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I'm always a bit confused when people call neural networks "universal function approximators" as if that makes them trivial or weak. Suppose we have a really s

I'm always a bit confused when people call neural networks "universal function approximators" as if that makes them trivial or weak. Suppose we have a really strong universal function approximator---stronger than current neural networks, whose generalization properties are not really that great in the grand scheme of things as of 2018. Tell it to approximate the action policy that maximizes some overly-simplistic geopolitical objective function, like GDP or territory controlled at time t+1. It doesn't seem at all obvious that this thing could not take over the world or at least cause significant havoc if given sufficient resources.

schoen 8y ago
At least, a lot of things that have conventionally been understood as very hard for AI (like catching a ball or playing Go) can be viewed as function approximations!
YeGoblynQueenne 8y ago
But what are "sufficient resources" in this case? How do you train a universal function approximator, even a good one, in, say "increasing GDP"? Where do you get the examples for that? The problem is that with such a vague objective as "maximise GDP" or "maximise controlled territory" you need to train a model that is extremely broad in scope - because the objective might be narrow, but the steps to realise it are extremely varied. In practice, you're trying to approximate a function that is outputting the state of the entire world at each time step. Good luck with achieving that in practice. Edit: The bit about collecting examples is not a trivial problem. Note that the successes of deep learning so far are in domains where not only the objective is well defined ("choose one of n categorical labels") but also the data associated with the objectives is easy to collect and has an obvious relation to the outputs. Say, if you want to train an image classifier to recognise images of dogs- obviously you need to collect images of dogs. This is not the case in "increase GDP" type objectives, where it is not even clear what exactly influences a country's GDP. In principle, you could feed the entire world as examples to the model, but in practice, that's just unfeasible.
- ShabbosGoy 8y ago
  > But what are "sufficient resources" in this case? How do you train a universal function approximator, even a good one, in, say "increasing GDP"? Where do you get the examples for that? You could specify a simpler goal like “increase economic output”, and an example might be something like optimizing the Cobb-Douglas production function. Even that very narrow goal in the context of say, manufacturing Teslas, would give me pause. Look up “instrumental convergence” to see why the above is a bad idea.
  - YeGoblynQueenne 8y ago
    When I say "examples" I mean training examples- a dataset to train (and validate) on. From what I can see on wikipedia, the parameters of Cobb-Douglas are the value of goods produced, labour, capital, "total factor productivity" (as I understand it, everything other than labour and capital that might contribute to productivity) and a couple of constants. For an AI to maximise the output of the function you'd have to somehow make it possible for it to manipulate those parameters- to hire or fire personel, to spend or acquire capital and to somehow manage all those unknown factors that might be contributing to the output. The question is: how do you do that? You can certainly collect, or even auto-generate examples of the inputs and outputs of the functions, since we're just talking numerical parameters, and find a maximum of the function. But for an AI to actually improve the productivity of a business, it would have to do a lot more than that. It would need the ability to manipulate those parameters directly in the real world. Otherwise, all it would do is calculate a number. Which is not that very threatening.
eli_gottlieb 8y ago
>some overly-simplistic geopolitical objective function, like GDP or territory controlled at time t+1. The hard part here is writing down that objective function. Remember, an AI/ML/cogsci algorithm is locked inside a black box, that being the hardware it runs on. Any objective function for RL must be expressed as a function (preferably a smoothly differentiable one, for gradient descent) of the sense-data available to the agent and the agent's hypothesis class about the world. Naive RL tends to optimize the function by, where at all possible, systematically decorrelating the agent's sense-data and reinforcement signal from the distal causes we intend them to represent.
- SiempreViernes 8y ago
  You mean write down a good objective function, making terrible ones are trivial. And the hard part is figuring out if the objective function you've spent six months refining actually gives sensible scores or if you just encoded all the mean of your data in that one hand tuned constant with six digits.
- AndrewKemendo 8y ago
  In my opinion, it's an impossible and undesirable task. So for example, write down the objective function for current General Intelligence: Humans. It's impossible, and has been the work of the field of Philosophy/Economics since we started seriously thinking about it.
  - eli_gottlieb 8y ago
    Ehhhh we're pretty close on that one, actually. https://www.nature.com/articles/s41562-017-0069 https://www.nature.com/articles/s41562-017-0069
    - AndrewKemendo 8y ago
      Did you link the right article? Nothing in that article discusses interpersonal neurological response systems or anything relating to how mores and boundaries are created. Seems like you're linking to something which may be on the track to narrow down consciousnesses which is a separate question - and one I also question the benefit of caring about.
stochastic_monk 8y ago
Mixtures of Gaussians are also universal function approximators. It more makes clear that it’s in a class of functions that could each do many of the things neural networks do.

schoen 8y ago

At least, a lot of things that have conventionally been understood as very hard for AI (like catching a ball or playing Go) can be viewed as function approximations!

