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hellrail t1_itcw9n1 wrote

Reply to comment by Real_Revenue_4741 in [D] What things did you learn in ML theory that are, in practice, different? by 4bedoe

@ "When practice deviates from theory, this usually means that the theory does not well-capture the results that people are getting in practice. This does not necessarily mean that the theory is incorrect, but that usually the implications of the theory and it’s common inductions don’t capture the entire picture."

Thats a rather stupid (sorry) interpretation of what the term "deviations from the theory" should mean. If one follows your interpretation, it means that you would declare an experiment, where someone tries to calculate some fluid dynamics by using maxwells equations and then gets results that not match the measurements, as a "deviation from the theory".

Thats nonsense, because obviously the theory IS JUST USED wrong: the theory around the Maxwell equations NEVER suggested to model the dynamics of fluids.

therefore, a more sensical interpretation for a "theory deviating from reality" is to include the assumption, that the theory "is used correctly" (meaning theory predictions are compared with measurements, for which the theory really is made for to predict up to a certain accuracy).

If then the theory is applied correctly, but the measurements deviate qualitatvely from the measured reality, that implies that the theory does not model the real mechanics accurately and therefore is wrong (in science we call that falsification).

At the example you gave: you named some ongoing discussion in an open research field. Of course, when humans try to come up with explanations for something (when they develop NEW theories), 99% of the ideas are wrong at first and are still being discussed. Through experiments and falsification, theories are adapted until they are not falsified anymore. That means, every theory, with time, gets filtered by the scientific process, until more and more experiments confirm it by not falsifying it. At the end of this process, a theory is well established and starts to being taught e.g. to students in universities.

Your example is not one for a well established theory, that the topic creator as a student could have learned as "truth" about in one of his lectures. And the topic name is "what .... did you LEARN".

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Real_Revenue_4741 t1_itd229a wrote

  1. This is a merely a matter of semantics. When a theory doesn’t extrapolate nicely in certain scenarios, you can state that the theory is incorrect. However, another way to view it is that there are still certain considerations that the theory is missing. It is often difficult to known exactly when a theory can and cannot be applied. Since you come from a physics background, a good example is CPT symmetry. Up until 1957, physicists believed CPT could be broadly applied to all of physical laws and until 1964 that CP symmetry cannot be violated as well. However, they were later disproven. You can say that the CPT theory was not applied correctly in those cases because they do not lie within the constraints we make today, but that is retroactively changing the story.
  2. Empirical risk minimization, VC dimension, and the classic bias and variance tradeoff are taught in undergrad machine learning classes and wete considered a well-established theories for a while. It goes without saying that there is no possible way to distinguish whether a scientific theory is truly infallible or may be refuted in the future.
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hellrail t1_itd4jqh wrote

  1. It is not a matter of semantics. Your interpretation included all reasons for deviations, that are caused by a "wrong usage", for which i have made an extrem example. My interpretation does exclude these cases. Distinguishing between wrong and correct usage can be clearly pinned to the assumptions of the experiment. To pick up my example from before: a guy trying to predict fluid dynamics with maxwells eqs started with the assumptions that maxwells eqs are capable of predicting fluid dynmaics. That is objectively wrong. Especially, it CANNOT be interpreted as "his assumption is correct, maxwells eqs just lack of certain aspects necessary to describe fluid dynamics". No.

The wrong usage of a theory can be pinned down to the assumptions, and these are not a matter of semantics.

  1. Not knowing the class you have visited, i can only comment on this if you link me that lecture, such that i can see what really was thought there as established theory and what not.

In classes i have visited or seen in the internet, i have never seen somebody stating that its a global rule that larger models, without exception, do increase the danger of overfitting or similar. Such topics were discussed at maximum in context of "intuition", resp. The teacher just shared his own experiences. And still, thats often true.

But i am open to see the example lecture, that teaches that as a general rule explicitly, such that it has been falsified later.

