Researchers just mathematically proved that AI can't recursively self-improve its way to superintelligence.
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@Quantensalat @devsimsek There's a setup around equations (9) and (10) where the distribution used for training the next generation is a linear combination of the distribution your current generation generates and external data. As the amount of external data goes to zero, you expect model collapse. This is hardly surprising. I don't know anyone who expects you can just keep training based on previous results and expect something radically new to happen. (Though something *useful* can happen - eg. you may improve performance this way. See "rectification" in flow-matching.)
Note that this doesn't rule out all forms of self-training - just one kind. As a concrete example, an LLM trained to generate code can learn from the output of the generated code. Such output is, in some sense, exogenous.
@dpiponi @Quantensalat @devsimsek that part, that is ultimately a rehash of well-known theory. THAT part IIRC goes back to like the 1940's or 1950's.
And it absolutely rules out all forms of 'self-training.' It is not just mathematically impossible but a total logical fallacy. How can a system with no reference make correct determinations? Simple: it can't.
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@anne_twain @devsimsek this requires two components LLMs do not, cannot, and will not ever have. Intent and originality.
Researchers have done self-modifying targeted things. It takes no time at all for things to become impossible for humans to understand. This does not mean they are better. Usually they weren't. Even when hyper-focused with specific controls. -
@devsimsek this is one of those things that seemed intuitive to us skeptics but it's great to see it proven
@huxley @devsimsek doesn't scepticism and intuation mitigate each other?
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@aka_quant_noir @devsimsek Oh I think we've achieved billionaire intelligence already. I just have a much dimmer view of billionaires.
@alahmnat @devsimsek
I think we're in the billionaire intelligence decline phase. They're going nuts. -
Researchers just mathematically proved that AI can't recursively self-improve its way to superintelligence.
Not "we think it's unlikely." Not "it seems hard." Formally proved.
The model doesn't climb toward AGI — it slowly forgets what reality looks like. They call it model collapse. The math calls it inevitable.
I wrote about it
https://smsk.dev/2026/04/26/ai-cannot-self-improve-and-math-behind-proves-it/
@devsimsek excellent. Thanks for the overview!
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Researchers just mathematically proved that AI can't recursively self-improve its way to superintelligence.
Not "we think it's unlikely." Not "it seems hard." Formally proved.
The model doesn't climb toward AGI — it slowly forgets what reality looks like. They call it model collapse. The math calls it inevitable.
I wrote about ithttps://smsk.dev/2026/04/26/ai-cannot-self-improve-and-math-behind-proves-it/
@devsimsek isn't the idea of self-improving AI that the AI modifies its code, so the underlying algorithm / architecture?
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Researchers just mathematically proved that AI can't recursively self-improve its way to superintelligence.
Not "we think it's unlikely." Not "it seems hard." Formally proved.
The model doesn't climb toward AGI — it slowly forgets what reality looks like. They call it model collapse. The math calls it inevitable.
I wrote about ithttps://smsk.dev/2026/04/26/ai-cannot-self-improve-and-math-behind-proves-it/
@devsimsek @qualia I think you claim too much here. As I understand it, this result deals only with the intrinsic failures of RL-flavored approaches and not things like self-play, let alone problems that might arise from merely very good AI that still outdoes humans economically.
And I largely agree! I'm glad that someone's finally formalized the intuition that synthetic data is sawdust to bulk out real-world data with and more carefully investigated catastrophic forgetting and the general weaknesses of gradient descent.
That said... to what extent did you have Claude write this post? Because the format is... distinctive.
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@Quantensalat @devsimsek There's a setup around equations (9) and (10) where the distribution used for training the next generation is a linear combination of the distribution your current generation generates and external data. As the amount of external data goes to zero, you expect model collapse. This is hardly surprising. I don't know anyone who expects you can just keep training based on previous results and expect something radically new to happen. (Though something *useful* can happen - eg. you may improve performance this way. See "rectification" in flow-matching.)
Note that this doesn't rule out all forms of self-training - just one kind. As a concrete example, an LLM trained to generate code can learn from the output of the generated code. Such output is, in some sense, exogenous.
@Quantensalat @devsimsek For something more formal on this subject see
https://arxiv.org/abs/2601.03220
The abstract starts "Can we learn more from data than existed in the generating process itself?"
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Researchers just mathematically proved that AI can't recursively self-improve its way to superintelligence.
Not "we think it's unlikely." Not "it seems hard." Formally proved.
The model doesn't climb toward AGI — it slowly forgets what reality looks like. They call it model collapse. The math calls it inevitable.
I wrote about ithttps://smsk.dev/2026/04/26/ai-cannot-self-improve-and-math-behind-proves-it/
@devsimsek “slowly forgets what reality looks like.” Sort of like billionaires.
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Researchers just mathematically proved that AI can't recursively self-improve its way to superintelligence.
Not "we think it's unlikely." Not "it seems hard." Formally proved.
