[HN Gopher] Turing Machines Are Recurrent Neural Networks (1996)
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       Turing Machines Are Recurrent Neural Networks (1996)
        
       Author : todsacerdoti
       Score  : 52 points
       Date   : 2022-12-05 18:24 UTC (4 hours ago)
        
 (HTM) web link (users.ics.aalto.fi)
 (TXT) w3m dump (users.ics.aalto.fi)
        
       | lisper wrote:
       | This is a very misleading title. The result here is not that TM's
       | _are_ recurrent neural networks, it is that it is possible to
       | construct an (infinite) recurrent neural network that emulates a
       | TM. But the fact that a TM can be built out of perceptrons is
       | neither surprising nor interesting. It 's pretty obvious that you
       | can build a NAND gate out of perceptrons, and so _of course_ you
       | can build a TM out them.
       | 
       | In fact, it's probably the case that you can build a NAND gate
       | (and hence a TM) out of _any_ non-linear transfer function. I 'd
       | be surprised if this is not a known result one way or the other.
        
         | whatshisface wrote:
         | I don't remember the name of the theorem, but you can
         | approximate any nonlinear multivariable function arbitrarily
         | with a multi-layer perceptron with any non-polynomial nonlinear
         | function, applied after the linear weights and bias. It has to
         | be non-polynomial because the set of all polynomials is closed
         | under linear combinations, adding a constant, and composition,
         | so if the nonlinear function was (say) x^3 you would only get
         | polynomials out of the model.
         | 
         | I'm not sure why that's a problem because polynomial
         | approximations are still useful.
        
           | jmalicki wrote:
           | https://en.wikipedia.org/wiki/Universal_approximation_theore.
           | ..
        
           | tsimionescu wrote:
           | Note that there are two caveats.
           | 
           | For one, only continuous functions can be represented.
           | 
           | Much more importantly, the theorem doesn't prove that it's
           | possible to learn the necessary weights to approximate any
           | function, just that such weights much exist.
           | 
           | With our current methods, only a subset of all possible NNs
           | are actually trainable, so we can only automate the
           | construcion approximations for certain continuous functions
           | (generally those that are differentiable, but there may be
           | exceptions, I'm not as sure).
        
           | kkylin wrote:
           | Are you talking about something like this?
           | 
           | https://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Arnold_repr.
           | ..
        
       | dang wrote:
       | Related:
       | 
       |  _Turing Machines Are Recurrent Neural Networks (1996)_ -
       | https://news.ycombinator.com/item?id=10930559 - Jan 2016 (12
       | comments)
        
         | adlpz wrote:
         | As a side note, it's fascinating to read the comments on that
         | thread when talking about RNNs and Deep Learning. So much has
         | changed in the last 6 years and feels so weird to read
         | dismissive comments about the capabilities of these systems
         | seeing what people are getting out of ChatGPT.
        
           | BlueTemplar wrote:
           | Not really ?
           | 
           | << Inflated >> expectations doesn't mean NO expectations...
           | 
           | People are still throwing << AI >> around as a buzzword like
           | it's something distinct from a computer program, in fact the
           | situation got worse because non-neural network programs are
           | somehow dismissed as << not AI >> now.
           | 
           | Autonomous cars are still nowhere to be seen, even more so
           | for << General << AI >> >>.
           | 
           | The singularity isn't much on track either looking at
           | Kurzweil's predictions : we should have had molecular
           | manufacturers by now, and nanobots connecting our brains to
           | the Internet, extending our lives, and brain scanning people
           | to recreate their avatars when they are dead, don't seem like
           | they are going to happen by the 2030s either. (2045 is still
           | far enough away that I wouldn't _completely_ bet against a
           | singularity by then.)
           | 
           | (And Kurzweil doesn't get to blame it on misunderstanding the
           | exponential function : how people have a too linear view of
           | the future and tend to overestimate changes in the near
           | future, but underestimate them in the long term !)
        
             | alexheikel wrote:
             | New technology need to be created for real AI to exist. As
             | we go, we are creating Hal, we aim to pass Turing using ai
             | and hi (human intelligence) http://gethal.com
        
           | whatshisface wrote:
           | ChatGPT hasn't overcome any of the fundamental issues, it's
           | just a huge improvement on the things that the original GPTs
           | were good at. Being able to stay coherent for a trained-in
           | length that gets longer with larger models is different from
           | the length-unlimited coherence that human beings can manage,
           | spanning lifetimes of thought and multiple lifetimes of
           | discourse.
        
             | dragonwriter wrote:
             | > ChatGPT hasn't overcome any of the fundamental issues,
             | it's just a huge improvement on the things that the
             | original GPTs were good at. Being able to stay coherent for
             | a trained-in length that gets longer with larger models is
             | different from being internally coherent for 90 years by
             | nature like people are.
             | 
             | People are very often not internally coherent over periods
             | much shorter than 90 years.
        
               | whatshisface wrote:
               | The hazily defined ideal of general intelligence - which
               | everyone imagines that they are, but most of us do not
               | live up to all the time, and nobody lives up to every
               | waking moment (or at least before we've had our morning
               | cup of coffee) isn't within the reach of present day
               | transformer architectures because the length of text they
               | can stay coherent over is limited by how far back they
               | can look through their own output. Human beings can form
               | new memories from their outputs that stay with them for
               | the rest of their lives.
        
       | Xcelerate wrote:
       | At what point have our neural networks crossed over to
       | demonstrating algorithmic behavior and we no longer consider them
       | fancy interpolating functions? Is there a way to quantify this?
        
         | whatshisface wrote:
         | A model with no training data would know nothing, so in a sense
         | they're always going to be something like a fancy form of
         | interpolation/extrapolation.
        
           | Xcelerate wrote:
           | There's a difference between interpolation and induction.
           | You're not going to interpolate a hash function.
        
             | whatshisface wrote:
             | There's no way a neural network could ever learn a hash
             | function directly (unless it had every possible input and
             | output in its table), and if there was an indirect way to
             | train it, you'd discover that it was interpolating between
             | (say) possible hash functions by working in a larger space,
             | for example if it was trained to generate and test C
             | programs that computed hashes.
        
       | jvm___ wrote:
       | Does the new chat AI bot pass the turing test?
        
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