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I am not convinced by this argument. It is very misleading to think that, since GPT is trained on data from the world, it must, necessarily, always produce an a

I am not convinced by this argument. It is very misleading to think that, since GPT is trained on data from the world, it must, necessarily, always produce an average of the ideas in the world. Humans have formulated laws of physics that "minimize loss" on our predictions of the physical world that are later experimentally determined to be accurate, and there's no reason to assume a language model trained to minimize loss on language won't be able to derive similar "laws" that stimulate human behavior. In short, GPT doesn't just estimate text by looking at frequencies. GPT works so well by learning to model the underlying processes (goal-directedness, creativity, what have you) that create the training data. In other words, as it gets better (and my claim is it has already gotten to the point where it can do the above), it will be able to harness the same capabilities that humans have to make something "not in the training set". Check out https://generative.ink/posts/simulators/ https://generative.ink/posts/simulators/ for a better treatment of this topic than I could possibly give. Here's a relevant section of said article: > Guessing the right theory of physics is equivalent to minimizing predictive loss. Any uncertainty that cannot be reduced by more observation or more thinking is irreducible stochasticity in the laws of physics themselves – or, equivalently, noise from the influence of hidden variables that are fundamentally unknowable. > If you’ve guessed the laws of physics, you now have the ability to compute probabilistic simulations of situations that evolve according to those laws, starting from any conditions28. This applies even if you’ve guessed the wrong laws; your simulation will just systematically diverge from reality. > Models trained with the strict simulation objective are directly incentivized to reverse-engineer the (semantic) physics of the training distribution, and consequently, to propagate simulations whose dynamical evolution is indistinguishable from that of training samples. I propose this as a description of the archetype targeted by self-supervised predictive learning, again in contrast to RL’s archetype of an agent optimized to maximize free parameters (such as action-trajectories) relative to a reward function.