The model doesn't climb toward AGI — it slowly forgets what reality looks like. They call it model collapse. The math calls it inevitable.
I wrote about ithttps://smsk.dev/2026/04/26/ai-cannot-self-improve-and-math-behind-proves-it/
@devsimsek The existence of humans disprove the paper.
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Researchers just mathematically proved that AI can't recursively self-improve its way to superintelligence.
Not "we think it's unlikely." Not "it seems hard." Formally proved.
The model doesn't climb toward AGI — it slowly forgets what reality looks like. They call it model collapse. The math calls it inevitable.
I wrote about ithttps://smsk.dev/2026/04/26/ai-cannot-self-improve-and-math-behind-proves-it/
@devsimsek did an LLM write this toot or do LLMs just write like you
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Researchers just mathematically proved that AI can't recursively self-improve its way to superintelligence.
Not "we think it's unlikely." Not "it seems hard." Formally proved.
The model doesn't climb toward AGI — it slowly forgets what reality looks like. They call it model collapse. The math calls it inevitable.
I wrote about ithttps://smsk.dev/2026/04/26/ai-cannot-self-improve-and-math-behind-proves-it/
@devsimsek "Don't worry bro, we can totally fix this by adding a committee of expert LLMs to reason about what training data to select, another committee of LLMs to plan the optimal training order, and then a larger one to evaluate the training output. We just need you to sign this cheque for our next three hyperscale GPU data centres..."
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@dpiponi @Quantensalat @devsimsek that part, that is ultimately a rehash of well-known theory. THAT part IIRC goes back to like the 1940's or 1950's.
And it absolutely rules out all forms of 'self-training.' It is not just mathematically impossible but a total logical fallacy. How can a system with no reference make correct determinations? Simple: it can't.
@rootwyrm @dpiponi @Quantensalat @devsimsek
"How can a system with no reference make correct determinations? Simple: it can't."
Especially since it has no model of "correctness" other than "similar to the symbol streams the neural net weights were initialized from".
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@devsimsek The existence of humans disprove the paper.
Large language models are fundamentally different from mammals on every level. They do not build models or reason about them. A rat is more "intelligent".
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@devsimsek and this is old math, old theory, old knowledge. Gods do I wish I'd kept the various papers.
We've literally known for over two decades that LLMs are dead-ends. It's why IBM spent billions hyper-focusing Watson. We already knew more context just made it worse, regardless of compute or method. It's not 'intelligence,' it's a bad search function. There's shit demonstrating that back to the 1980's.
Mark V. Shaney.
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@devsimsek Is that a thing people believe, that LLMs generate themselves towards the singularity simply by eating their own output and no other feedback?
@Quantensalat @devsimsek the main issue is that unless you maintain an external signal (so human input in the form of token sequences that are actually carefully curated for coherence) the models become more and more incoherent. Sounds like you're on board with that. The next step is that we're quickly devaluing money spent on human creativity and the world is awash in LLM garbage. So the human signal *is* disappearing.
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@musicman @devsimsek As with all mathematical theorems, there's probably a not too far-fetched loophole circumventing some of their assumptions, doesn't mean skynet is becoming self-aware any time soon once that is the case.
@Quantensalat @musicman @devsimsek depends on what you mean by far fetched, certainly nothing as easy as "their more compute at it' which is what made this jump in investment so dramatic.
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Researchers just mathematically proved that AI can't recursively self-improve its way to superintelligence.
Not "we think it's unlikely." Not "it seems hard." Formally proved.
The model doesn't climb toward AGI — it slowly forgets what reality looks like. They call it model collapse. The math calls it inevitable.
I wrote about ithttps://smsk.dev/2026/04/26/ai-cannot-self-improve-and-math-behind-proves-it/
@devsimsek so it doesn't get stuck in a local optimum, it hill-climbs a non-existent one?
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@Quantensalat @devsimsek tech bros have been claiming their AIs are alive for years so if the average person who knows nothing about computers thinks we already have AGI, who can really blame them. Anthropic all but claims to have invented Terminator.
Maybe something like this will stop the panic.
Which is not to say people shouldn't be concerned in general and very specifically about environmental impacts
@musicman @Quantensalat @devsimsek Anyone who ever copied an audio tape (or worse a VHS tape) knows that the copy is always worse than the original. And in the video case, soon unwatchable.
Ever heard a repeating echo on a video meeting that just turns to a buzz? Same phenomenon.
So what you need is an AI that can perform experiments in the real world to learn how to do better whatever it is you want it to do.
Inbreeding animals doesn't work too well either.
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@anne_twain @devsimsek there is no process. There is no intelligence. There never was and there never will be.
It's a bad stochastic parrot written by children who should have been flunked out of 7th grade math and 3rd grade English as illiterate. Used and pushed by people who aren't capable of reviewing a fast food order, or even placing one.And guess what? All irrelevant because it takes an incomprehensible level of stupidity to even use a tool that fails dangerously constantly.
