Dataflow matrix machines (by Anhinga anhinga)

"Mathematics of the Future", by Pavel Etingof and Slava Gerovitch

2026-10-11T06:01:16Z

An Oct 6, 2026 essay, "Mathematics of the Future", by Pavel Etingof and Slava Gerovitch:

www.dropbox.com/scl/fi/zmqzdrneyunkueu1th9iq/futuremath8.pdfrlkey=oarhqm8savaef4umcb60ldb4e&dl=0

The essay "tries to make sense of the AI-induced changes in mathematics and imagine a way forward for mathematicians". I am finding it quite useful.

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Dataflow matrix machines

2026-08-22T13:19:55Z

Dataflow matrix machines: a class of expressive self-modifiable neural machines

which can fluently modify their own weights, connectivity patterns, and size;
and can serve as a programming platform, resulting in a programming formalism with continuously deformable programs.

Reference paper: Dataflow Matrix Machines and V-values: a Bridge between Programs and Neural Nets

arxiv.org/abs/1712.07447

More details:
anhinga-anhinga.dreamwidth.org/83104.html
anhinga-anhinga.dreamwidth.org/82703.html

*** Dataflow Matrix Machines internet resources: anhinga.github.io

Interdisciplinary list of open research directions (I am looking for collaborators): dmm-collaborative-research-agenda.pdf

*** My blogs:

Main Dreamwidth blog: dmm.dreamwidth.org (partial mirror: anhinga-travel.livejournal.com )
Main LiveJournal: anhinga-anhinga.livejournal.com (mirror: anhinga-anhinga.dreamwidth.org )
Auxiliary LiveJournal: anhinga-drafts.livejournal.com (mirror: anhinga-drafts.dreamwidth.org )

🇺🇦 🇺🇦 🇺🇦 🇺🇦 🇺🇦 🇺🇦 🇺🇦

Sep 5, 2026 update: GPT-6-Astra is a "proto-AGI".

The model has convincingly beaten humans on ARC-AGI-3, while demonstrating some rather remarkable properties:

arcprize.org/blog/astra

"A key behavior observed in GPT-6 Astra was its ability to turn unfamiliar environments into compact symbolic world models. It represented game mechanics as logical rules and developed its own domain-specific language shorthand to track state and plan actions."

And also excellent "continual learning" capability:

"... how well does a model perform when it can use the context-management features its provider designed for it? For Astra, this means preserving the opaque reasoning state (which we don’t see) between requests and using compaction to manage longer conversations.

With the Provider Adapter harness, Astra's best observed score on ARC-AGI-3 Semi-Private increased from 62.7% to 99.9%. Looking across Public and Semi-Private and all reasoning levels, Provider Adapter runs were approximately 3.66x faster by aggregate recorded elapsed time and used 49% fewer total tokens across the 167 game-reasoning pairs both harnesses solved."

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Scott-Solovay approach to Continuum Hypothesis

2026-04-27T22:52:08Z

I have finally read the 1967 paper by Dana Scott, "A Proof of the Independence of the Continuum Hypothesis"

www2.karlin.mff.cuni.cz/~krajicek/scott67.pdf

That's so much better than Cohen's original approach. With Cohen's result, not only his "forcing technique" is difficult, but Cohen had to work with countable models, so a reader was left with the impression that something was "morally wrong" (ощущение что фокусник вытащил кролика из шляпы). Yes, logic is typically about finite texts over a finite alphabet, so one can often build countable models of this and that, but does the result actually shed any light on the nature of cardinalities, or only on the limitations of our formal methods?

Here the approach is very different and much more "elementary". First, one rewrites the Continuum Hypothesis as a property of subsets of real numbers (for any subset X of reals, either there is a surjective function from natural numbers onto X, or there is a surjective function from X onto reals).

