Researchers just mathematically proved that AI can't recursively self-improve its way to superintelligence.
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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 it
https://smsk.dev/2026/04/26/ai-cannot-self-improve-and-math-behind-proves-it/
@devsimsek I said this a few years ago, and I am no
Matematician. Simple combinatorics and discrete math
over sets will tell you that. -
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 I think AGI and self-improvement is possible. But definitely not with the technology (neural LLMs) that is being marketed as "AI" today.
I think that AGI needs to be able to think logically. -
@devsimsek I think AGI and self-improvement is possible. But definitely not with the technology (neural LLMs) that is being marketed as "AI" today.
I think that AGI needs to be able to think logically.@LunaDragofelis
@devsimsek ^ this tbh. The single-minded focus on scaling LLMs is seemingly caused by parts of the AI crowd being hammers that view every problem as a nail.The path to better products will involve many different technologies being glued together.
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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@universeodon.com I don’t think this is the usual formulation of RSI though – in the one I know the input of the AI is not it’s output, but the environment plus (a representation of) itself. So I would say the way the article (and blogpost) formulates its thesis is misleading.
(I used to worry about AGI and the current focus on LLMs stopped that. Not because such a self-improvement loop is impossible (which I don’t expect it to be tbh), but rather because it’s extremely unlikely due to their very low homoiconicity.)
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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 An inevitable melting into slop.
Every time you copy something, you lose some detail. Continue long enough and you eventually do get a Singularity. All information compressed to a single "1". -
@devsimsek The paper doesn't prove that. It proves that "if the proportion of exogenous, externally grounded signal vanishes asymptotically, the system undergoes degenerative dynamics."
The necessary asymptotic condition is not met in real use.@thearrivingdeparture @devsimsek
Even if that were true, it would still be in contrast to, say, being able to play zillions of chess games against yourself to become a stronger player, which does work.
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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 This was my intuition as soon as I understood that they were fundamentally just a statistical distribution predictive model: of course if you feed the output of the statistics machine back into itself it's going to degrade as a model, that's just how statistical modeling works... But still nice that someone actually "did the math" to prove it though.
What's particularly interesting about this process from what I understand is that in isolation none of the synthetic data looks "wrong" which is what makes it so 'tempting' for the bubble-pumpers desperate for training data. And despite none of it looking that bad, the entire model can easily collapse into an incoherent pile of gibberish with enough of it due to subtle statistical butterflies.
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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 sicko-to-sicko communication
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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 Compare how cryptographic RNGs are usually Pseudo-RNGs fed with entropy, and which fail to output random-approximate values (of a given strength) once the entropy falls too low.
It's almost as if there is a pattern to this.
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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/
i'm here for the inevitable model collapse. let's immanentize this bitch!
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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... let me get this straight. Autocoprophagic #RSI •doesn't• lead to #AGI? Say it ain't so!
#AI -
@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 I'm sure you'll find plenty of straw men who do
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@devsimsek Chatting with U Toronto AI profs 6, 7 years ago, I posed a problem.
"Teach your AI everything about whole, integer, rational and real numbers. Ask it to solve a problem that requires it to invent complex numbers."
Reply: "Oh... It doesn't work that way."
I knew that, but the ability to frame your observations as the product of a higher order system is IMHO key to what we call "intelligence". Collecting evidence that can disprove your hypothesis is science.
LLM approaches are neither, in a very expensive way.
I'll have to read the paper, though. I'm looking forward to the AI equivalent of Goedel's Theorem that shuts down this annoying iteration of the field.
@TallSimon @devsimsek I haven’t looked at the proof, but I wonder if Gödel plays a role in it. Seems like at least Gödel would strongly imply this new proof.
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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 this is one of those things that seemed intuitive to us skeptics but it's great to see it proven
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@Quantensalat @devsimsek I'm sure you'll find plenty of straw men who do
@dpiponi @devsimsek I find the paper interesting but I would like to understand the exact
premises. "AI" is not equal to gen AI or LLMs, it probably makes little sense to sell it as a general statement about "AI" -
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 wow, almost as if this was a problem known as overtraining for well over 30 years
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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 it's the only thing that makes sense if you know just a little about how they work (I don't know more than a little)
Like if you output whatever is most likely, and input that again, it's only logical (at least to me) that eventually you'll get a mushy average -
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 This feels like a weird argument, because it proves a version that I've never heard anyone arguing for. Like, when I've heard people talk about AI itself accelerating AI's improvement (on both pro and con sides), the argument wasn't that AI would self-train on its own output. The argument was that AI would replace AI developers and accelerate the development of better AI code.
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@devsimsek wow, almost as if this was a problem known as overtraining for well over 30 years
@SRAZKVT Exactly.
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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 Nobody ever claimed that llms get better by being trained on their own synthetic data. This blog post is very misleading.
The idea of self-improvement and singularity is that llms write improved versions of their own codebase and perform the research and experiments for coming up with better models themselves.
The idea of singularity is interesting but also full of hidden assumptions. I'm always confused when people act like singularity would exist. It's just science fiction.
