[YeGoblynQueenne]

As far as I can tell from a quick heuristic perusal, the "Generalization Beyond Overfitting" paper reports "generalisation" _on the validation set_. That's not particularly impressive and it's not particularly "generalisation" either.

Actually, I really don't grokk this (if I may). I often see deep learning work reporting generalisation on the validation set. What's up with that? Why is generalisation on the validation set more interesting than on the test set, let alone OOD data?

[Isinlor]

The point of the paper is to show that NN can still learn long after fully memorizing the train dataset.

This behavior goes against current paradigm of thinking about training NNs. It is just very unexpected, similarly as double descent is unexpected from classical statistics point of view that more parameters lead to more over-fitting.

They could have split validation test set into validation and test sets, but I don't know what that would achieve in their case.

Fig. 1 center shows different train / validate splits. Fig 2. shows a swoop between different optimization algorithms if you are concerned about hyperparameters over-fitting.

But to me really interesting is the Fig 3. that shows that NN learned the structure of the problem.

[YeGoblynQueenne]

>> The point of the paper is to show that NN can still learn long after fully memorizing the train dataset.

That is the claim in the paper. I don't understand how it is supported by measuring results on the validation set.

Figure 3 looks nice but it doesn't say anything on its own. I don't know what's the best way to interpret it. The paper offers some interpretation that convinces you, but not me. Sorry, this kind of work is too fuzzy for me. What happened to good, old-fasion proofs?

[Isinlor]

The paper shows that their model first overfitted the data. By overfitting I mean 100% train dataset accuracy and ~0% validation dataset accuracy. The model never gets any feedback from the validation dataset trough the training procedure.

Everyone's expectation would be that this is it. The model is overfitted, so it is useless. The model is as good as a hash map, 0 generalization ability.

The paper provides empirical, factual evidence that as you continue training there is still something happening in the model. After the model memorized the whole training dataset and while it still has not received any feedback information from the validation dataset, it starts to figure out how to solve validation dataset.

Mind you, this is not interpretation, this is factual. Long after 100% overfitting, the model is able to keep increasing its accuracy on dataset it has not seen.

It's as we discovered that water can flow upwards.

Grokking was discovered by someone forgetting to turn off their computer.

Nobody knows why. So, nobody is able to make any theoretical deductions about it.

But I agree that fig 3. requires interpretation. By itself it does not say a lot, but similar structures appear in other models like in the one where we discuss elements sequence prediction. To me, the models figure out some underlying structure of the problem, and we are able to interpret that structure.

I tend to look at it from Bayesian perspective. This type of evidence increases my belief that the models are learning what I would call semantics. It's a separate line of evidence from looking at benchmark results. Here we can get a glimpse at how some models may be doing some simple predictions and it does not look like memorization.

[YeGoblynQueenne]

>> The paper shows that their model first overfitted the data. By overfitting I mean 100% train dataset accuracy and ~0% validation dataset accuracy. The model never gets any feedback from the validation dataset trough the training procedure.

Yes, but the researchers get plenty of feedback from the validation set and there's nothing easier for them than to tweak their system to perform well on the validation set. That's overfitting on the validation set by proxy. It's absolutely inevitable when the validation set is visible to the researchers and it's very difficult to guard against because of course a team who has spent maybe a month or two working on a system with a publication deadline looming are not going to just give up on their work once they figure it it doesn't work very well. They're going to tweak it and tweak it and tweak it, until it does what they want it to. They're going to converge -they are going to converge- on some ideal set of hyperparameters that optimises their system's performance on its validation set (or the test set, it doesn't matter what it's called, it matters that it is visible to the authors). They will even find a region of the weight space where it's best to initialise their system to get it to perform well on the validation set. And, of course, if they can't find a way to get good performance out of their system, you and I will never hear about it because nobody ever publishes negative results.

So there are very strong confirmation and survivorship biases at play and it's not surprising to see, like you say, that the system keeps doing better. And that suffices to explain its performance, without the need for any mysterious post-overfitting grokking ability.

But maybe I haven't read the paper that carefully and they do guard against this sort of overfitting-by-proxy? Have you found something like that in the paper? If so, sorry for missing it myself.

[Isinlor]

> And that suffices to explain its performance, without the need for any mysterious post-overfitting grokking ability.

It actually still does not suffice. It is just not expected no matter what the authors would be doing.

Just the fact that they managed to get that effect is interesting.

Granted, the phenomenon may be limited in scope. For example, on ImageNet it may require ridiculously long time scales. But maybe there is some underlying reason we can exploit to get to grokking faster.

It's basically all in fig 2.:

- they use 3 random seeds per result

- they show results for 12 different simple algorithmic datasets

- they evaluate 12 different combinations of hyperparameters

- for each hyperparameters combination they use 10+ different ratios of train to validation splits

So they do some 10*12*3*2 = 720 runs.

They conclude that hyperparameters are important. Seems like weight decay is especially important for the grokking phenomenon to happen when model has access to low ratio of training data.

Also, at least 2 other people managed to replicate that results:

https://twitter.com/sea_snell/status/1461344037504380931

https://twitter.com/lieberum_t/status/1480779426535288834

One hypothesis may be that models are just biased to randomly stumble upon wide, flat local minima. And wide, flat local minima generalize well.

[YeGoblynQueenne]

I don't agree. Once a researcher has full control of the data, they can use it to prove anything at all. This is especially so in work like the one we discuss, where the experiments are performed on artificial data and the researchers have even more control on it than usual. As they say themselves, such effects are much harder to obtain on real-world data. This hints to the fact that the effect depends on the structure of the dataset and so it's unlikely to, well, generalise to data that cannot be strictly controlled.

You are impressed by the fact that one particular, counter-intuitive result was obtained, but of course there is an incentive to publish something that stands out, rather than something less notable. There is a well-known paper by John Ioannidis on cognitive biases in medical research:

Why most published research findings are false

https://journals.plos.org/plosmedicine/article?id=10.1371/jo...

It's not about machine learning per sé, but its observations can be applied to any field where empirical studies are common, like machine learning.

Especially in the field of deep learning where scholarly work tends to be primarily empirical and where understanding the behaviour of systems is impeded by the black-box nature of deep learning models, observing something mysterious and unexpected must be cause for suspicion and scrutiny of methodology, rather than accepted unconditionally as an actual observation. In particular, any hypothesis that tends towards magick, for example suggesting that a change in quantities (data, compute, training time) yields qualitative improvements (prediction transmogrifying into understanding, overfitting transforming into generalisation), should be discarded with extreme prejudice.