return answer2;
etc.

>>2
Oops, I indeed made a mistake (I added some values to correct the weights, plus I didn't realize it's the activated, weighted neurons that summed and not their weights.)
Anyway, now I can get them to generalize (somewhat) but it takes insanely long to converge. If I make the training set size large enough for it to generalize, the error seems to decrease exponentially when training (means it takes way too long) and I can see it getting closer and closer to the solution, but it's too slow! If I decrease the training set size, it converges quick as fuck but doesn't generalize. I could be still doing something wrong, but I just want to ask does good generalization mean slow convergence?