Dataflow matrix machines (by Anhinga anhinga)

> On when to use coordinates and other concrete constructions in mathematics, and when to use coordinate-free formulations and abstractions:

> 1. If your priority is to perform computations in mathematics, use coordinates and concrete constructions.
> 2. If your priority is to generalize to as broad a range of use cases as possible, use coordinate-free formulations and abstractions.
> 3. If your priority is to actually understand what is going on behind the mathematical formalism, learn how the coordinate-based and coordinate-free approaches are equivalent.

mathstodon.xyz/@tao/114456756661540097

"Narrow AGI" is mostly an AGI-level artificial software engineer, an AGI-level artificial mathematician, an AGI-level artificial AI researcher (and probably a single entity combining these three application areas, because a strong AI researcher has to be a decent software engineer and a decent mathematician).

It seems that at least OpenAI (and, perhaps, other entities) should have this by the middle of 2025, if not earlier, at least for their internal use (assuming no major disasters, that is, assuming that San Fransisco Bay Area is intact, and AI companies continue functioning normally).

What do we know about the technical aspects? We see o1 performance (and can experience it directly), we see the claimed (and partially confirmed) numbers for the demo versions of o3 and o3-mini, in math and in software engineering. We know that the jump from o1 to o3 took about 3 months. Two more jumps like that would probably be sufficient (and one can add "scaffolding" on top of that).

Another thing we know is that Sam Altman sounds much more confident recently. I've come to these conclusions a number of days ago, but now it turns out that Sam's mood has also shifted in a similar fashion. I'll put some links in the comments.

Jan 19 update: Sam Altman will allegedly do a closed-door government briefing on Jan 30 (that's apparently is not a very big secret and has been leaked; the main topic is presumably as follows: many people in the leading AI labs have approximately the same degree of techno-optimism as I have myself, and so their timelines are tentatively quite short). www.axios.com/2025/01/19/ai-superagent-openai-meta

This is a non-trivial angle: x.com/StringChaos/status/1869571815548596308 (UC Berkeley)

For some reason, I keep losing this remarkable blog by Grigory Sapunov and finding it again, instead of just reading it regularly:


gonzoml.substack.com/

Говорят, что Денис Гайцгори и его коллеги доказали достаточно общий вариант геометрической гипотезы Ленглендса.

Это вполне эпохальное событие, и надо собрать вместе всякие линки, относящиеся к этому делу. Вместе с тем, это для меня слишком сложно (может быть, ИИ (современный или будущий) сможет мне, со временем объяснить детали всего этого так, чтобы у меня возникло уверенное понимание).

"Enhancement for categories and homotopical algebra", arxiv.org/abs/2409.17489

600 pages

"We develop foundations for abstract homotopy theory based on Grothendieck's idea of a "derivator". The theory is model-independent, and does not depend on model categories, nor on simplicial sets. It is designed to accomodate all the usual potential applications, such as e.g. enhancements for derived categories of coherent sheaves, in a way that is as close as possible to usual category theory."

He also released references [K3] and [K4]:

arxiv.org/abs/2409.18380 and arxiv.org/abs/2409.18378

OpenAI is finally releasing their next set of models. Those models take time to ponder and reason internally before talking. This is what has been known as mysterious "Q*" and "Strawberry", but is now released as "o1 series of models".

They promise a preview version availability today for ChatGPT+ users.

Links in the comments.

There are breaking changing (this includes breaking binary compatibility):

blog.scientific-python.org/numpy/numpy2/

numpy.org/devdocs/numpy_2_0_migration_guide.html

The author of Kolmogorov-Arnold Networks will present at 11am Eastern time.

OpenAI "Spring Updates" livestream at 1pm Eastern time.

Both events should be recorded.

Most of the devices (mobile phones, computers) can be switched to grayscale mode (and back).

This is usually under "Accessibility/Ease of Access" via turning "Color Filters" on (and off).

I like the effect :-)