3 ms·

We definitely are not on an exponential. Don't say we are because this isn't up for debate. AI progress is logarithmic the million dollar question is 2x or 10x

by casey2 2mo ago

We definitely are not on an exponential. Don't say we are because this isn't up for debate. AI progress is logarithmic the million dollar question is 2x or 10x for linear improvement. The nearest qualitative shift would be very fast inference so people could start writing real software on top of LLMs. A 0.001% optimization on a packing problem just isn't interesting for the amount of investment.

akoboldfrying 2mo ago
> A 0.001% optimization on a packing problem just isn't interesting for the amount of investment. I think you have completely misunderstood what OpenAI have accomplished here. Almost certainly no one cares about the specific concrete results achieved; they only care about (a) how difficult it would be for an intelligent human to achieve the same feat (ETA: the feat is the proof), which can be estimated by the amount of time the problem has remained open/a public conjecture, and (b) how general this artificial "intelligence" appears to be, which can be estimated by the diversity of topics where it was able to prove a difficult result. It's as if I showed you a dog that I had taught to speak German fluently, and you remarked: "What point is a dog that can speak a language that less than 2% of the world speaks? Nothing to see here."
- andsoitis 2mo ago
  > It's as if I showed you a dog that I had taught to speak German fluently And you’re thinking this is an accurate comparison?
  - vasco 2mo ago
    It's more funny than the dog doing differential equations I'll tell you that. Specially when it gets mad.
- koe123 2mo ago
  On the other hand, if provided the financial incentive would mathematicians have solved these problems? Its not hard to imagine a world where some hard problems were not selected by the sparse experts for whatever reason (lack of interest, whatever), which could have been solved if someone was throwing down millions for solutions.
  - techpression 2mo ago
    This is what most people seem to forget, OpenAI has probably spent more money the last year than all of math research has during human existence.
  - DoctorOetker 2mo ago
    nothing prevented us from defining cryptocurrencies, auto-rewarding new math in objective manners, grading theorem surprisal objectively, etc. before the advent of LLM's. being lucky enough to receive the opportunity of hiding in some academic closet, poking your hand out begging for scraps, was a different, perfectly alternative path humans decided to take instead. It's a bit late to start standing up for your rights when the robot overlords arrive.
    - koe123 2mo ago
      Thats true, although once it stops being a party trick I expect the LLM proof mining to also be paid by someone else and be expensive as shit, the question same remains: who?
      - DoctorOetker 2mo ago
        who? the state on advice of the intelligence community: machine learning inference bruteforcing not bits in private keys, but bruteforcing proof search space modulo machine intuition. At some point cryptography evolves faster than human cryptographers can follow, at that point anyone can only trust cryptographic schemes proposed by their own LLM models, since they will be direct witness to useful responses for apparently unbreakable cryptoschemes with a mathematically known backdoor for the designing LLM. Why would one power block accept usage of LLM-derived crypto from another power block, if they know it is likely backdoored? The same within a power block: why would one ally financially trust crypto from another ally in the same power block, if they are witness to how easy it will be to request new convincing crypto schemes with a backdoor? The same within a single nation state: why would one bank accept the cryptography proposed by another bank, if they are witness to how easy it would be to ensnare one another with LLM-designed crypto schemes with backdoors. Its not that humans are incapable of pulling power plugs when the machines start organizing human-on-human violence, it's that no side, no party feels like they can afford a gentleman's agreement to not consult LLM's to find vulnerable hardness assumptions in mathematical cryptography. Perhaps many powerful entities would be more than willing to pull such a plug, but not before others have provably demonstrated pulling the plug,... which is basically waiting until no other human factions exist. And there's who pays it, and they will pay private companies to compete in order to assure competitive prices for the government.
energy123 2mo ago
What is the y-axis in this claim about logarithmic improvements? Any exponential curve can be trivially turned into a logarithmic and vice-versa, and the y-axis redefined as "progress", with no loss of accuracy. One example that always bugs me is when people point to "exponential" or "sigmoidal" progress on benchmarks. Benchmarks are artificial constructions (saturation at 100% by definition) and benchmark scores should not be mapped to these words when talking about overall progress. Example - progress on ARC-AGI-3 at the moment is exponential, steeper than 2^t and e^t. Does that mean AI is progressing "exponentially" in the colloquial sense? No, it doesn't support or refute that colloquialism. Likewise with MMLU saturation. We can't go above 100% by construction. Therefore we have a "sigmoid". Gah. The colloquialism is not helpful to begin with.

