The generalization hypothesis

You might say that this is a less binding or more general form of "history will repeat itself". - Adam  

Are you making a joke, Adam?   
-rich

---

Kudos to Mark for such a succinct and elegant hypothesis!
-rich

These six words support a variety of interpretations.  The one i like is that we arrange things so that it is true.  That is, we structure our representations, based on past experience, so that they generalize well in the future.

Another interpretation is that the hypothesis is an assumption.  This one does not appeal to me.

Another is that it is something that must be true in order for learning to be possible.

rich  

Doesn't the fact that it supports a variety of interpretations mean it could be rewritten?  I really support the idea, but I want something to sink my teeth into.  By using precise, carefully chosen words maybe this hypothesis could mean something that challenges the reader a little more.

Since I've thrown the first stone, I should try and help.

     Aspects of the future that are necessary to get reward will be well characterized by the past, otherwise no learning agent (man or machine) can hope to succeed.

It's not perfect, but maybe it adds something.  Maybe not :)

My earlier comment was on the lighter side, but was also intended to incite a little more detail or "meat" as Brian refered to. This hypothesis seems strong but maybe needs more discussion to appreciate it. Being able to structure representations based on the past so that they generalize implies that some aspects/compoments from our history will be unchanged or epsilon close in the future. You can think of it as knowing that the future will be a function of your (agents) history. Both are useful.

Adam  

I'm going to number Rich's interpretations, 1, 2 and 3, and start with the second.  

2) I'm not 100% sure what "assumption" means in this case; in mathematical proofs we often assume a point that leads to a contradiction and thereby prove the point is false.  In such cases, we "assume" things we know to be false.  In other areas of human discourse we assume things to avoid doubting them, and I agree this holds no appeal.

1) I believe interpretation one may contain such an assumption, because we cannot construct representations now to work in the future if, when that future arrives, the past had contained no information about it.  This is the broadest meaning of "resemble": one thing resembles another to the extent that the two things share information.

3) Interpretation three is closest to my meaning.  We make null hypotheses because they allow us to examine the resulting consequences of a line of thought (and then to discredit the hypothesis if the consequences are untenable).  We hypothesize that the past has something to say about the future for two reasons: 1) it has always been the case so far, and 2) predictions are otherwise meaningless (and since science and machine learning are both in the business of making predictions, they would also be meaningless).  So perhaps the generalization hypothesis is really a postulate or axiom (which, I hope, is not the meaning of "assumption" Rich had in mind).

Anna's point seems therefore to be exactly right: is this a scientific hypothesis?  I would have to say that it is (for very interesting reasons) not falsifiable.  To falsify the hypothesis would be to make a statement as to its validity.  Yet if there is no information shared between the past and the future, then just as the past can say nothing about the future, the future can also say nothing about the past, including about a hypothesis made in the past.  Consequently (interestingly), it seems I have now proven that the hypothesis can never be shown to be false (in any universe).  Does that mean it must be true? 

Mark