Then one considers models where statements are valued not in [0,1], but in a complete Boolean algebra. Namely one considers a set Omega, a sigma-algebra of its subsets, and a countably additive probability measure over that. One considers the "sigma-ideal" of subsets having measure zero and factors the original sigma-algebra over that sigma-ideal to avoid algebraic pathologies. This factor serves as our complete Boolean algebra B of logical values.

Then it turns out that real random variables over B are a B-valued model of the theory of real numbers.

Then one takes the set Omega of sufficiently high cardinality (higher than continuum), and one can use a subset of Omega of an intermediate cardinality to build a "subset X of those real random variables", such that one can't "surjectively map naturals onto X", and one can't "surjectively map X onto the whole set of those random variables" (pages 18-20). So one gets a model where that rewrite of the Continuum Hypothesis is false.

This work and its neighborhood is also a start of the whole approach to "generalized fuzzy mathematics", where one uses Boolean algebras or Heyting algebras or even more general structures as spaces of logical values.

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From the latest Scott Aaronson

2026-04-07T13:43:03Z

scottaaronson.blog/?p=9668

The wise child asks, “what are the main classes of problems that are currently known to admit superpolynomial quantum speedups?” To this child, you can talk about quantum simulation and finding hidden structures in abelian and occasionally nonabelian groups, as well as Forrelation, glued trees, HHL, and DQI—explaining how the central challenge has been to find end-to-end speedups for non-oracular tasks.

The wicked child asks, “so can I buy a quantum computer right now to help me pick stocks and search for oil and turbocharge LLMs, or is this whole thing basically a fraud?” To this child you answer: “the quantum computing people who seek you as their audience are frauds.”

The simple child asks, “what is quantum computing?” You answer: “it’s a strange new way of harnessing nature to do computation, one that dramatically speeds up certain tasks, but doesn’t really help with others.”

And to the child who doesn’t know how to ask—well, to that child you don’t need to bring up quantum computing at all. That child is probably already fascinated to learn classical stuff.

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Сборник разнообразных артистических манифестов (2001)

2026-02-20T05:08:16Z

Есть на сети стараниями бразильских профессоров: www.professores.uff.br/ricardobasbaum/wp-content/uploads/sites/164/2017/11/mary-ann-caws-manifesto-a-century-of-isms-1.pdf

Редактор до сих пор иногда пишет в своём блоге, несмотря на возраст: en.wikipedia.org/wiki/Mary_Ann_Caws

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some Oct-Nov posts I wrote

2025-12-18T04:53:56Z

LessWrong organized a blog writing program encouraging people to create 30 relatively long blog posts in Oct-Nov as an exercise (relatively long meant being 500+ words).

I have actually done that, here are the posts (mostly AI-related, although there were some diary-like posts too; 30 posts + 2 auxiliary ones): mishka-discord.dreamwidth.org/

(They are open for commenting, but I don't expect to continue posting new posts there.)

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Helion details

2025-09-02T05:41:07Z

Their CEO wrote a more detailed post a few weeks ago on how their fusion scheme is expected to work:

www.helionenergy.com/articles/how-to-make-fusion-electricity-without-ignition/

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Tao on coordinate vs coordinate-free math reasoning

2025-05-12T14:05:41Z

> 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

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"Aging as a loss of goal-directedness"

2025-05-07T06:15:47Z

osf.io/preprints/osf/m5bnx_v1 (Michael Levin's collaboration, Feb 2025)

Aging as a loss of goal-directedness: an evolutionary simulation and analysis unifying regeneration with anatomical rejuvenation

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"Narrow AGI" this year?

