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People keep repeating that LLMs are "just generating text based on probabilities". That statement doesn't mean anything. I think people who say this are imagin

People keep repeating that LLMs are "just generating text based on probabilities". That statement doesn't mean anything. I think people who say this are imagining LLMs work something like a statistical model. Maybe it's doing a linear regression or works like a Markov chain. It's not. A single artificial neuron sort of works like that. But that's sort of like saying a single transistor is just an electronically controlled switch, so the only thing computers can do is switching. It's true in some sense that computers are just doing a lot of switching, but it turns out all this switching is Turing-complete. That means computers can theoretically compute anything that's possible to compute given enough time and memory, which includes anything a human could figure out. Similar principle applies to LLMs. Using probabilities is part of what they do, but that doesn't preclude them from using logic and rules of inference.

vidarh 4y ago
It's worth noting that "just generating text based on probabilities" describe Markov algorithms [1], which are Turing-complete. People overestimate how much it takes to end up with something Turing-complete.[Markov algorithms only generate text with probability 100% or 0% based on whether a certain rule matches or not, so it's even simpler] (A Markov algorithm is distinct from a Markov chain, but as far as I can tell you could emulate a Markov algorithm with a Markov chain with sufficient number of input states, transitions clamped to 0% or 100%, and allowing it to iterate over its own output; with a large enough state machine, iteration, and a mechanism to provide memory it's almost hard not to end up with a Turing machine) [1] https://en.wikipedia.org/wiki/Markov_algorithm https://en.wikipedia.org/wiki/Markov_algorithm
simonh 4y ago
That's a valid point in that we don't fully understand how LLMs solve some problems and using logic and rules of inference isn't excluded by the architecture, but on the other hand understanding that they are generating probabilistic token sequences is a very powerful and effective way to understanding how to engineer prompts and understand some of their failure modes. If we discard that insight, reasoning about their many failure modes and limitations becomes near impossible. For example we often see people thinking that because an LLM can explain how to do something that therefore it knows how to do it, like arithmetic. That's because if a human can explain how to do something, we know that they can. Yet for an LLM outputting a token sequence for an explanation of something, and outputting a token sequence for solving a problem statement for that problem domain are fundamentally different tasks. We can get round this with very clever prompt engineering to 'force' chain of reasoning behaviour, as this discussion shows, but the reason we have to do that is precisely because the cognitive architecture of these LLMs is fundamentally different from humans. Yet these systems are clearly highly capable, and it is possible to dramatically improve their abilities with clever engineering. I think what this means is that LLMs may be incredibly powerful components or elements of systems that may become far more advanced and sophisticated AIs. However to do that engineering and build dramatically more capable systems, we need to have a clear understanding of how and why LLMs work, what their advantages and limitations are, and how to reason about and work with those features.
- vidarh 4y ago
  > For example we often see people thinking that because an LLM can explain how to do something that therefore it knows how to do it, like arithmetic. That's because if a human can explain how to do something, we know that they can. I think example shows LLMs to be more like people not less. It's not at all unusual to see humans struggle to do something until you remind them that they know an algorithm for doing so, and nudge them to apply it step by step. Sometimes you even have to prod them through each step. LLMs definitely have missing pieces, such as e.g. a working memory, an ability to continue to learn, and an inner monologue, but I don't think their sometimes poor ability to recall and follow a set of rules is what sets them apart.
  - simonh 4y ago
    >I don't think their sometimes poor ability to recall and follow a set of rules is what sets them apart It's not really that, it's that recalling a set of rules and following a set of rules are fundamentally different tasks for an LLM. This is why we need, and have implemented different training and reinforcement strategies to close that gap. The chain of reasoning ability has had to be specifically trained into the LLMs, it didn't arise spontaneously. However clearly this limitation can be, and is being worked around. The issue is that it's a real and very significant problem that we can't ignore, and which must be worked around in order to make these systems more capable. The fact is LLMs as they are today have a radically different form of knowledge compared to us and their reasoning ability is very different. This can lead people to look at an LLMs performance on one task and infer things about it's other abilities we think of as being closely related which simply don't apply. I see a lot of naive statements to the effect that these systems already reason like humans do and know things in the same way that humans do, when investigation into the actual characteristics of these systems shows that we can characterise very important ways in which they are completely unlike us. Yet they do know things and can reason. That's really important because if we're going to close that gap, we need to really understand that gap very well.
    - vidarh 4y ago
      > It's not really that, it's that recalling a set of rules and following a set of rules are fundamentally different tasks for an LLM. My point is that this appears to be the case for people too. It is often necessary to explicitly remind people to recall a set of rules to get them to follow the specific rules rather than act in a way that may or may not match the rules. Having observed this many times, I simply don't believe that most humans will see e.g. an addition and go "oh, right, these are the set of rules I should follow for addition, let me apply them step by step". If we've had the rules reinforced through repetitive training many enough times, we will end up doing them. But a lot of the time people will know the steps but still not necessarily apply them unless prompted, just like LLMs. Quite often people will still give an answer. Sometimes even the correct one. But without applying the methods we've been taught. To the point where when dealing e.g. with new learners - children in particular - who haven't had enough reinforcement in just applying a method, it's not at all unusual to find yourself having conversations like this: "Ok, so to do X, what are the steps you've been taught? Ok, so you remember that they are A, B and C. Great. Do A. You've done A? Now do B..." and so on. To me, getting a child to apply a method they know to solve a problem is remarkably close to getting an LLM to actually recall and follow these methods. But even for professionals, checklists exist for a reason: We often forget steps, or do them wrong, and forget to even try to explicitly recall a list of steps and do them one by one when we don't have a list of steps in front of us.
guenthert 4y ago
> That means computers can theoretically compute anything that's possible to compute given enough time and memory, which includes anything a human could figure out. Whoa, that's quite a leap there. Not sure where we (as society) are with our understanding of intuition, but I doubt a million monkeys would recognize that the falling of an apple is caused by the same agent as the orbit of planets.
- nearbuy 4y ago
  I think you misunderstood. I'm not making any claim there. I'm just defining what Turing-complete means for those who don't already know.
  - deleted 4y ago
    [deleted]

