4 ms·

But in an LLM it is not an arbitrary computation. Very specifically, it is a single forward pass through a neural network. Neural networks are very general fun

by lukev 3y ago

But in an LLM it is not an arbitrary computation. Very specifically, it is a single forward pass through a neural network. Neural networks are very general function approximators so yes, there is some room for emergent behavior. But it could _not_ be "quite literally anything." It's plugging in values for a single (very big) equation. I think we do ourselves a disservice by pretending it's more of a black box than it is.

famouswaffles 3y ago
How many passes it is irrelevant. You can perform any computation you like in a single pass if you have enough compute time. Trained transformers have limited computer time per token so each query is compute limited, but this is trivially increased, by increasing tokens, or by increasing dimensions in the next training round so that each token permits more compute time. A forward pass is not one big equation and I have no clue who you think it is. It's a series of computations, computations that depends on the query awaiting prediction. It's not even the same series of computations for each query because not all neurons are getting activated period and even when the same neurons get activated, they are not necessarily getting activated in the same way.
- dwattttt 3y ago
  > You can perform any computation you like in a single pass if you have enough compute time. You can't perform _any_ computation. A single forward pass through a neutral network can perform many classes of computation, and it can _approximate_ all... but that's not a guarantee that the approximation will be good (and there's classes for which the approximation is pretty much guaranteed to be bad).
  - famouswaffles 3y ago
    You're right but I didn't say anything about guarantees since that wasn't really the point of the argument. Yes, you can guarantee nothing but the point of discussion was whether a forward pass would deny specific classes of computations simply because it was just a forward class. It won't.
    - foobarqux 3y ago
      Yes in the same way that a lookup table can compute anything if you make it large enough (and where you need to know the size beforehand). "Transformers are not Turing complete" https://www.lifeiscomputation.com/transformers-are-not-turing-complete/ https://www.lifeiscomputation.com/transformers-are-not-turin... See here for example for a survey of work on the limits of computational expressivity of transformers https://www.semanticscholar.org/paper/Transformers-as-Recognizers-of-Formal-Languages%3A-A-Strobl-Merrill/6624065bd2825f500e93624671793d963187d066 https://www.semanticscholar.org/paper/Transformers-as-Recogn...
      - famouswaffles 3y ago
        No, Transformers with memory are turing complete. Like i said, the modifications are trivial. https://arxiv.org/abs/2301.04589 https://arxiv.org/abs/2301.04589
        foobarqux 3y ago
        First the discussion seemed to be about systems as implemented today (presumably you now concede that those actually do have practical computational limitations?) not systems that could theoretically be implemented. (Moreover adding memory is no longer the simple "forward pass" system that you were arguing had no significant computational limitations). Second, and more importantly, the fact that through clever human manipulation you can express a Turing machine using an LLM does not mean that such a machine is learned through gradient descent training. There is no basis to the claim that today's systems have converged on model weights that implement "higher-order" computation.
        famouswaffles 3y ago
        >First the discussion seemed to be about systems as implemented today (presumably you now concede that those actually do have practical computational limitations?) You are not Turing complete. We do like to pat ourselves on the back and say, "Humans? Of course, they're Turing complete" but you're not. You do not have infinite memory either theoretically (all else fails, you'll die) or practically (boredom, lack of concentrating, lack of interest, and a memory that is very prone to making stuff up or discarding vital details at a disturbing frequency). In fact, you are a very poor excuse for a Turing machine. Simulate any computation? You wish you could. Your brain is a finite state machine through and through. So why do we continue to deceive and pat ourselves on the back ? Because, well besides the dash of human exceptionalism and narcissism we're so well known for, limited =/ trivial. You see, I don't really care how precisely Transformers meet some imaginary goal humans don't meet themselves. It's not important how Turing complete transformers are, only that they could potentially learn any class of computations necessary via training. >Moreover adding memory is no longer the simple "forward pass" system that you were arguing had no significant computational limitations Memory or not, all the computation is still being performed just in the forward pass. >Second, and more importantly, the fact that through clever human manipulation you can express a Turing machine using an LLM does not mean that such a machine is learned through gradient descent training. It also doesn't mean it couldn't be. >There is no basis to the claim that today's systems have converged on model weights that implement "higher-order" computation. Results are basis enough. If I say, "you're intelligent", it's because you appear to be so. It's an assumption, not truth I've verified after peeking into your brain. All the properties I might ascribe to humans: 'intelligence', 'conciousness' are all assumptions I ascribe based on the results I see and nothing else. I have no proof you are performing any 'higher order computation' either.