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Real_Revenue_4741 t1_itd9ziu wrote

  1. Even the assumptions themselves can be in contention. The point of the CPT example was to show that the assumptions that theories make often need to be revisited. Therefore, a deviation between theory and practice can, and often will, take the form of a change of assumptions about when the theory can be applied.
  2. http://www.ai.mit.edu/courses/6.867-f04/lectures/lecture-12-ho.pdf We can clearly see that in the model selection slide, it states to choose the model with the lowest upper bound on the expected error.
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hellrail t1_itdde95 wrote

  1. I disagree. Give me an example where the assumption is just a matter of semantics.

I state that every correct (and by that i mean scientific) formulation of assumptions can be even abstracted and formalized, and even incorporated in an automated algorithm yielding the answer weather this assumption is true or not, w.r.t the theories assumptions.

Proof: take an arbritrary assumption formulation and convert it to mathmatical formulation. Then us goesels numbers to formalize.

If you say now, well the conversion to a mathmatical formulation can be ambigious, i would ask you to clearly state the assumptions in a language that is suited for a scientific discussion.

  1. On the model selection slide, i see its just stated that model/hyperp optimization aims at selecting optimal parameters. Thats ofc trivially true.

If you Talk about the subsequent slides, i see it introduces one idea, to get some guidance in finding the opt settings, called bayesian occams razor. Occams razor is a HEURISTICS. Thats so to say the opposite of a rule/theory.

A property of heuristics is explicitly, that it does not guarantee to yield a true or optimal solution. A heuristics can by definition not be wrong or correct. its a heuristics, a strategy that has worked for many ppl in the past and might fail in many cases. A heuristics does not claim to provide a found rule or similiar.

Now on the last slide they even address the drawbacks of this heuristics. What do you expect more?

As i expected, this is not an example of a theory stating something that deviates from reality. Its just a HEURISTIC strategy they give you at hand, when you want to start with hyperparameter finding but you have no clue how. Thats when you go back to heuristics (please wikipedia heuristics) and i bet this proposed heuristics is not the worst you can do even today, where more knowledge has been accquired.

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Real_Revenue_4741 t1_itddwyd wrote

I believe you are looking at the wrong slides. Reddit did something weird with the hyperlink

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hellrail t1_itde28m wrote

Then please point mento the right slide by gibing the slide number

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Real_Revenue_4741 t1_itdehtz wrote

It should be from MIT (try copying/pasting the address linked above)

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hellrail t1_itewyaw wrote

One thing i must add regarding the topic of presentation as "established knowledge".

The lecture you quoted, is lecture number 12. It is embedded in a course. There are of course lecture 11, 10, 9 etc. If you check these, which are also accessible with slightly midifying the given link, you see the context of this lecture. Specifically, a bunch of classifiers are explicitly introduced, and the v-dim theory on lecture 12 are still valid of these. The course does not adress deep networks yet.

So its a bit unfair to say these lecture does teach you a theory that deviates. Its does not deviate for the there introduced classifiers.

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hellrail t1_itdlgvb wrote

Ok found the right one.

Well, generally i must say good example. I accepted it at least as a very interesting example to talk about, worth mentioning in this context.

Nevertheless, its still valid for all NON cnn, resnet, transformer models.

Taking into account, that its based on an old theory (prior 1990), where these deep networks have not existed yet, one might take into account its limitedness (as it doesnt try to model effects taking place during learning of such complex deep models, which hasnt been a topic back then).

So if I would be really mean, i would say u cant expect a theory making predictions about entities (in this case modern deep networks) that had not been invented yet. One could say that the v-dim theory's assumptions include the assumption of a "perfect" learning procedure (therefore exclude any dynamic effects from the learning procedure), which is still valid for decision trees, random forrest, svms, etc, which have their relevance for many problems.

But since im not that mean, i admit that this observations in these modern networks do undermine the practicability of the V-dimension view for modern deep networks of the mentioned types, and that must have been a mediocre surprise before having tried out if v-dims work for cnn/resnet/transformers, therefore good example.

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trutheality t1_itegpue wrote

Your theory about what it means for theory to deviate from practice seems to deviate from practice.

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hellrail t1_iteuwcw wrote

Yes you are right. That is, because in most cases, not the theory is wrong but its wrongly understood, artifically extended, wrongly used.

It is therefore important to distinguish between deviations from theory, and deviations from misuse/misinterpretation.

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trutheality t1_itewkwz wrote

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.

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hellrail t1_itf78g0 wrote

Wrong.

Due to minimum 2 reasons:

  1. 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!

  1. 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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