> a shift of skills away from things that mattered more in the past toward other things that are not measured/perceived by the older generation.

Do you have any ideas what these things might be? As someone in his twenties, I’m sometimes saddened by observing that some of the skills I acquired over a long time (e.g., writing, coding) may become obsolete or won’t be respected anymore just now that I‘m finally getting good at them.

However, in the role of personal teachers they may allow especially our young generations to reach a deeper understanding of maths (and also other topics) much quicker than before. If everyone can have a personal explanation machine to very efficiently satisfy their thirst for knowledge this may well lead to more good mathematicians.

Of course this heavily depends on whether we can get LLMs‘ outputs to be accurate enough.

> arXiv requires that users be endorsed before submitting their first paper to arXiv or a new category.

[1] https://info.arxiv.org/help/endorsement.html

[1] https://en.wikipedia.org/wiki/Socratic_method

https://enzyme.mit.edu

> these AI systems will be flying our airplanes, running our power grids, and possibly even governing entire countries.

I guess we should figure out how to include the three laws of robotics in connectionist models asap…

I want to note there is hope. Contrary to what the root comment says, some publishers try to endorse reproducible results. See for example the ACM reproducibility initiative [1]. I have participated in this before and believe it is a really good initiative. Reproducing results can be very labor intensive though, loading a review system already struggling under massive floods of papers. And it is also not perfect, most of the time it is only ensured that the author-supplied code produces the presented results, but I still think more such initiatives are healthy. When you really want to ensure the rigor of a presented method, you have to replicate it, i.e., using a different programming language or so, which is really its own research endeavor. And there is also a place to publish such results in CS already [2]! (although I haven‘t tried this one). I imagine this may be especially interesting for PhD students just starting out in a new field, as it gives them the opportunity to learn while satisfying the expectation of producing papers.

[1] https://www.acm.org/publications/policies/artifact-review-an... [2] https://rescience.github.io

This also reminds me of using Hopfield networks to store images. Seems like Hopfield networks are a special case of this where the activation function of each cell is a simple sum, but I’m not sure. Another difference is that Hopfield networks are fully connected, so the neighborhood is the entire world, i.e., they are local in time but not local in space. Maybe someone can clarify this further?

[1] https://www.qtrac.eu/diffpdf-foss.html

Just to clarify: we do a kind of source-to-source transformation by transparently injecting some API-calls in the right places (e.g., before branching-statements) before compilation. However, the compiled program then returns the program output alongside the gradient.

For the continuous parts, the AD library that comes with DiscoGrad uses operator overloading.

So if you can express your test cases in a numerical way and make the placeholders for the "magic numbers" visible to the tool by regarding them as "inputs" (which should generally be possible), this may be a possible use-case. Hope this clarifies it.