2025-01-07T02:38:29Z

"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

Dec 31 update: no, we did not get "Narrow AGI" this year. But we had 2 revolutions, one centered in June plus/minus 2 months (o3---GPT5, "mature reasoning"), and one centered on the border of October/November plus/minus 6 weeks (GPT5-Codex---GPT5.2-Codex/Opus 4.5/Gemini 3, "competent programming software agents"). The distance between subsequent revolutions keeps shrinking: 7.5 years - 3 years - 18 months - about 9 months - about 4-5 months, mishka-discord.dreamwidth.org/4806.html (we don't know if this trend of distance between subsequent revolution shrinking continues, but we are watching what happens in January in this sense, in particular, whether we can progress to "trustworthy autonomy" in January; the current generation of agents is competent in software engineering, but there is no expectation of trust, so one has to work really hard to carefully organize security, quality control, and such, the whole lifecycle of software engineering can't be outsourced yet).

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Automating the Search for Artificial Life with Foundation Models

2024-12-24T07:19:58Z

pub.sakana.ai/asal/

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C to safe Rust automatic translation using LLMs and dynamic analysis

2024-12-19T05:29:59Z

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

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"Anatomy of a Formal Proof"

2024-11-20T13:47:32Z

A really nice Lean tutorial: arxiv.org/abs/2411.11885

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GonzoML

2024-11-17T04:51:55Z

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/

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Transformers as a Computational Model (workshop)

2024-11-12T23:55:15Z

End of September 2024; video recordings are available:

https://simons.berkeley.edu/workshops/transformers-computational-model/schedule

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Geometric Langlands correspondence

2024-10-06T16:26:28Z

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).

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Massachusetts - "Yes" on Question 4

2024-10-05T15:49:07Z

Voting by mail has started in Massachusetts.

I am urging "Yes" on Question 4 (legalization of benign psychedelics)

We passed Question 2 in 2008, Question 3 in 2012, and Question 4 in 2016 and our quality of life is better because we did that.

Let's do this again!

Links are in the comments

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A new book by Dima Kaledin

2024-09-27T17:17:16Z

"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

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On exploding pagers and walkie-talkies

2024-09-26T00:59:43Z

With all discussions on how this has been technically possible, I've seen only one person to offer a version which makes any sense.

"Причем, надо отдать должное устроителям, взорвались только те модели, которые были снабжены функцией самоуничтожения, при попадании девайса к врагам."

This is the only thing which makes sense. They themselves equipped their own devices with the ability to explode (and with the ability to trigger those explosions remotely).

After that, all it took was a bit of successful hacking by adversaries...

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The next AI revolution

2024-09-12T18:03:47Z

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.

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A possible anti-aging breakthrough

2024-07-08T13:00:26Z

"Gene Therapy-Mediated Partial Reprogramming Extends Lifespan and Reverses Age-Related Changes in Aged Mice"

A Feb 24 paper seems to claim an impressive result in "wild-type" mice via a partial cellular reprogramming protocol, which includes cyclic administration of doxycycline for temporal control of reprogramming, and which does not seem to be particularly cancer-inducing (that's usually a big problem with cellular reprogramming).. 124-week male mice, Doxycycline-treated controls average survival till 133 weeks, treatment group average survival till 142.5 weeks (for a human something like this would roughly double remaining life expectancy of a 75-year old male from about 10 more years to about 20 more years if equally efficient).

It would be nice if this turns out to be a real breakthrough (we have learned from experience to be very skeptical about claims in this field of study).

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NumPy 2.0

2024-06-19T14:14:10Z

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

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

numpy.org/devdocs/numpy_2_0_migration_guide.html

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Golden Gate Claude

2024-05-24T14:29:55Z

I think humans tend to have these idée fixes:

www.anthropic.com/news/golden-gate-claude

A pretty interesting example of conversation by a very experienced interlocutor:

www.lesswrong.com/posts/cxuzALcmucCndYv4a/daniel-kokotajlo-s-shortform#hyXAiafwbwfEPiX5Q

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Two AI events today

2024-05-13T14:30:40Z

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.

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A study of untrained, random-weight networks

2024-05-01T14:30:00Z

"Neural Redshift: Random Networks are not Random Functions", arxiv.org/abs/2403.02241

Interesting geometry to explore.

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