mjburgess 3y ago
> Guessing the right theory of physics is equivalent to minimising predictive loss. No it's not. It's minimising "predictive loss" only under extreme non-statistical conditions imposed on the data. The world itself can be measured an infinite number of ways. There are an infinite number of irrelevant measures. There are an infinite number of low-reliability relevant measures. And so on. Yes, you can formulate the extremely narrow task of modelling "exactly the right dataset" as loss minimization. But you cannot model the production of that dataset this way. Data is a product of experiments.
- XorNot 3y ago
  This is just you declaring "no you can't" without supporting that in any way. How is a theory of physics not a loss minimisation process? The history of science is literally described in these terms i.e. the Bohr model of the atom is wrong, but also so useful that we still use it to describe NMR spectroscopy. Why did we come up with it? Because their aren't infinite ways to measure the universe, there are in fact very limited ways defined by our technology. Good ones, high loss minimisation, generally then let us build better technology to find more data. You're invoking infinities which don't exist as a handwave for "understanding is a unique part of humanity" to try and hide that this is all metaphysical special pleading.
  - mjburgess 3y ago
    Alright... What loss was being minimised to find F=GMm/r^2? Or any law of physics you like.
    - XorNot 3y ago
      Gravitation was literally about predicting future positions of the stars, and was successful because it did so much better then any geocentric model. How is that not a loss minimization activity? And before we had it, epicycles were steadily increasing in complexity to explain every new local astronomical observation, but that model was popular because it gives a very efficient initial fit of the easiest data to obtain (i.e. the moon actually does go around the Earth, and with only 1 reference point the Sun appears to go round the Earth too). But of course once you have a heliocentric theory, you can throw all those parameters and every new prediction lines up nearly perfectly (accounting for how much longer it would take before we had precise enough orbital measurements to need Relativity to fully model it).
      - sudosysgen 3y ago
        When the law of gravitation was formulated, it could not in fact be used to predict orbits reliably (Kepler's ellipses are the solution to the two body problem anyways, and for a more complex system integration was impossible to any useful precision at the time), and Kepler's theories came out long before it did. It took more than 70 years after its formulation for the law to actually be conclusively tested against observations in a conclusive manner.
mordymoop 3y ago
Even very simple and small neural networks that you can easily train and play with on your laptop readily show that this “outputs are just the average of inputs” conception is just wrong. And it’s not wrong in some trickle philosophical sense, it’s wrong in a very clear mathematical sense, as wrong as 2+2=5. One example that’s been used for something like 15+ years is in using the MNIST handwritten digits dataset to recognize and then reproduce the appearances of handwritten digits. To do this, the model finds regularities and similarities in the shapes of digits and learns to express the digits as combinations of primitive shapes. The model will be able to produce 9s or 4s that don’t quite look like any other 9 or 4 in the dataset. It will also be able to find a digit that looks like a weird combination of a 9 and a 2 if you figure out how to express a value from that point in the latent space. It’s simply mathematically naive to call this new 9-2 hybrid an “average” of a 9 and a 2. If you averaged the pixels of a 9 image and a 2 image you would get an ugly nonsense image. The interpolation in the latent space is finding something like a mix between the ideas behind the shape of 9s and the shape of 2s. The model was never shown a 9-2 hybrid during training, but its 9-2 will look a lot like what you would draw if you were asked to draw a 9-2 hybrid. A big LLM is something like 10 orders of magnitude bigger than your MNIST model and the interpolations between concepts it can make are obviously more nuanced than interpolations in latent space between 9 and 2. If you tell it write about “hubristic trout” it will have no trouble at all putting those two concepts together, as easily as the MNIST model produced a 9-2 shape, even though it had never seen an example of a “hubristic trout.” It is weird because all of the above is obvious if you’ve played with any NN architecture much, but seems almost impossible to grasp for a large fraction of people, who will continue to insist that the interpolation in latent space that I just described is what they mean by “averaging”. Perhaps they actually don’t understand how the nonlinearities in the model architecture give rise to the particular mathematical features that make NNs useful and “smart”. Perhaps they see something magical about cognition and don’t realize that we are only ever “interpolating”. I don’t know where the disconnect is.
- mnky9800n 3y ago
  i think a partial explanation is that people don't move away from parametric representations of reality. We simply must be organized into a nice, neat gaussian distribution with very easy to calculate means and standard deviations. The idea that organization of data could be relational or better handled by a decision tree or whatever is not really presented to most people in school or university. Especially not as frequently or holistically as is simply thinking the average represents the middle of a distribution. you see this across social sciences where you can see a lot of fields have papers that come out every decade or so since the 1980s saying that linear regression models are wrong because they don't take into account several concepts such as hierarchy (e.g., students go to different schools), frailty (there is likely unmeasured reasons why some people do the things they do), latent effects (there is likely non-linear processes that are more than the sum of the observations, e.g., traffic flows like a fluid and can have turbulence), auto-correlations/spatial correlations/etc. In fact, I would argue that a decision tree based model (i.e., gradient boosted trees) will always arrive at a better solution to a human system than any linear regression. But at this point I suppose I have digressed from the original point.
YeGoblynQueenne 3y ago
>> Guessing the right theory of physics is equivalent to minimizing predictive loss. A model can reduce predictive loss to almost zero while still not being "the right theory" of physics, or anything else. That is a major problem in science, and machine learning approaches don't have any answer to it. Machine learning approaches can be used to build more powerful predictive models, with lower error, but nothing tells us that one such model is, or even isn't, "the right theory". As a very famous example, or at least the one I hold as a classic, consider the theory of epicyclical motion of the planets [1]. This was the commonly accepted model of the motion of the observable planets for thousands of years. It persisted because it had great predictive accuracy. I believe alternative models were proposed over the years, but all were shot down because they did not approach the accuracy of the theory of epicycles. Even Copernicus' model, that is considered a great advance because it put the Sun in the center of the universe, continued to use epicycles and so did not essentially change the "standard" model. Eventually, Kepler came along, and then Newton, and now we know why the planets seem to "double back" on themselves. And not only that, but we can now make much better predictions than we ever could do with the epicyclical model, because now we have an explanatory model, a realist model, not just an instrumentalist model, and it's a model not just of the observable motion of the planets but a model of how the entire world works. As a side point, my concern with neural nets is that we get "stuck in a rut" with them, because of their predictive power, like we got stuck with the epicyclical model, and that we spend the next thousand years or so in a rut. That would be a disaster, at this point in our history. Right now we need models that can do much more than predict; we need models that are theories, that explain the world in terms of other theories. We need more science, not more modelling. _________ [1] https://en.wikipedia.org/wiki/Deferent_and_epicycle https://en.wikipedia.org/wiki/Deferent_and_epicycle

mjburgess 3y ago

> Guessing the right theory of physics is equivalent to minimising predictive loss. No it's not. It's minimising "predictive loss" only under extreme non-statistical conditions imposed on the data. The world itself can be measured an infinite number of ways. There are an infinite number of irrelevant measures. There are an infinite number of low-reliability relevant measures. And so on. Yes, you can formulate the extremely narrow task of modelling "exactly the right dataset" as loss minimization. But you cannot model the production of that dataset this way. Data is a product of experiments.

XorNot 3y ago
This is just you declaring "no you can't" without supporting that in any way. How is a theory of physics not a loss minimisation process? The history of science is literally described in these terms i.e. the Bohr model of the atom is wrong, but also so useful that we still use it to describe NMR spectroscopy. Why did we come up with it? Because their aren't infinite ways to measure the universe, there are in fact very limited ways defined by our technology. Good ones, high loss minimisation, generally then let us build better technology to find more data. You're invoking infinities which don't exist as a handwave for "understanding is a unique part of humanity" to try and hide that this is all metaphysical special pleading.
- mjburgess 3y ago
  Alright... What loss was being minimised to find F=GMm/r^2? Or any law of physics you like.
  - XorNot 3y ago
    Gravitation was literally about predicting future positions of the stars, and was successful because it did so much better then any geocentric model. How is that not a loss minimization activity? And before we had it, epicycles were steadily increasing in complexity to explain every new local astronomical observation, but that model was popular because it gives a very efficient initial fit of the easiest data to obtain (i.e. the moon actually does go around the Earth, and with only 1 reference point the Sun appears to go round the Earth too). But of course once you have a heliocentric theory, you can throw all those parameters and every new prediction lines up nearly perfectly (accounting for how much longer it would take before we had precise enough orbital measurements to need Relativity to fully model it).
    - sudosysgen 3y ago
      When the law of gravitation was formulated, it could not in fact be used to predict orbits reliably (Kepler's ellipses are the solution to the two body problem anyways, and for a more complex system integration was impossible to any useful precision at the time), and Kepler's theories came out long before it did. It took more than 70 years after its formulation for the law to actually be conclusively tested against observations in a conclusive manner.

