3 ms·

I've looked at the chapter on neurall networks. It does not seem to address operations with symbols, only numbers...

hhm 19y ago
You can always encode symbols as numbers, and otherwise. That's what computers do, that's what you do when you do a sum by yourself, and that's what such a neural network should do too. (You should encode the symbols to a binary input, then decode the neural network output to symbols).
- pixcavator 19y ago
  So given a function with f('1','1')='2', the computer will figure out that f('1','2')='3', right?
  - hhm 19y ago
    Yes, that's what I'm talking about.
    - pixcavator 19y ago
      Wow!
aswanson 19y ago
hhm is right. You would end up with a network with connection weights of 1. As long as your sigmoidal transfer functions are biased such that they have no multiplying effect your output would be an addition of the inputs.
- pixcavator 19y ago
  What if the machine does not know that it is dealing with numbers? It's all symbolic: '1'+'1'='2', etc.
  - aswanson 19y ago
    The neural network doesn't "know" that it is dealing with anything, just as you don't "know" the function your body uses to expand and contract your heart. You could be feeding it stock quotes, rgb pixel values, your daily weight, anything. If the information can reduced to numeric values (it can) the network will determine the relationship in the form of a function.
    - pixcavator 19y ago
      If the input is numbers then what happens is simply extrapolation (or regression etc). If the input is symbols, then what? The fact that you can associate numbers to the symbols does not help. The extrapolation will be meaningless. Unless you happen to have the correspondence '1'->1, '2'->2, etc,
      - aswanson 19y ago
        How are you defining symbols? How are you defining meaningless, or meaning at all for that matter?
        pixcavator 19y ago
        Suppose you have a function f of two variables and all you know about it is that f(x,y)=x+y for a few values of x,y. With this data, the computer extrapolates linearly and finds f(x,y) for _all_ values of x,y. The computer just "learnt" how to add! If all you have is symbols, however, you have to have numbers associated with those symbols. But you can't expect 1 correspond to '1' and 2 to '2'. As a result, your function f - and its extrapolation - will have nothing to do with addition (f won't even be linear).
        aswanson 19y ago
        So am I correct in assuming that you are looking for a machine that can do the mapping of a symbol into a form that the function can learn from? Your visual and auditory systems do this, and since they are physical systems this mapping is computable. By the way, for the addition example , the neural network needs only one example, e.g. 1+1=2, applied repeatedly to discover the addition of any two inputs. There is no extrapolation between examples needed in this case.

hhm 19y ago

You can always encode symbols as numbers, and otherwise. That's what computers do, that's what you do when you do a sum by yourself, and that's what such a neural network should do too. (You should encode the symbols to a binary input, then decode the neural network output to symbols).

pixcavator 19y ago
So given a function with f('1','1')='2', the computer will figure out that f('1','2')='3', right?
- hhm 19y ago
  Yes, that's what I'm talking about.
  - pixcavator 19y ago
    Wow!

aswanson 19y ago

hhm is right. You would end up with a network with connection weights of 1. As long as your sigmoidal transfer functions are biased such that they have no multiplying effect your output would be an addition of the inputs.

pixcavator 19y ago
What if the machine does not know that it is dealing with numbers? It's all symbolic: '1'+'1'='2', etc.
- aswanson 19y ago
  The neural network doesn't "know" that it is dealing with anything, just as you don't "know" the function your body uses to expand and contract your heart. You could be feeding it stock quotes, rgb pixel values, your daily weight, anything. If the information can reduced to numeric values (it can) the network will determine the relationship in the form of a function.
  - pixcavator 19y ago
    If the input is numbers then what happens is simply extrapolation (or regression etc). If the input is symbols, then what? The fact that you can associate numbers to the symbols does not help. The extrapolation will be meaningless. Unless you happen to have the correspondence '1'->1, '2'->2, etc,
    - aswanson 19y ago
      How are you defining symbols? How are you defining meaningless, or meaning at all for that matter?
      - pixcavator 19y ago
        Suppose you have a function f of two variables and all you know about it is that f(x,y)=x+y for a few values of x,y. With this data, the computer extrapolates linearly and finds f(x,y) for _all_ values of x,y. The computer just "learnt" how to add! If all you have is symbols, however, you have to have numbers associated with those symbols. But you can't expect 1 correspond to '1' and 2 to '2'. As a result, your function f - and its extrapolation - will have nothing to do with addition (f won't even be linear).
        aswanson 19y ago
        So am I correct in assuming that you are looking for a machine that can do the mapping of a symbol into a form that the function can learn from? Your visual and auditory systems do this, and since they are physical systems this mapping is computable. By the way, for the addition example , the neural network needs only one example, e.g. 1+1=2, applied repeatedly to discover the addition of any two inputs. There is no extrapolation between examples needed in this case.