by lukev 3y ago

famouswaffles 3y ago

How many passes it is irrelevant. You can perform any computation you like in a single pass if you have enough compute time. Trained transformers have limited computer time per token so each query is compute limited, but this is trivially increased, by increasing tokens, or by increasing dimensions in the next training round so that each token permits more compute time. A forward pass is not one big equation and I have no clue who you think it is. It's a series of computations, computations that depends on the query awaiting prediction. It's not even the same series of computations for each query because not all neurons are getting activated period and even when the same neurons get activated, they are not necessarily getting activated in the same way.

dwattttt 3y ago
> You can perform any computation you like in a single pass if you have enough compute time. You can't perform _any_ computation. A single forward pass through a neutral network can perform many classes of computation, and it can _approximate_ all... but that's not a guarantee that the approximation will be good (and there's classes for which the approximation is pretty much guaranteed to be bad).
- famouswaffles 3y ago
  You're right but I didn't say anything about guarantees since that wasn't really the point of the argument. Yes, you can guarantee nothing but the point of discussion was whether a forward pass would deny specific classes of computations simply because it was just a forward class. It won't.
  - foobarqux 3y ago
    Yes in the same way that a lookup table can compute anything if you make it large enough (and where you need to know the size beforehand). "Transformers are not Turing complete" https://www.lifeiscomputation.com/transformers-are-not-turing-complete/ https://www.lifeiscomputation.com/transformers-are-not-turin... See here for example for a survey of work on the limits of computational expressivity of transformers https://www.semanticscholar.org/paper/Transformers-as-Recognizers-of-Formal-Languages%3A-A-Strobl-Merrill/6624065bd2825f500e93624671793d963187d066 https://www.semanticscholar.org/paper/Transformers-as-Recogn...
    - famouswaffles 3y ago
      No, Transformers with memory are turing complete. Like i said, the modifications are trivial. https://arxiv.org/abs/2301.04589 https://arxiv.org/abs/2301.04589
      - foobarqux 3y ago
        First the discussion seemed to be about systems as implemented today (presumably you now concede that those actually do have practical computational limitations?) not systems that could theoretically be implemented. (Moreover adding memory is no longer the simple "forward pass" system that you were arguing had no significant computational limitations). Second, and more importantly, the fact that through clever human manipulation you can express a Turing machine using an LLM does not mean that such a machine is learned through gradient descent training. There is no basis to the claim that today's systems have converged on model weights that implement "higher-order" computation.
        famouswaffles 3y ago
        >First the discussion seemed to be about systems as implemented today (presumably you now concede that those actually do have practical computational limitations?) You are not Turing complete. We do like to pat ourselves on the back and say, "Humans? Of course, they're Turing complete" but you're not. You do not have infinite memory either theoretically (all else fails, you'll die) or practically (boredom, lack of concentrating, lack of interest, and a memory that is very prone to making stuff up or discarding vital details at a disturbing frequency). In fact, you are a very poor excuse for a Turing machine. Simulate any computation? You wish you could. Your brain is a finite state machine through and through. So why do we continue to deceive and pat ourselves on the back ? Because, well besides the dash of human exceptionalism and narcissism we're so well known for, limited =/ trivial. You see, I don't really care how precisely Transformers meet some imaginary goal humans don't meet themselves. It's not important how Turing complete transformers are, only that they could potentially learn any class of computations necessary via training. >Moreover adding memory is no longer the simple "forward pass" system that you were arguing had no significant computational limitations Memory or not, all the computation is still being performed just in the forward pass. >Second, and more importantly, the fact that through clever human manipulation you can express a Turing machine using an LLM does not mean that such a machine is learned through gradient descent training. It also doesn't mean it couldn't be. >There is no basis to the claim that today's systems have converged on model weights that implement "higher-order" computation. Results are basis enough. If I say, "you're intelligent", it's because you appear to be so. It's an assumption, not truth I've verified after peeking into your brain. All the properties I might ascribe to humans: 'intelligence', 'conciousness' are all assumptions I ascribe based on the results I see and nothing else. I have no proof you are performing any 'higher order computation' either.