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An overview of the theory of overparameterized machine learning

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Re: An overview of the theory of overparameterized machine learning

#21

Post by r-zip »

sdenton4 wrote: post #18
quocanh wrote: post #17

Earlier quoted context omitted.

When you say hash function, do you mean a cryptographic hash function? How on earth could the performance of that be anywhere near the simplest probabilistic algorithm on unseen examples?

No, nothing cryptographic here. All I'm saying is that you can memorize the dataset by extracting a small fingerprint of each training example and associating it with an output label: ie, learn by lookup table. Then you don't need to memorize the whole training set, you just need to find/learn the fingerprinting function. With no augmentation, you might as well use MD5... With augmentation, you do need to do some act…

Has this been implemented? What kinds of hashing functions are you talking about? How would you guarantee the same hash for all the augmentations?

It seems like the approach you describe just moves the complexity of the task solved by neural networks into the hashing function.

Re: An overview of the theory of overparameterized machine learning

#22

Post by andrewnc »

talolard wrote: post #2

A quick summary/translation for those of us who don't speak ML. We keep hearing about these giant models like GPT3 with 1.5 billion paramaters. Parameters are the things that change when we train a model, you can think about them as degrees of freedom. If you have a lot of parameters, theory made us believe that the model would just "overfit" the training data, e.g. memorize it. That's bad, because when new data come…

Super pedantic comment. GPT-3 has 175 Billion parameters. GPT-2 was the 1.5 Billion model.

Re: An overview of the theory of overparameterized machine learning

#23

Post by 988747 »

talolard wrote: post #2

A quick summary/translation for those of us who don't speak ML. We keep hearing about these giant models like GPT3 with 1.5 billion paramaters. Parameters are the things that change when we train a model, you can think about them as degrees of freedom. If you have a lot of parameters, theory made us believe that the model would just "overfit" the training data, e.g. memorize it. That's bad, because when new data come…

> In practice, these huge models are, in laymans terms, fucking awesome and work really well e.g. they generalize and work in production. No one understands why.

How about the resulting weights? If most of them are close to 0, then that would mean that a part of the training is for NN to learn which of 1.5B parameters are relevant, and which are not.

Re: An overview of the theory of overparameterized machine learning

#24

Post by derbOac »

I have to reread it but the model misspecification interpretation (that highly overparameterized models exhibit DD because they reduce misspecification error) is the only thing I've read in this area that makes some sense to me theoretically.

I think DD is a huge issue for a number of fields and is really underappreciated a lot. Without meaning to sound disrespectful, much of this literature seems a little superficial or dismissive, not aware of the broad implications of the claims often being made.

This is because of the ties between information-theory and statistics/modeling. In some sense, at least in the way I've thought about it, the DD seems to imply some kind of violations of fundamental information theory and comes across to me a bit as if someone in chemistry started claiming that some basic laws of thermodynamics in physics didn't apply anymore. Basically, the DD seems to imply that someone can extract more information from a string than the string contains. If you put it this way, it makes no sense, which is why I think this is such a hugely important issue.

On the other hand, the empirical results are there, so figuring out what's going on is worthwhile and I have an open mind.

This paper seems nice with the misspecification angle, because it is realistic and seems to open a path to some interpretations that might not violate some fundamental identities in IT. Misspecification (mismatched coding in IT) can lead to some weird phenomena that's not always intuitive.

Another thing in the paper that's made clear is that DD might not always happen, and it seems informative to figure out when that's the case.

In the background I have to say I'm still skeptical of the empirical breadth of DD. These weird cases of ML failures due to subtle challenge inputs (the example of errors in identifying Obama based on positioning and ties (?) is one example) to me seems like prime examples of overfitting. I still have a hunch that something about the training and test samples relative to the universe of actual intended samples is at play, or the whole phenomenon of DD is misleading because the overfitting problem is really in terms of model flexibility versus data complexity, and not necessarily in terms of number of parameters per se versus sample size.

Re: An overview of the theory of overparameterized machine learning

#25

Post by rich_sasha »

yldedly wrote: post #15
talolard wrote: post #2

A quick summary/translation for those of us who don't speak ML. We keep hearing about these giant models like GPT3 with 1.5 billion paramaters. Parameters are the things that change when we train a model, you can think about them as degrees of freedom. If you have a lot of parameters, theory made us believe that the model would just "overfit" the training data, e.g. memorize it. That's bad, because when new data come…

>In practice, these huge models are, in laymans terms, fucking awesome and work really well e.g. they generalize and work in production. No one understands why. To add nuance to this, these models are awesome at interpolation, but not so much at extrapolation. Or in different terms, they generalize very well to an IID test set, but don't generalize under (even slight) distribution shift. The main reason for this is t…

It depends. It really doesn’t take that much data to train a pretty stunning (if simple) RNN character-level “language model” that beats any n-gram. Or on mnist. ANNs really are a useful tool for a vast class of problems, many of which can be solved with comparatively little data.

Maybe your point stands, and it’s just that some domains need less data, just saying.