YeGoblynQueenne 8y ago

But what are "sufficient resources" in this case? How do you train a universal function approximator, even a good one, in, say "increasing GDP"? Where do you get the examples for that? The problem is that with such a vague objective as "maximise GDP" or "maximise controlled territory" you need to train a model that is extremely broad in scope - because the objective might be narrow, but the steps to realise it are extremely varied. In practice, you're trying to approximate a function that is outputting the state of the entire world at each time step. Good luck with achieving that in practice. Edit: The bit about collecting examples is not a trivial problem. Note that the successes of deep learning so far are in domains where not only the objective is well defined ("choose one of n categorical labels") but also the data associated with the objectives is easy to collect and has an obvious relation to the outputs. Say, if you want to train an image classifier to recognise images of dogs- obviously you need to collect images of dogs. This is not the case in "increase GDP" type objectives, where it is not even clear what exactly influences a country's GDP. In principle, you could feed the entire world as examples to the model, but in practice, that's just unfeasible.

ShabbosGoy 8y ago
> But what are "sufficient resources" in this case? How do you train a universal function approximator, even a good one, in, say "increasing GDP"? Where do you get the examples for that? You could specify a simpler goal like “increase economic output”, and an example might be something like optimizing the Cobb-Douglas production function. Even that very narrow goal in the context of say, manufacturing Teslas, would give me pause. Look up “instrumental convergence” to see why the above is a bad idea.
- YeGoblynQueenne 8y ago
  When I say "examples" I mean training examples- a dataset to train (and validate) on. From what I can see on wikipedia, the parameters of Cobb-Douglas are the value of goods produced, labour, capital, "total factor productivity" (as I understand it, everything other than labour and capital that might contribute to productivity) and a couple of constants. For an AI to maximise the output of the function you'd have to somehow make it possible for it to manipulate those parameters- to hire or fire personel, to spend or acquire capital and to somehow manage all those unknown factors that might be contributing to the output. The question is: how do you do that? You can certainly collect, or even auto-generate examples of the inputs and outputs of the functions, since we're just talking numerical parameters, and find a maximum of the function. But for an AI to actually improve the productivity of a business, it would have to do a lot more than that. It would need the ability to manipulate those parameters directly in the real world. Otherwise, all it would do is calculate a number. Which is not that very threatening.

eli_gottlieb 8y ago

>some overly-simplistic geopolitical objective function, like GDP or territory controlled at time t+1. The hard part here is writing down that objective function. Remember, an AI/ML/cogsci algorithm is locked inside a black box, that being the hardware it runs on. Any objective function for RL must be expressed as a function (preferably a smoothly differentiable one, for gradient descent) of the sense-data available to the agent and the agent's hypothesis class about the world. Naive RL tends to optimize the function by, where at all possible, systematically decorrelating the agent's sense-data and reinforcement signal from the distal causes we intend them to represent.

SiempreViernes 8y ago
You mean write down a good objective function, making terrible ones are trivial. And the hard part is figuring out if the objective function you've spent six months refining actually gives sensible scores or if you just encoded all the mean of your data in that one hand tuned constant with six digits.
AndrewKemendo 8y ago
In my opinion, it's an impossible and undesirable task. So for example, write down the objective function for current General Intelligence: Humans. It's impossible, and has been the work of the field of Philosophy/Economics since we started seriously thinking about it.
- eli_gottlieb 8y ago
  Ehhhh we're pretty close on that one, actually. https://www.nature.com/articles/s41562-017-0069 https://www.nature.com/articles/s41562-017-0069
  - AndrewKemendo 8y ago
    Did you link the right article? Nothing in that article discusses interpersonal neurological response systems or anything relating to how mores and boundaries are created. Seems like you're linking to something which may be on the track to narrow down consciousnesses which is a separate question - and one I also question the benefit of caring about.

stochastic_monk 8y ago

Mixtures of Gaussians are also universal function approximators. It more makes clear that it’s in a class of functions that could each do many of the things neural networks do.