Update:
I am now working on the code to compare the performance between
the logical and non-logical ("plain") version, but this was delayed a bit
by the transition to pyTorch.
This will make the experiment more meaningful, instead of just
demonstrating convergence.
I hope the paper would be accepted because it describes a new
perspective on AGI that should be communicated to the broader
AGI research community... despite the fact that experimentally
it has not demonstrated much....
YKY
On 7/22/21, YKY (Yan King Yin, 甄景贤) <[email protected]> wrote:
> On 7/20/21, Matt Mahoney <[email protected]> wrote:
>
>> The paper describes an experiment in which a neural network was trained
>> to
>> play tic tac toe. But instead of describing what was actually done, here
>> is
>> a meaningless graph that it produced and a link to the source code.
>
> The paper described the neural network architecture in the previous
> section.
> The graph shows early convergence, but afterwards convergence is very slow
> and unstable with respect to the optimal value. This unstable behavior is
> also
> observed in the "control" test, so it may be due to the policy
> gradient algorithm
> itself, rather than the symmetric neural network.
>
>> In the pages where we would normally find a description of the algorithm
>> and the motivation for doing it this way, we instead find an incoherent
>> collection of math and logic tidbits that are irrelevant to the problem
>> at
>> hand.
>
> I explained how logic formulas are treated by the symmetric neural network,
> and then the tic-tac-toe problem was tested with such an architecture and
> with propositional representation of the play moves. What do you find
> incoherent?
>
>> Does the tic tac toe program use a Curry Howard transform or the pair of
>> pants from string theory? Did it help? How will this shorten the path to
>> AGI?
>
> Curry-Howard provides an interpretation, which is not essential for
> designing the symmetric neural network. But Curry-Howard is essential
> to understanding the whole theory of categorical logic... it's at the very
> foundation of the theory and cannot be ignored. So I spent some time
> explaining it in the paper, otherwise readers would be lost when trying
> to read the texts that are referenced.
>
> The "pair of pants" is just mentioned for general interest... it doesn't
> play a role in the current implementation...
>
> Like I said in the introduction, I hope that describing AGI in mathematical
> terms will enable more people to discover connections between AGI
> and other mathematical structures....
>
> YKY
>
--
YKY
"The ultimate goal of mathematics is to eliminate any need for intelligent
thought" -- Alfred North Whitehead
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Artificial General Intelligence List: AGI
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