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>The training and loss function of the foundation models are completely oriented towards next-token accuracy. This doesn't mean anything. Loss function and tr

>The training and loss function of the foundation models are completely oriented towards next-token accuracy. This doesn't mean anything. Loss function and training only concern themselves with the result of the prediction. The in-between, the computation, training does not care except as a means to an end. It's not Input A > Output B. It's Input A > Computation > Output B. That Computation could quite literally be anything. And no, we do not automatically know what this computation might represent or if it even represents anything that would be understandable by us. If you train a Transformer meticulously on predicting the token that is the result of an addition, you might hope the computation it learns is some algorithm for addition but you wouldn't actually know until you attempted to and successfully probed the model.

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.

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.