vidarh 4y ago

It's worth noting that "just generating text based on probabilities" describe Markov algorithms [1], which are Turing-complete. People overestimate how much it takes to end up with something Turing-complete.[Markov algorithms only generate text with probability 100% or 0% based on whether a certain rule matches or not, so it's even simpler] (A Markov algorithm is distinct from a Markov chain, but as far as I can tell you could emulate a Markov algorithm with a Markov chain with sufficient number of input states, transitions clamped to 0% or 100%, and allowing it to iterate over its own output; with a large enough state machine, iteration, and a mechanism to provide memory it's almost hard not to end up with a Turing machine) [1] https://en.wikipedia.org/wiki/Markov_algorithm https://en.wikipedia.org/wiki/Markov_algorithm

simonh 4y ago

That's a valid point in that we don't fully understand how LLMs solve some problems and using logic and rules of inference isn't excluded by the architecture, but on the other hand understanding that they are generating probabilistic token sequences is a very powerful and effective way to understanding how to engineer prompts and understand some of their failure modes. If we discard that insight, reasoning about their many failure modes and limitations becomes near impossible. For example we often see people thinking that because an LLM can explain how to do something that therefore it knows how to do it, like arithmetic. That's because if a human can explain how to do something, we know that they can. Yet for an LLM outputting a token sequence for an explanation of something, and outputting a token sequence for solving a problem statement for that problem domain are fundamentally different tasks. We can get round this with very clever prompt engineering to 'force' chain of reasoning behaviour, as this discussion shows, but the reason we have to do that is precisely because the cognitive architecture of these LLMs is fundamentally different from humans. Yet these systems are clearly highly capable, and it is possible to dramatically improve their abilities with clever engineering. I think what this means is that LLMs may be incredibly powerful components or elements of systems that may become far more advanced and sophisticated AIs. However to do that engineering and build dramatically more capable systems, we need to have a clear understanding of how and why LLMs work, what their advantages and limitations are, and how to reason about and work with those features.

vidarh 4y ago
> For example we often see people thinking that because an LLM can explain how to do something that therefore it knows how to do it, like arithmetic. That's because if a human can explain how to do something, we know that they can. I think example shows LLMs to be more like people not less. It's not at all unusual to see humans struggle to do something until you remind them that they know an algorithm for doing so, and nudge them to apply it step by step. Sometimes you even have to prod them through each step. LLMs definitely have missing pieces, such as e.g. a working memory, an ability to continue to learn, and an inner monologue, but I don't think their sometimes poor ability to recall and follow a set of rules is what sets them apart.
- simonh 4y ago
  >I don't think their sometimes poor ability to recall and follow a set of rules is what sets them apart It's not really that, it's that recalling a set of rules and following a set of rules are fundamentally different tasks for an LLM. This is why we need, and have implemented different training and reinforcement strategies to close that gap. The chain of reasoning ability has had to be specifically trained into the LLMs, it didn't arise spontaneously. However clearly this limitation can be, and is being worked around. The issue is that it's a real and very significant problem that we can't ignore, and which must be worked around in order to make these systems more capable. The fact is LLMs as they are today have a radically different form of knowledge compared to us and their reasoning ability is very different. This can lead people to look at an LLMs performance on one task and infer things about it's other abilities we think of as being closely related which simply don't apply. I see a lot of naive statements to the effect that these systems already reason like humans do and know things in the same way that humans do, when investigation into the actual characteristics of these systems shows that we can characterise very important ways in which they are completely unlike us. Yet they do know things and can reason. That's really important because if we're going to close that gap, we need to really understand that gap very well.
  - vidarh 4y ago
    > It's not really that, it's that recalling a set of rules and following a set of rules are fundamentally different tasks for an LLM. My point is that this appears to be the case for people too. It is often necessary to explicitly remind people to recall a set of rules to get them to follow the specific rules rather than act in a way that may or may not match the rules. Having observed this many times, I simply don't believe that most humans will see e.g. an addition and go "oh, right, these are the set of rules I should follow for addition, let me apply them step by step". If we've had the rules reinforced through repetitive training many enough times, we will end up doing them. But a lot of the time people will know the steps but still not necessarily apply them unless prompted, just like LLMs. Quite often people will still give an answer. Sometimes even the correct one. But without applying the methods we've been taught. To the point where when dealing e.g. with new learners - children in particular - who haven't had enough reinforcement in just applying a method, it's not at all unusual to find yourself having conversations like this: "Ok, so to do X, what are the steps you've been taught? Ok, so you remember that they are A, B and C. Great. Do A. You've done A? Now do B..." and so on. To me, getting a child to apply a method they know to solve a problem is remarkably close to getting an LLM to actually recall and follow these methods. But even for professionals, checklists exist for a reason: We often forget steps, or do them wrong, and forget to even try to explicitly recall a list of steps and do them one by one when we don't have a list of steps in front of us.

guenthert 4y ago

> That means computers can theoretically compute anything that's possible to compute given enough time and memory, which includes anything a human could figure out. Whoa, that's quite a leap there. Not sure where we (as society) are with our understanding of intuition, but I doubt a million monkeys would recognize that the falling of an apple is caused by the same agent as the orbit of planets.

nearbuy 4y ago
I think you misunderstood. I'm not making any claim there. I'm just defining what Turing-complete means for those who don't already know.
- deleted 4y ago
  [deleted]