Submitted by 4bedoe t3_yas9k0 in MachineLearning
trutheality t1_itewkwz wrote
Reply to comment by hellrail in [D] What things did you learn in ML theory that are, in practice, different? by 4bedoe
Well, in CS theory is mathematical, and mathematical theory cannot be wrong because it's logically derived and makes statements about conclusions that can be made if certain conditions are met. So it would be nonsensical to discuss cases where such a theory is wrong. It stands to reason that the only practical discussion of deviation of practice from theory occurs in the realm of what you call misuse.
hellrail t1_itf78g0 wrote
Wrong.
Due to minimum 2 reasons:
- You dont take into account the time dimension. As doc Brown already said, "think 4-dimensional"!
It is a difference, if one has just misunderstood the theory, but could have known better. Or if that one has "done everything right" up to the point of science's knowledge, at that point of time.
In the first case, its the "users" fault, in the second, its on the current state of the theory. The first one is rubbish, only the second one yields knowledge. If you submit a paper of the first case, it gets rejected. If you submit one of the second one, you get attention.
You are just "projecting" everything into one pseudo-abstract (cp. Reason 2.) timeless dimension, washing away the core in my "theories of theories":
By misuse i would clearly say its of the first case category, where the "user" fucked it up, the second should NOT be labelled as misuse.
Reason for this partition as already said: the first category is rubbish, the second one is valueable.
Or another equally good reason: it cannot semantically be a misuse, if the "user" does not violate any assumption known at that time, because the current "rules" do define what a misuse is. Misuse is dynamic, not static. Think four dimensional, Doc Brown!
- It is further not true, that CS theories are purely abstract and basically formal logic and cannot be wrong.
Even in mathmatics itself, only a subset of the disciplines are purely abstract.
One example, where this is not the case, is coincidently the greatest mathmatical question currently: by what rule are the prime numbers distributed? This is in the field of number theory.
The earliest theory was, that they are log-distributed, by Gauß. His log approximation of the step function of primes was good, bur clearly deviates. Meanwhile, many other mathmatical theories, such as a log distribution, have been developed, leading up to the riemann hypothesis.
In this example u see, that a mathmatical model (here the log fct) is APPLIED TO DESCRIBE a natural phenomenon (the distribution of primes). Now the correctness is not decided in some formal level, but in the question if the natural phenomenon can be accurately enough described by the suggested mathmatical model.
What you say, that math. theories cannot be wrong because they are deduced/proven/whatever, is totally off-topic in this example, and could at maximum refer to the formal correctness of the theory around the log function involved here, e.g. the rules of adding two logs or similar, which are itself proven to be correct.
But that is not of interest here, the log theory is just taken, and suggested to model a natural phenomenon. The mathmatical theory here is that the step fct. of primes follows a log distribution.
By the way, there is also no conditions to be met, there is just one step fct. and one candidate theory to predict it.
The answer to the correctness of a theory about the distribution of primes does not lie in some formal deduction, but lies directly in the difference of the predicted and real distribution of primes.
In CS theories, of course you have questions from the CS domain that you want to answer with your mathmatical model. Only a small subset of CS theory deals with purely abstract proofs that stand for itself, e.g. in formal verification. The majority has a domain question to be answered and very often that question is quantitative, such that CS theories predict numbers that can be measured against real data measured from the phenomenon of interest, which then detetmines the correctness of the theory
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