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“Recursive” is a reasonable term because the generation N AIs will train the Generation N+1 AIs. The term “iterative” doesn’t reflect this nuance as well IMO.
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Recursion reduces each step toward a base case: each step is defined in terms of previous/simpler steps, not more advanced ones. The "recursive" in "recursive self improvement" has things precisely backward. Iteration correctly describes a process where each step is the starting point of its successive step, so it should be "iterative self improvement" but I guess that didn't sound as cool.
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I think you’re conflating the direction of definition with the direction of evaluation.

Compare the similarity of:

  AI(n) = improve(AI(n-1))
With:

  Fib(n) = Fib(n-1) + Fib(n-2)
The latter is a classic example of recursion. So why isn’t the former?

Edit: formatting

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It's not a nuance, it's a sequence.
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I felt like the scaling laws were magical thinking, but apparently they work. However I still do not understand why we should expect exponential improvements due to this automated process. My intuition is that the first iteration of it should result in a noticeable capability increase (though I think these labs were already using a lot of AI to orchestrate training the current model anyway), and then the second iteration of it should be nearly identical in capability to the first, unless more data is involved, more compute is involved, or the model is bigger.
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AI can compress AI nearly losslessly.
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Yes the exponential self improvement folks have never heard of an eigenvalue I guess. You can loop forever using output as input but at some point the result will stop changing (depending on the function)
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The name you are looking for is "fixed points", not "eingevalues".
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that's not really how eigenvalues work... they specifically also model the case where the result keeps changing exponentially.
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The claim is that the RSI operation is just finding a fixed point of improvement,

RSI(LLM) = RSI(LLM) -- for an optimal LLM* which is a fixed point of RSI

As for eigenvalues/vectors, they're fixed points of (1/val)A or A*val

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Eigenvectors represent fixed directions, not fixed magnitudes. From Wikipedia:

> More precisely, an eigenvector v of a linear transformation T is scaled by a constant factor lambda when the linear transformation is applied to it: Tv = lambda v .

In other words, repeated multiplication of an eigenvector by a matrix can still create exponential growth.

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>AI "recursively" improving itself in some exponential fashion until there is a bright flash of white light

Sounds like repetitive stress to me.

>loop forever using output as input but at some point the result will stop changing

Running in place will eventually wear you out too. Plus with some things it can be difficult to know for sure if that's where you are at the time.

Even worse may be if you were almost running in place, it could be orders of magnitude more difficult to discern, especially if the scale was massive to an unprecedented degree.

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What will prevent LLMs from designing robot control circuitry and participating in increase of chip production/design and physical experimentation?

How do you think why there's this fad of producing general purpose humanoid robots?

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> How do you think why there's this fad of producing general purpose humanoid robots?

For doing physical work?

So a swarm of robots builds the shell of your fab overnight, and then what? Where is the EUV machine coming from?

So far the most we're seen TeslaBot do is serve drinks via tele-operation, and I don't think it's exactly built for construction site work.

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For example, TSMC uses behavioral cloning to scale up human-bottlenecked parts of the manufacturing process to meet the growing demand, while automated research laboratories do thousands experiments in parallel to find better manufacturing processes.
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> What will prevent LLMs from designing robot control circuitry and participating in increase of chip production/design and physical experimentation?

Money, regulations, EUV machine lead-times, global helium supply, reality ...

It's funny that we've got the Dwarkesh contingent saying that GPUs will become infinitely expensive, and now another contingent saying that they will become infinitely abundant.

Even if compute were free, and/or the AI was so smart that it picked the right experiments to run every time ("make no mistakes"), you still have to actually train the model, which takes months, and if model Ver. N+1 depends on model Ver. N, then it's iterative regardless of how much compute you have.

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Who's saying that compute will become infinitely abundant? "Singularity" is just a way of saying that known models begin to give absurd predictions. Anyway, intelligence is a way of overcoming obstacles. 10 million tonnes of helium is a nice head start and retraining models from scratch is not guaranteed to last forever.
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AFAIK the notion of a/the technological "singularity" is a point in time where technology is building upon itself (RSI!) so fast, at an ever increasing pace, that the speed of change effectively becomes infinite and incomprehensible to humans.

The word "singularity" is presumably coming from math or space, like a black hole singularity where matter becomes infinitely dense and the known laws of physics break down.

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> 10 million tonnes of helium is a nice head start

Yeah, but then you need to refine it to 99.9999% purity, to be able to use it.

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