As far as I can tell the replications are on the same dataset, or at least the
same task, of modular arithmetic. Until we've seen comparable results on
radically different datasets, e.g. machine vision datasets, replications aren't
really telling us much. Some dudes ran the same program and they got the same
results. No surprise.

I confess that I'd be less suspicious if it reached less than full accuracy on
the validation set. 100% accuracy on anything is a big red flag and there's a
little leprechaun holding it and jumping up and down pointing at something. I'm
about 80% confident that this "grokking" stuff will turn out to be an artifact
of the dataset, or the architecture, or some elaborate self-deception of the
researchers by some nasty cognitive bias.

Perhaps one reason I'm not terribly surprised by all this is that uncertainties
about convergence are common in neural nets. See early stopping as a
regularisation procedure, and also, yes, double descent. If we could predict
when and how a neural net should converge, neural networks research would be a
more scientific field and less a
let's-throw-stuff-at-the-wall-and-see-what-sticks kind of field.

But, who knows. I may be wrong. It's OK to be wrong, even mostly wrong, as long
as you 're wrong for the right reasons. Science gives us the tools to know when
we're wrong, nothing more. The scientist must make peace with that. Thinking one
can be always right is hubris.

Speaking of which, John Ioannidis is one of my personal heroes of science
(sounds like an action figure line, right? The Heroes of Science!!
dun-dun-duuunnn). I was a bit shocked that he came out so strongly sceptical
against the mainstream concerns about Covid-19, and I've heard him make some
predictions that soon proved to be false, like the number of people who would
get Covid-19 in the USA (I think he said something like 20,000 people?). He
really seemed to think that it was just another flu. Which btw kills lots of
people and we're just used to it, so perhaps that's what he had in mind. But, I
have the privilege of sharing my maternal language with Ioannidis (he's Greek,
like me) and so I've been able to listen to him speak in Greek news channels, as
well as in English-speaking ones, and he remains a true scientist, prepared to
express his knowledgeable opinion, as is his responsibility, even if it may be
controversial, or just plain wrong. In the end, he's an infectious disease
expert and even his contrarian views lack that certain spark of madness in the
eye of most others who share his opinions. I mean, because he's speaking with
knowledge, rather than just expressing some random view he's fond of. He's still
a role model for me. Even if he was wrong in this case.

>> Unfortunately, it applies to theoretical findings too. For example, universal
approximation theorem, no free lunch theorem or incompleteness theorems, are
widely misunderstood. There are also countless less known theoretical results
that are similarly misunderstood.

I guess? Do you have some example you want to share? For my part, I try to avoid
talking of things I don't work with on a daily basis, on the internet. I know
what I know. I don't need to know -or have an opinion- on everything...