[FOM] Learnability

Patrik Eklund peklund at cs.umu.se
Fri Jan 18 00:27:33 EST 2019

The authors are manipulative already at start. They say "Approximate a 
target concept given a bounded amount of data about it." This is wrong. 
It's not "bounded", it's finite. It can be very big (Big Data), but it 
is nevertheless finite.

Then they bridge that to PAC (probably approximately correct), and then 
we are in probability with the reals. Now we are departing from the 
essence of learning.

Note also things like "access to a training sample of visitors drawn 
from an (unknown) distribution P". In learning we do not not "draw". As 
they say at the beginning, "given ... amount of data".

Learning is approximating to given and finite data.

The authors don't give up. As if they by that point feel they are on 
thin ice, they start to speak about "posted ads are to be chosen from a 
given pool of ads". Now they enter the realm of social media marketing, 
with Facebook, Google, etc. Just take Facebook as an example. There are 
Adsets and Ads. Ads in Adsets. And a Campaign is a set of Adsets. But 
again, it's finite. It's very finite. We could play around with the 
creative (the content of the add) and start to include real numbers for 
assigning distance between one cup of coffee to another in an add, or in 
videoclips saying that time is continuous (but in a moving picture it 


This paper is Artificial Artificial Intelligence, where their "The ad 
problem above becomes an instance of the following EMX problem" is giant 
leap from AI to their AAI. It may seem as a small step in their paper, 
but it's an all too giant leap for practical learning. After that, the 
paper has nothing to do with AI and learning.


What I would like to see is a totally new approach to brain, cognition 
and AI. Why not look at reception in cells, pathways, transcription, 
RNA/DNA and all that. Hormones come into play. They are transported by 
the nerves and through the blood, into the cells. Intestines are 
permeable. The large intestines and the bladder "communicate", as do the 
kidney and the heart e.g. in the cardiorenal syndrome, and so on and so 
forth. Water retention in the body. The role of sodium , potassium and 
many other things like calsium channels. Why don't we analyze these 
things? We could analyze stress otherwise than using arithmetics? 
Doctors are totally unable because they are stuck with populations and 
comparing mean values. That's baby mathematics.

The brain is finite, but the brain of the gut may be infinite. The brain 
of the gut may be undecidable?! It certainly cannot be modelled by baby 



On 2019-01-17 11:36, Dennis Müller wrote:
> The following twitter thread by John Carlos Baez summarizes the issue
> in a rather concise manner:
> https://twitter.com/johncarlosbaez/status/1083047483368890368
> Basically: The question of whether a ML agent can generalize a
> classification scheme with a certain accuracy from a finite set of
> training data is reducible to finding a finite subset of [0,1] with a
> sufficiently large P-measure, where the measure P itself is unknown
> except for N iid samples. The latter is apparently possible iff
> there's at most finitely many uncountable cardinals < 2^aleph0.
>> During a routine perusal of the site RealClearScience.com, I read the 
>> piece
>> about the article "Learnability can be undecidable", by S. Ben-David, 
>> P. Hrubes
>> et.al. The piece is published in the journal Nature Machine 
>> Intelligence.
>> In that paper the authors appear to show that certain aspect of 
>> machine learning
>> (pretty practical task) is equivalent (in ZFC) to Continuum Hypothesis 
>> which
>> is (as we know since P.J. Cohen) undecidable in ZFC.
>> I never did Machine Learning, and this appears to be absolutely 
>> incredible.
>> The piece in RealClearScience is a product of a science writer, not 
>> necessarily
>> knowing what s/he is talking about.
>> Obviously, the matter is relevant to F.O.M. Could someone in the 
>> community make
>> this matter clearer for pedestrians such as I?
>> Thanks,
>> Victor Marek
>> Victor W. Marek Department of Computer Science
>> marek at cs.uky.edu University of Kentucky
>> marek at cs.engr.uky.edu Lexington, KY 40506-0633
>> 859-257-3496 (office) 859-257-3961 (Dept)
>> http://www.cs.uky.edu/~marek 859-257-1505 (FAX)
>> _______________________________________________
>> FOM mailing list
>> FOM at cs.nyu.edu
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> --
> Dennis M. Müller
> logicalphalluses.net
> "Mathematics is the music of reason. To do mathematics is to engage in
> an act of discovery and conjecture, intuition and inspiration; to be
> in a state of confusion— not because it makes no sense to you, but
> because you gave it sense and you still don’t understand what your
> creation is up to; to have a breakthrough idea; to be frustrated as an
> artist; to be awed and overwhelmed by an almost painful beauty; to be
> alive, damn it. Remove this from mathematics and you can have all the
> conferences you like; it won’t matter. Operate all you want, doctors:
> your patient is already dead."
>  - Paul Lockhart (on mathematics in school)
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