mordymoop 3y ago

Even very simple and small neural networks that you can easily train and play with on your laptop readily show that this “outputs are just the average of inputs” conception is just wrong. And it’s not wrong in some trickle philosophical sense, it’s wrong in a very clear mathematical sense, as wrong as 2+2=5. One example that’s been used for something like 15+ years is in using the MNIST handwritten digits dataset to recognize and then reproduce the appearances of handwritten digits. To do this, the model finds regularities and similarities in the shapes of digits and learns to express the digits as combinations of primitive shapes. The model will be able to produce 9s or 4s that don’t quite look like any other 9 or 4 in the dataset. It will also be able to find a digit that looks like a weird combination of a 9 and a 2 if you figure out how to express a value from that point in the latent space. It’s simply mathematically naive to call this new 9-2 hybrid an “average” of a 9 and a 2. If you averaged the pixels of a 9 image and a 2 image you would get an ugly nonsense image. The interpolation in the latent space is finding something like a mix between the ideas behind the shape of 9s and the shape of 2s. The model was never shown a 9-2 hybrid during training, but its 9-2 will look a lot like what you would draw if you were asked to draw a 9-2 hybrid. A big LLM is something like 10 orders of magnitude bigger than your MNIST model and the interpolations between concepts it can make are obviously more nuanced than interpolations in latent space between 9 and 2. If you tell it write about “hubristic trout” it will have no trouble at all putting those two concepts together, as easily as the MNIST model produced a 9-2 shape, even though it had never seen an example of a “hubristic trout.” It is weird because all of the above is obvious if you’ve played with any NN architecture much, but seems almost impossible to grasp for a large fraction of people, who will continue to insist that the interpolation in latent space that I just described is what they mean by “averaging”. Perhaps they actually don’t understand how the nonlinearities in the model architecture give rise to the particular mathematical features that make NNs useful and “smart”. Perhaps they see something magical about cognition and don’t realize that we are only ever “interpolating”. I don’t know where the disconnect is.

mnky9800n 3y ago
i think a partial explanation is that people don't move away from parametric representations of reality. We simply must be organized into a nice, neat gaussian distribution with very easy to calculate means and standard deviations. The idea that organization of data could be relational or better handled by a decision tree or whatever is not really presented to most people in school or university. Especially not as frequently or holistically as is simply thinking the average represents the middle of a distribution. you see this across social sciences where you can see a lot of fields have papers that come out every decade or so since the 1980s saying that linear regression models are wrong because they don't take into account several concepts such as hierarchy (e.g., students go to different schools), frailty (there is likely unmeasured reasons why some people do the things they do), latent effects (there is likely non-linear processes that are more than the sum of the observations, e.g., traffic flows like a fluid and can have turbulence), auto-correlations/spatial correlations/etc. In fact, I would argue that a decision tree based model (i.e., gradient boosted trees) will always arrive at a better solution to a human system than any linear regression. But at this point I suppose I have digressed from the original point.

YeGoblynQueenne 3y ago

>> Guessing the right theory of physics is equivalent to minimizing predictive loss. A model can reduce predictive loss to almost zero while still not being "the right theory" of physics, or anything else. That is a major problem in science, and machine learning approaches don't have any answer to it. Machine learning approaches can be used to build more powerful predictive models, with lower error, but nothing tells us that one such model is, or even isn't, "the right theory". As a very famous example, or at least the one I hold as a classic, consider the theory of epicyclical motion of the planets [1]. This was the commonly accepted model of the motion of the observable planets for thousands of years. It persisted because it had great predictive accuracy. I believe alternative models were proposed over the years, but all were shot down because they did not approach the accuracy of the theory of epicycles. Even Copernicus' model, that is considered a great advance because it put the Sun in the center of the universe, continued to use epicycles and so did not essentially change the "standard" model. Eventually, Kepler came along, and then Newton, and now we know why the planets seem to "double back" on themselves. And not only that, but we can now make much better predictions than we ever could do with the epicyclical model, because now we have an explanatory model, a realist model, not just an instrumentalist model, and it's a model not just of the observable motion of the planets but a model of how the entire world works. As a side point, my concern with neural nets is that we get "stuck in a rut" with them, because of their predictive power, like we got stuck with the epicyclical model, and that we spend the next thousand years or so in a rut. That would be a disaster, at this point in our history. Right now we need models that can do much more than predict; we need models that are theories, that explain the world in terms of other theories. We need more science, not more modelling. _________ [1] https://en.wikipedia.org/wiki/Deferent_and_epicycle https://en.wikipedia.org/wiki/Deferent_and_epicycle