An overview of the theory of overparameterized machine learning • Hacker News Board

Re: An overview of the theory of overparameterized machine learning

#31

Post by [deleted] » Tue, Sep 21, 2021, 7:18 PM UTC

naomisperfume wrote: post #16

baron_harkonnen wrote: post #12

Earlier quoted context omitted.

> In practice, these huge models are, in laymans terms, fucking awesome and work really well A similarly surprising result from an adjacent community, Bayesian Statistics, is that in the case of hierarchical models, increasing your number of parameters can paradoxically reduce overfitting. The scale of parameters in Bayesian model's is no where near that of these deep neural nets, but nonetheless this is a similarly…

Do you have any good references of this phenomenon in hierarchical models?

[deleted]

Re: An overview of the theory of overparameterized machine learning

#32

Post by thisiszilff » Tue, Sep 21, 2021, 7:24 PM UTC

underanalyzer wrote: post #19

sdenton4 wrote: post #18

Earlier quoted context omitted.

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…

I have nothing to do with machine learning but it seems like the hashing approach would only work if you are “training” on the evaluation set instead of a separate training set. Afaik in image net like challenges the set of labeled training images does not contain any of the evaluation images so there wouldn’t be any hashes matching any of the evaluation data.

Yes, you're right. You should never see the test/evaluation dataset during training so it would be impossible to "memorize" the test cases. You would get good near perfect accuracy on the training data, but not the test set. I think the closest analogue would be models that produce conceptual embeddings somewhere in them -- those are kind of like hashes with the property that similar things have similar embeddings. Many classification neural networks kind of operate like that -- the initial layers produce a representation of the data and then the final layer actually performs the classification.

Re: An overview of the theory of overparameterized machine learning

#33

Post by sdenton4 » Tue, Sep 21, 2021, 7:37 PM UTC

r-zip wrote: post #21

sdenton4 wrote: post #18

Earlier quoted context omitted.

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.

https://openreview.net/forum?id=Sy8gdB9xx

"our experiments establish that state-of-the-art convolutional networks for image classification trained with stochastic gradient methods easily fit a random labeling of the training data. This phenomenon is qualitatively unaffected by explicit regularization, and occurs even if we replace the true images by completely unstructured random noise."

Re: An overview of the theory of overparameterized machine learning

#34

Post by sjg007 » Tue, Sep 21, 2021, 8:11 PM UTC

baron_harkonnen wrote: post #12

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 A similarly surprising result from an adjacent community, Bayesian Statistics, is that in the case of hierarchical models, increasing your number of parameters can paradoxically reduce overfitting. The scale of parameters in Bayesian model's is no where near that of these deep neural nets, but nonetheless this is a similarly…

This is likely part of the reason. The only problem is said models require a lot of data but Humans can learn from a very small number of examples.

Re: An overview of the theory of overparameterized machine learning

#35

Post by gwern » Tue, Sep 21, 2021, 8:17 PM UTC

bsmith89 wrote: post #6

I'm not sure if it's related, but I've seen discussions of modern ML methods (in particular those trained using stochastic algorithms...maybe also models with low float precision...?) approximating Bayesian methods. The way I've imagined it is that the training path, by virtue of its stochasticity, resembles MCMC sampling and therefore tends to end up in regions of high posterior volume (the "typical set"), rather th…

You're looking for flat minima / wide basins. (Amusingly, this one actually does go back to Schmidhuber etc.) Explains a lot of phenomenon like poorer generalization of second-order optimizers, SGD sometimes working surprisingly better, stochastic weight averaging / EMA, grokking, or patient teachers.

Re: An overview of the theory of overparameterized machine learning

#36

Post by marius_k » Tue, Sep 21, 2021, 8:51 PM UTC

unemphysbro wrote: post #5

Briefly skimmed the paper and I'm not a ML or math dude but familiar with the double descent problem. I wonder if there's a good way to measure information content in models and how it scales with model parameters, if there are any invariants, scaling law's that arise etc. Reminds me of renormalization group methods which could be applied to a space of models, etc... Again, I'm no expert in any of this stuff, just ar…

Would it work to measure the size of compressed model?

Re: An overview of the theory of overparameterized machine learning

#37

Post by cs702 » Tue, Sep 21, 2021, 9:09 PM UTC

I'll come out and say what's on many practicioners' minds:

It could very well be that generations of academics have been WRONG about the relationship between the number of parameters (or complexity) of a model and its ability to generalize to new, previously unseen data, particularly when the data is drawn from many naturally occurring distributions -- as opposed to, say, distributions randomly chosen from the space of all possible distributions, as assumed by many theoretical frameworks (e.g., No Free Lunch theorem). It could be that generations of students have been taught The Wrong Thing™.

In many cases we must increase, not decrease, model complexity to improve generalization!

Re: An overview of the theory of overparameterized machine learning

#38

Post by oleg_myrk » Tue, Sep 21, 2021, 9:19 PM UTC

baron_harkonnen wrote: post #12

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 A similarly surprising result from an adjacent community, Bayesian Statistics, is that in the case of hierarchical models, increasing your number of parameters can paradoxically reduce overfitting. The scale of parameters in Bayesian model's is no where near that of these deep neural nets, but nonetheless this is a similarly…

Any chance you could share a link to a relevant paper?

Re: An overview of the theory of overparameterized machine learning

#39

Post by jcranberry » Tue, Sep 21, 2021, 9:26 PM UTC

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…

My sister works in the NLP arm of ML and analogized it to the Clever Hans effect.

Re: An overview of the theory of overparameterized machine learning

#40

Post by xyzzy21 » Tue, Sep 21, 2021, 9:30 PM UTC

I'm not surprised. In physics/engineering related model fitting, there is a double-edged risk of over-parametrization as well as under-parameterization. The former is almost always non-physical - it fits but the parameters are meaningless as predictor, conclusions or tying to ANYTHING physical as a design strategy. The latter fits only certain corners of the data space and if you don't know which ones, you can get yourself in to trouble that way as well.

The former can be worse than the latter in terms of meaningful use for engineering.