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  • Neural Networks cover Rule Based in Zero Order Logic (Was: Higher Order

    From Mild Shock@21:1/5 to All on Sat Mar 15 16:42:49 2025
    A storm of symbolic differentiation libraries
    was posted. But what can these Prolog code
    fossils do?

    Does one of these libraries support Python symbolic
    Pieceweise ? For example one can define rectified
    linear unit (ReLU) with it:

    / x x >= 0
    ReLU(x) := <
    \ 0 otherwise

    With the above one can already translate a
    propositional logic program, that uses negation
    as failure, into a neural network:

    NOT \+ p 1 - x
    AND p1, ..., pn ReLU(x1 + ... + xn - (n-1))
    OR p1; ...; pn 1 - ReLU(-x1 - .. - xn + 1)

    For clauses just use Clark Completion, it makes
    the defined predicate a new neuron, dependent on
    other predicate neurons,

    through a network of intermediate neurons. Because
    of the constant shift in AND and OR, the neurons
    will have a bias b.

    So rule based in zero order logic is a subset
    of neural network.

    Python symbolic Pieceweise https://how-to-data.org/how-to-write-a-piecewise-defined-function-in-python-using-sympy/

    rectified linear unit (ReLU) https://en.wikipedia.org/wiki/Rectifier_(neural_networks)

    Clark Completion
    https://www.cs.utexas.edu/~vl/teaching/lbai/completion.pdf

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  • From Mild Shock@21:1/5 to Mild Shock on Sat Mar 15 17:05:19 2025
    Hi,

    There are some ideas to realize the neuronal neuron used
    for belief networks on the computer. Via so called
    “Repeat-Until-Success” (RUS) circuits maybe?

    See also:

    Towards a Real Quantum Neuron
    Wei Hu - 2018
    https://www.scirp.org/journal/paperinformation?paperid=83091

    Quantum Neuron
    Yudong Cao et al. - 2017
    https://arxiv.org/abs/1711.11240

    Bye

    Mild Shock schrieb:

    A storm of symbolic differentiation libraries
    was posted. But what can these Prolog code
    fossils do?

    Does one of these libraries support Python symbolic
    Pieceweise ? For example one can define rectified
    linear unit (ReLU) with it:

                    /   x      x  >= 0
        ReLU(x) := <
                    \   0      otherwise

    With the above one can already translate a
    propositional logic program, that uses negation
    as failure, into a neural network:

    NOT     \+ p             1 - x
    AND     p1, ..., pn      ReLU(x1 + ... + xn - (n-1))
    OR      p1; ...; pn      1 - ReLU(-x1 - .. - xn + 1)

    For clauses just use Clark Completion, it makes
    the defined predicate a new neuron, dependent on
    other predicate neurons,

    through a network of intermediate neurons. Because
    of the constant shift in AND and OR, the neurons
    will have a bias b.

    So rule based in zero order logic is a subset
    of neural network.

    Python symbolic Pieceweise https://how-to-data.org/how-to-write-a-piecewise-defined-function-in-python-using-sympy/


    rectified linear unit (ReLU) https://en.wikipedia.org/wiki/Rectifier_(neural_networks)

    Clark Completion
    https://www.cs.utexas.edu/~vl/teaching/lbai/completion.pdf

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    * Origin: fsxNet Usenet Gateway (21:1/5)