Is it really a culture divide or is it an economic incentives divide? Many AI researchers are mathematicians. Any theoretical AI research paper will typically be filled with eye-wateringly dense math. AI dissolves into math the closer you inspect it. It's math all the way down. What differs are the incentives. Math rewards openness because there's no real concept of a "competitive edge", you're incentivized to freely publish and share your results as that is how you get recognition and hopefully a chance to climb the academic ladder. (Maybe there might be a competitive spirit between individual mathematicians working on the same problems, but this is different than systemic market competition.) AI is split between being a scientific and capitalist pursuit; sharing advances can mean the difference between making a fortune or being outmaneuvered by competitors. It contaminates the motives. This is where the AI researcher's typical desire for "novel results" comes from as well, they are inheriting the values of industry to produce economic innovations.
It's a tidier explanation to tie the culture differences to material motive.
> Many AI researchers are mathematicians. Any theoretical AI research paper will typically be filled with eye-wateringly dense math. AI dissolves into math the closer you inspect it. It's math all the way down.
There is a major caveat here. Most 'serious math' in AI papers is wrong and/or irrelevant!
It's even the case for famous papers. Each lemma in Kingma and Ba's ADAM optimization paper is wrong, the geometry in McInnes and Healy's UMAP paper is mostly gibberish, etc...
I think it's pretty clear that AI researchers (albeit surely with some exceptions) just don't know how to construct or evaluate a mathematical argument. Moreover the AI community (at large, again surely with individual exceptions) seems to just have pretty much no interest in promoting high intellectual standards.
I'd be interested to read about the gibberish in UMAP, I know the paper "An improvement of the convergence proof of the
ADAM-Optimizer" for the lemma problem in the original ADAM but hadn't heard of the second one. Do you have any further info on it?
> Each lemma in Kingma and Ba's ADAM optimization paper is wrong
Wrong in the strict formal sense or do you mean even wrong in “spirit”?
Physicists are well-known for using “physicist math” that isn’t formally correct but can easily be made as such in a rigorous sense with the help of a mathematician. Are you saying the papers of the AI community aren’t even correct “in spirit”?
Much physicist math can't be made rigorous so easily! Which isn't to say that much of it doesn't still have great value.
However the math in AI papers is indeed different. For example, Kingma and Ba's paper self-presents as having a theorem with a rigorous proof via a couple of lemmas proved by a chain of inequalities. The key thing is that the mathematical details are purportedly all present, but are just wrong.
This isn't at all like what you see in physics papers, which might just openly lack detail, or might use mathematical objects whose existence or definition remain conjectural. There can be some legitimate problems with that, but at least in the best cases it can be very visionary. (Mirror symmetry is a standard example.) By contrast I'm not sure what 'spirit' is even possible in a detailed couple-page 'proof' that its authors probably don't even fully understand. In most cases, the 'theorem' isn't remotely interesting enough as pure mathematics and is also not of any serious relevance to the empirical problem at hand. It just adds an impressive-looking section to the paper.
I do think it's possible that in the future there will be very interesting pure mathematics inspired by AI. But it hasn't been found yet, and I'm very certain it won't come from reconsidering these kinds of badly-written theorems and proofs.
There's a related section about 'mathiness' in section 3.3 of the article "Troubling Trends in Machine Learning Scholarship" https://arxiv.org/abs/1807.03341. I would say the situation has only gotten worse since that paper was written (2018).
However the discussion there is more about math which is unnecessary to a paper, not so much about the problem of math which is unintelligible or, if intelligible, then incorrect. I don't have other papers off the top of my head, although by now it's my default expectation when I see a math-centric AI paper. If you have any such papers in mind, I could tell you my thoughts on it.
