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author: niplav, created: 2024-01-30, modified: 2024-05-20, language: english, status: in progress, importance: 3, confidence: certain

Some thoughts on discontinuous and/or fast takeoff during TAI development, in response to a twitter question.

On Discontinuous and Fast Takeoff

The most fleshed-out model of AI takeoff is Davidson 2023, which makes the median prediction of 20% automation to 100% automation in ~3 years (10th percentile: 0.8 years, 90th percentile: 12.5 years).

Along the axes of {fast, slow}×{continuous, discountinuous}, that feels quite fast to me, even if it isn't very discountinuous.

The other reasons make me move towards "but it might be a lot faster than that". One reason is that the Davidson model assumes that the human brain performs 10¹⁵ FLOP/s, and that the AI systems will be at most that efficient or slightly less efficient. So a lot of my disagreement is around: how much the ceiling of cognitive algorithms is above humans (my belief: very high80%), and the rest of the disagreement is how quickly can AI systems move towards that ceiling (my belief: not sure, but potentially within days40%).

Better Algorithms Exist

One reason is that human brains don't seem like the optimal substrate for performing cognition: Warm & wet, very low information transmission speed (signals on neurons are limited to at most 200 m/s) Kokotajlo 2021, needing to self-construct and self-repair — and still brains are incredibly sample-efficient! And I suspect that, if anything, humans are at best at a subspace optimum of cognitive algorithms.

Then there's the power of error-corrected/discrete/serial computation: Digital computers can make very long inferences in discrete domains without problems, and when I introspect, I have the strong intuition that my system 2 tries to approximate this, especially when trying to enumerate options in a decision, recursively decompose a plan into its components (which gets much easier once you have a world model), perform abstraction (while caching which parts of the abstraction are tight and which are leaky)—but my system 2 only has 7±2 (or maybe actually just 4?) usable slots. And unless the limit is due to combinatorial explosion (which might be handleable by careful pruning, or prioritized search), AI systems could have larger (perhaps vastly larger?) working memories.

The standard rejoinder here is that evolution has optimized human brains really really hard, and our current technology is usually 2-6 orders of magnitude worse than what evolution has come up with. But if we believe that error-corrected computation is quite rare in biology, then this opens up a new niche to make progress in, similar to how there are no plants in space because they couldn't evolve rocket-like tech and transparent shells that were resistant enough in vacuum.

This points at an intuition I have: There is a bunch of α left in combining error-corrected/discrete/serial computation (which computers are good at) with error-resistant/continuous/parallel computation (à la neural networks or brains). And especially if I think about cognition through the lens of algorithms, it feels like there's a deep mine of algorithms: The space of possible algorithms is vast, and even in very simple problem domains we have found surprising innovations (such as going from the Karatsuba algorithm to the Schönhage-Strassen algorithm, or from the naive algorithm for the maximum subarray problem to Kadane's algorithm). My "optimism" here has been hindered somewhat by some evidence on how well old chess algorithms perform on new hardware, and the observation that the surprising algorithms we find are usually galactic (such as in the case of the decreasing shrinking rate of the best-case exponent in the computational complexity of matrix multiplication—where yet we still only use Strassen's algorithm).

Additionally, there's some domains of computation of which we have made little use, because our minds are limited in a way that makes it difficult to think about them. As the adage goes, programming is divided into four levels of difficulty: if statements, while loops, recursion and parallelism; but what about domains like self-modifying code (where, except maybe Gödel machines, there is no respectable theory, and except Alexia Massalin's superoptimization there isn't really any application)? Although, to be fair, neural architecture search might be getting there, sometime.

My view on better algorithms existing is not informed very much by specific observations about evolution.

Better Algorithms are Quickly Reachable

As in the section about better algorithms existing, many of my intuitions here come from algorithm design and/or regular software engineering.

One argument against discountinuous takeoff is a response to the hypothesis of recursive self-improvement, in which AI systems start finding improvements to their own architectures more and more quickly (which I try to model here). The counterargument says that before there will be AI systems that are really good at self-improvement, there will be systems that are first crappy and then merely okay at self-improvement.

But usually, with algorithms, having a 99%-finished implementation of the algorithm doesn't give you 99% of the benefit, nor does it give you 50% or even 1% of the benefit. It simply doesn't work. And here intuitions collide: I find it plausible that, in this case, the The Gods of Straight Lines do not interfere, and instead something far stranger is afoot, but the machine learning intuition tells people that everything in neural networks is continuous, so why wouldn't there be a continous path to a TAI architecture?

See Also