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Are you saying that a neural network can learn addition symbolically? Can you recommend a book or site to read about this?
by pixcavator 19y ago
Are you saying that a neural network can learn addition symbolically? Can you recommend a book or site to read about this?
- dpapathanasiou 19y agoCan you recommend a book or site to read about this? David MacKay wrote a good intro book on Bayesian, neural networks, and related topics: http://www.inference.phy.cam.ac.uk/mackay/itila/ http://www.inference.phy.cam.ac.uk/mackay/itila/
- jsackmann 19y agoWhether you're interested in the book or not, don't miss this page: http://www.inference.phy.cam.ac.uk/mackay/itila/Potter.html http://www.inference.phy.cam.ac.uk/mackay/itila/Potter.html Should you buy the MacKay text or one by J.K. Rowling?
- pixcavator 19y agoI've looked at the chapter on neurall networks. It does not seem to address operations with symbols, only numbers...
- hhm 19y agoYou 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 agoSo given a function with f('1','1')='2', the computer will figure out that f('1','2')='3', right?
- hhm 19y agoYes, that's what I'm talking about.
- pixcavator 19y agoWow!
- aswanson 19y agohhm 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 agoWhat if the machine does not know that it is dealing with numbers? It's all symbolic: '1'+'1'='2', etc.
- aswanson 19y agoThe 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 agoIf 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 agoHow are you defining symbols? How are you defining meaningless, or meaning at all for that matter?
- pixcavator 19y agoSuppose 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).
- zyroth 19y agoNo, I'm saying that a neural network can learn addition. See, a bayesian cannot really understand that there are relations between two numbers (like "is bigger than" or "is the following number of"), but a neural network can, since addition is part of a NN. My personal recommendation on machine learning is 'Pattern Recognition and Machine Learning' by Chris Bishop. But you definately do need a solid mathematical background for that.
- pixcavator 19y agoWhere would the idea of "is bigger than" or "is the following number of" come from if not from the person who creates the network?
- zyroth 19y agoTraining examples.
- pixcavator 19y agoComputers can form concepts, really?
- zyroth 19y agoIf you want them to learn a specific concept that we know, they can learn it, yes.