3 ms·

The model partially solves the problem but fails to learn the correct loop length: > An investigation of model errors (Section 5) reveals that, whereas large l

by esafak 11mo ago

The model partially solves the problem but fails to learn the correct loop length: > An investigation of model errors (Section 5) reveals that, whereas large language models commonly “hallucinate” random solutions, our models fail in principled ways. In almost all cases, the models perform the correct calculations for the long Collatz step, but use the wrong loop lengths, by setting them to the longest loop lengths they have learned so far. The article is saying the model struggles to learn a particular integer function. https://en.wikipedia.org/wiki/Collatz_conjecture https://en.wikipedia.org/wiki/Collatz_conjecture

spuz 11mo ago
That's a bit of an uncharitable summary. In bases 8, 12, 16, 24 and 32 their model achieved 99.7% accuracy. They would never expect it to achieve 100% accuracy. It would be like if you trained a model to predict whether or not a given number is prime. A model that was 100% accurate would defy mathematical knowledge but a model that was 99.7% would certainly be impressive. In this case, they prove that the model works by categorising inputs into a number of binary classes which just happen to be very good predictors for this otherwise random seeming sequence. I don't know whether or not some of these binary classes are new to mathematics but either way, their technique does show that transformer models can be helpful in uncovering mathematical patterns even in functions that are not continuous.
- jacquesm 11mo ago
  A pocket calculator that would give the right numbers 99.7% of the time would be fairly useless. The lack of determinism is a problem and there is nothing 'uncharitable' about that interpretation. It is definitely impressive, but it is fundamentally broken, because when you start making chains of things that are 99.7% correct you end up with garbage after very few iterations. That's precisely why digital computers won out over analog ones, the fact that they are deterministic.
  - fkarg 11mo ago
    yeah it's only correct in 99.7% of all cases, but what if it's also 10'000 times faster? There's a bunch of scenarios where that combination provides a lot of value
    - jacquesm 11mo ago
      Correctness in software is the first rung of the ladder, optimizing before you have correct output is in almost all cases a complete waste of time. Yes, there are a some scenarios where having a ballpark figure quickly can be useful if you can produce the actual result as well and if you are not going to output complete nonsense the other times but something that approaches the final value. There are a lot of algorithms that do this (for instance: Newton's method for finding square roots). 99.7% of the time good and 0.3% of the time noise is not very useful, especially if there is no confidence indicating that the bad answers are probably incorrect.
    - lkey 11mo ago
      Ridiculous counterfactual. The LLM started failing 100% of the time 60! orders of magnitude sooner than the point at which we have checked literally every number. This is not even to mention the fact that asking a GPU to think about the problem will always be less efficient than just asking that GPU to directly compute the result for closed algorithms like this.
  - pixl97 11mo ago
    Why do people keep using LLMs as algorithms? LLMs are not calculators. If you want a calculator use a calculator. Hell, have your LLM use a calculator. >That's precisely why digital computers won out over analog ones, the fact that they are deterministic. I mean, no not really, digital computers are far easier to build and far more multi-purpose (and technically the underlying signals are analog). Again, if you have a deterministic solution that is 100% correct all the time, use it, it will be cheaper than an LLM. People use LLMs because there are problems that are either not deterministic or the deterministic solution uses more energy than will ever be available in the local part of our universe. Furthermore a lot of AI (not even LLMs) use random noise at particular steps as a means to escape local maxima.

by esafak 11mo ago

spuz 11mo ago

That's a bit of an uncharitable summary. In bases 8, 12, 16, 24 and 32 their model achieved 99.7% accuracy. They would never expect it to achieve 100% accuracy. It would be like if you trained a model to predict whether or not a given number is prime. A model that was 100% accurate would defy mathematical knowledge but a model that was 99.7% would certainly be impressive. In this case, they prove that the model works by categorising inputs into a number of binary classes which just happen to be very good predictors for this otherwise random seeming sequence. I don't know whether or not some of these binary classes are new to mathematics but either way, their technique does show that transformer models can be helpful in uncovering mathematical patterns even in functions that are not continuous.

jacquesm 11mo ago
A pocket calculator that would give the right numbers 99.7% of the time would be fairly useless. The lack of determinism is a problem and there is nothing 'uncharitable' about that interpretation. It is definitely impressive, but it is fundamentally broken, because when you start making chains of things that are 99.7% correct you end up with garbage after very few iterations. That's precisely why digital computers won out over analog ones, the fact that they are deterministic.
- fkarg 11mo ago
  yeah it's only correct in 99.7% of all cases, but what if it's also 10'000 times faster? There's a bunch of scenarios where that combination provides a lot of value
  - jacquesm 11mo ago
    Correctness in software is the first rung of the ladder, optimizing before you have correct output is in almost all cases a complete waste of time. Yes, there are a some scenarios where having a ballpark figure quickly can be useful if you can produce the actual result as well and if you are not going to output complete nonsense the other times but something that approaches the final value. There are a lot of algorithms that do this (for instance: Newton's method for finding square roots). 99.7% of the time good and 0.3% of the time noise is not very useful, especially if there is no confidence indicating that the bad answers are probably incorrect.
  - lkey 11mo ago
    Ridiculous counterfactual. The LLM started failing 100% of the time 60! orders of magnitude sooner than the point at which we have checked literally every number. This is not even to mention the fact that asking a GPU to think about the problem will always be less efficient than just asking that GPU to directly compute the result for closed algorithms like this.
- pixl97 11mo ago
  Why do people keep using LLMs as algorithms? LLMs are not calculators. If you want a calculator use a calculator. Hell, have your LLM use a calculator. >That's precisely why digital computers won out over analog ones, the fact that they are deterministic. I mean, no not really, digital computers are far easier to build and far more multi-purpose (and technically the underlying signals are analog). Again, if you have a deterministic solution that is 100% correct all the time, use it, it will be cheaper than an LLM. People use LLMs because there are problems that are either not deterministic or the deterministic solution uses more energy than will ever be available in the local part of our universe. Furthermore a lot of AI (not even LLMs) use random noise at particular steps as a means to escape local maxima.