Re: An overview of the theory of overparameterized machine learning

#26

Post by yldedly »

derbOac wrote: post #24

I have to reread it but the model misspecification interpretation (that highly overparameterized models exhibit DD because they reduce misspecification error) is the only thing I've read in this area that makes some sense to me theoretically. I think DD is a huge issue for a number of fields and is really underappreciated a lot. Without meaning to sound disrespectful, much of this literature seems a little superficia…

DD disappears when doing Bayesian model averaging: https://arxiv.org/pdf/2002.08791.pdf It seems DD is a phenomenon specific to point estimates.

>overfitting problem is really in terms of model flexibility versus data complexity, and not necessarily in terms of number of parameters per se versus sample size

Yep, well put.

Re: An overview of the theory of overparameterized machine learning

#27

Post by rich_sasha »

988747 wrote: post #23
talolard wrote: post #2

A quick summary/translation for those of us who don't speak ML. We keep hearing about these giant models like GPT3 with 1.5 billion paramaters. Parameters are the things that change when we train a model, you can think about them as degrees of freedom. If you have a lot of parameters, theory made us believe that the model would just "overfit" the training data, e.g. memorize it. That's bad, because when new data come…

> In practice, these huge models are, in laymans terms, fucking awesome and work really well e.g. they generalize and work in production. No one understands why. How about the resulting weights? If most of them are close to 0, then that would mean that a part of the training is for NN to learn which of 1.5B parameters are relevant, and which are not.

There is something called the golden ticket theory (maybe mentioned in the paper, I’m on my phone), that says indeed that the large models are effectively ensembles of massive random models, and the top levels of the network pick the one or two that randomly happen to work.

Maybe true but even then only part of the story, kernels in CNN genuinely seem to learn features like edges and textures.

Re: An overview of the theory of overparameterized machine learning

#28

Post by talolard »

988747 wrote: post #23
talolard wrote: post #2

A quick summary/translation for those of us who don't speak ML. We keep hearing about these giant models like GPT3 with 1.5 billion paramaters. Parameters are the things that change when we train a model, you can think about them as degrees of freedom. If you have a lot of parameters, theory made us believe that the model would just "overfit" the training data, e.g. memorize it. That's bad, because when new data come…

> In practice, these huge models are, in laymans terms, fucking awesome and work really well e.g. they generalize and work in production. No one understands why. How about the resulting weights? If most of them are close to 0, then that would mean that a part of the training is for NN to learn which of 1.5B parameters are relevant, and which are not.

There are two answers to this. First, empirically we see that the more parameters we add the better the model performs ==> Weights continue to contribute (and aren't dead) .

Second, there is a very popular paper called "The lottery ticket hypothesis" [1] that in any network you can find subnetworks that work just as well. e.g. The parameters are redundant. This was written in 2018, which is a long time ago in big NN world, so I'm not sure how it holds up to current insanity sized models.

[1]https://arxiv.org/abs/1803.03635

Re: An overview of the theory of overparameterized machine learning

#29

Post by IX-103 »

sdenton4 wrote: post #9
talolard wrote: post #2

A quick summary/translation for those of us who don't speak ML. We keep hearing about these giant models like GPT3 with 1.5 billion paramaters. Parameters are the things that change when we train a model, you can think about them as degrees of freedom. If you have a lot of parameters, theory made us believe that the model would just "overfit" the training data, e.g. memorize it. That's bad, because when new data come…

My big beef with a lot of the 'leading edge' ML research is that it tends to be waaaaay too focused on classification problems, and ImageNet in particular. And, last I checked, you /do/ still fight with overfitting in classification models, by cleverly choosing learning rate schedules and using early stopping schemes, 'double descent' be damned. You can solve classification with a hash function: Hash the image, and t…

Memorization is only an issue if you allow it to be. If design the model with a "narrow" enough inner stage then that limits the level of detail (in terms of distinct representable values) passed to subsequent stages. This should give you an ML algorithm that consists of a fingerprint (approximates your hashing) stage followed by a classifier that works based on the fingerprint input (approximates a table lookup). Such an algorithm should not have such a problem with over-fitting was you describe.

Re: An overview of the theory of overparameterized machine learning

#30

Post by yldedly »

rich_sasha wrote: post #25
yldedly wrote: post #15

Earlier quoted context omitted.

>In practice, these huge models are, in laymans terms, fucking awesome and work really well e.g. they generalize and work in production. No one understands why. To add nuance to this, these models are awesome at interpolation, but not so much at extrapolation. Or in different terms, they generalize very well to an IID test set, but don't generalize under (even slight) distribution shift. The main reason for this is t…

It depends. It really doesn’t take that much data to train a pretty stunning (if simple) RNN character-level “language model” that beats any n-gram. Or on mnist. ANNs really are a useful tool for a vast class of problems, many of which can be solved with comparatively little data. Maybe your point stands, and it’s just that some domains need less data, just saying.

>ANNs really are a useful tool for a vast class of problems, many of which can be solved with comparatively little data.

For sure, it all depends on how robust the model needs to be, how strongly it needs to generalize. If your dataset covers the entire domain, you don't need a robust model. If you need strong generalization, then you need to build in stronger priors.

Take f(x) = x^2. If your model only needs to work in finite interval, you just need a decent sample that covers that interval. But if it needs to generalize outside that interval, no amount of parameters will give you good performance. Outside the boundaries of the interval, the NN will either be constant (with a sigmoid activation) or linear (with ReLU type activations).

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