by casey2 2mo ago

akoboldfrying 2mo ago

> A 0.001% optimization on a packing problem just isn't interesting for the amount of investment. I think you have completely misunderstood what OpenAI have accomplished here. Almost certainly no one cares about the specific concrete results achieved; they only care about (a) how difficult it would be for an intelligent human to achieve the same feat (ETA: the feat is the proof), which can be estimated by the amount of time the problem has remained open/a public conjecture, and (b) how general this artificial "intelligence" appears to be, which can be estimated by the diversity of topics where it was able to prove a difficult result. It's as if I showed you a dog that I had taught to speak German fluently, and you remarked: "What point is a dog that can speak a language that less than 2% of the world speaks? Nothing to see here."

andsoitis 2mo ago
> It's as if I showed you a dog that I had taught to speak German fluently And you’re thinking this is an accurate comparison?
- vasco 2mo ago
  It's more funny than the dog doing differential equations I'll tell you that. Specially when it gets mad.
koe123 2mo ago
On the other hand, if provided the financial incentive would mathematicians have solved these problems? Its not hard to imagine a world where some hard problems were not selected by the sparse experts for whatever reason (lack of interest, whatever), which could have been solved if someone was throwing down millions for solutions.
- techpression 2mo ago
  This is what most people seem to forget, OpenAI has probably spent more money the last year than all of math research has during human existence.
- DoctorOetker 2mo ago
  nothing prevented us from defining cryptocurrencies, auto-rewarding new math in objective manners, grading theorem surprisal objectively, etc. before the advent of LLM's. being lucky enough to receive the opportunity of hiding in some academic closet, poking your hand out begging for scraps, was a different, perfectly alternative path humans decided to take instead. It's a bit late to start standing up for your rights when the robot overlords arrive.
  - koe123 2mo ago
    Thats true, although once it stops being a party trick I expect the LLM proof mining to also be paid by someone else and be expensive as shit, the question same remains: who?
    - DoctorOetker 2mo ago
      who? the state on advice of the intelligence community: machine learning inference bruteforcing not bits in private keys, but bruteforcing proof search space modulo machine intuition. At some point cryptography evolves faster than human cryptographers can follow, at that point anyone can only trust cryptographic schemes proposed by their own LLM models, since they will be direct witness to useful responses for apparently unbreakable cryptoschemes with a mathematically known backdoor for the designing LLM. Why would one power block accept usage of LLM-derived crypto from another power block, if they know it is likely backdoored? The same within a power block: why would one ally financially trust crypto from another ally in the same power block, if they are witness to how easy it will be to request new convincing crypto schemes with a backdoor? The same within a single nation state: why would one bank accept the cryptography proposed by another bank, if they are witness to how easy it would be to ensnare one another with LLM-designed crypto schemes with backdoors. Its not that humans are incapable of pulling power plugs when the machines start organizing human-on-human violence, it's that no side, no party feels like they can afford a gentleman's agreement to not consult LLM's to find vulnerable hardness assumptions in mathematical cryptography. Perhaps many powerful entities would be more than willing to pull such a plug, but not before others have provably demonstrated pulling the plug,... which is basically waiting until no other human factions exist. And there's who pays it, and they will pay private companies to compete in order to assure competitive prices for the government.

energy123 2mo ago

What is the y-axis in this claim about logarithmic improvements? Any exponential curve can be trivially turned into a logarithmic and vice-versa, and the y-axis redefined as "progress", with no loss of accuracy. One example that always bugs me is when people point to "exponential" or "sigmoidal" progress on benchmarks. Benchmarks are artificial constructions (saturation at 100% by definition) and benchmark scores should not be mapped to these words when talking about overall progress. Example - progress on ARC-AGI-3 at the moment is exponential, steeper than 2^t and e^t. Does that mean AI is progressing "exponentially" in the colloquial sense? No, it doesn't support or refute that colloquialism. Likewise with MMLU saturation. We can't go above 100% by construction. Therefore we have a "sigmoid". Gah. The colloquialism is not helpful to begin with.