Given that any stock is a function over time as well, there should theoretically exist a neural net that can approximate the stock price for the future? This reasoning is obviously wrong, what is my exact error of thought though?
Sure we do. Partition your neurons into a few billion independent networks, embed them on a spinning globe of mostly molten rock, and put each one in a leaky bag of mostly water.
Wait long enough, and one leaky bag will emit the number "42". If you get the initial conditions just right (and quantum nondeterminism isn't really a thing), then you'll also get a good approximation to the stock market.
No need for infinite-length books to encode all possible functions, as there are notations to express infinity in finite space (e.g. programs, encoding an infinity of behaviour in a finite number of instructions).
The library of babel contain every possible finite description of every possible function.
besides karelp's sister comment, there's also the "obvious" fact that stock price is not a function of time, it's not P(t), it's a function of time and the entire f universe that also evolves through time, more like P(t, U(t, ....)) ....you can simplify things by assuming the laws of physics are deterministic and you only need one instance of the state of the universe, U, so you'd have P(t, U)
...now if you don't explicitly represent U as a parameter, you'll have it implicit in the function. So your "neural network" contains the entire state of the freakin universe (!!).
Ergo, contingent on your stance on theologic immanence vs. transcendence, what you'd call "neural network approximation of the stock's price function" is probably quite close to what other call... God (!).
(Now, if relativity as we know it is right, you might get aways with a "smaller slice of U" - lear about "light cone". And to phrase this in karelp's explanation context: you'd need to know U to know which of the practically infinitely many such neural networks to pick. The core of (artificial) intelligence is not neural networks in themselves, it's learning, the NN is a quite boring computational structure, but you can implement tractable learning strategies for it, both in code, and in living cells as evolution has shown...)
And you'd have to know the state of U to infinite precision. Which makes me wonder whether neural nets have any hope with a simple chaotic function. Maybe they do but just in the short term, like predicting the weather.
There isn't one, you're just overestimating the value of existence-propositions.
In practice, knowing that something exists is not a very useful result - it is often more useful to know that something does NOT exist (e.g. solution to the halting problem).
Theoritically, there exists a model that predicts all future stock prices EXACTLY at any given time in the future, as long as the results are completely isolated from all market participants (i.e. the knowledge of the result is COMPLETELY isolated from the market). Here is how you can theoritically prove it exists:
Train a model today so that it is overfitting for a given stock. It would predict everything very accurately upto today. The ONLY way to make sure that the results are completely isolated from the market is to not make the result available to ANYONE (how do you know that an isolated human observer is not leaking data with some unknown phenomena... say quantum entanglement with particles in other people's brains, for example). So, the ONLY way to test the models is back-testing.
You can extend that to saying that for any given point in the future (say, this is a reference point), there will be an overtrained model which will backtest perfectly i.e. the theoritical model that works at any time during the past to predict the exact stock price in the future upto the point of reference.
It is just that the neural network would have to compute a model of the entire world or even the universe on an atomic scale. It would be computationally unfeasible but not theoretically impossible.
It is theoretically possible that the universe we live is already being computed on a neural network in some other external universe.
Contrary to the recent top comment on this, which fails to show that such a net existing could be no coincidence, I guess, the answer to your problem might be deeply physical and information theoretic, as soon as you speak of time. Simply speaking, any model is good enough if the approximation is tolerably accurate. In that sense, crude nets as well as expert systems that trigger off clear signals and ample evidence may already exist.
In particular, the way the stockmarkets are distributed the function of time is likely relativistic and every participant is acting under incomplete information even in the infinite limit.
Also, you have to be cautious what any function in this context really means, as I imagine it means differentiable functions (after somebody mentioned the Ackermann function, which is not anywhere differentiable).
The error is that stock price is not a function over time, but instantaneous demand which we record over time. That demand is a function over an undefined number of variables.
With the same type of reasoning, we could plot whatever output our brain gives and there will be some type of neural network that can predict what we'll think/see/feel in the future.
What you said and the thing i just said were both ideas i had when starting learning how ai works, sadly it's something we can still not reach.at least for now
If I understand you correctly, we are very far away from that example as that is AGI and then some. You will not see that in your lifetime so ‘we can still’ seems an interesting (overly optimistic?) take on it.
AGI, since it lacks a technical/mathematical definition, can be anything. It’s mere philosophy at this point, actually even vaguer than most philosophical problems.
I meant it to mean, indeed in a vague way, what we call human intelligence or beyond; the parent says to make a neural network that can predict what someone will think/feel in the future, which seems the same or at least indistinguishable from the subject’s human intelligence as it will result in the same outputs. So to create the network implied by the parent, we would have to a) be able to make networks of that (unknown) complexity and b) ‘copy’ , or rather make it learn from the outputs, the current ‘state’ of the subject’s brain in it. That is incredibly far removed from anything cutting edge we know how to do. If it is at all possible.
So I was just surprised by their use of language as it seems to imply parent thought we would be closer to or there already with our developments of AI tech.
Although I share your sentiment in general, I would presume that @tluyben's take is fairly true to the broader philosophical view. The ritique of this view being at least as weak as the views on intelligence per se is a drop in the ocean really.
Implying, there is a wealth of thought devoted to inteligence! That fact is actually proving the conjecture in a nicely constructive way by itself, that we are thoughtful indeed, if only you believe this axiomatically like. The quintessential theorem was distiled by Descartes, of course, wherefore he is remembered.
Your input features are incomplete and mixed with noise.
The value of a dice is also a function over time. Can we learn this function with a neural net? No, because our features don't include the nitty gritty details of each throw so it's essentially random.
Stock prices are not well modelled as continuous functions- the prices you see are generally trades (discrete function) and the price may or may not have been available to you at the volume you wanted (there are more variables than time).
Your mistake is that you left off "given the right inputs". There are a lot of inputs to stock prices that are unlikely to be readily available to your function.
Doesn't seem wrong to me, the tricky part is to find this network and convince yourself that it is indeed predicts correctly over the period of interest.
