Gary—do you think "operations [over variables] a la logic" and "symbolic techniques" can be learned within the differentiable framework, or do you imagine that they are hard-wired or are very strong structural priors?
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Symbolic operations can certainly be learned by differentiable frameworks. But by default they learn propositional rules and not first-order rules (with universally quantified variables). Neural networks suffer, by default from what McCarthy called the "propositional fixation".
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The vectors are discrete components of the symbols being manipulated, but we don't need to model consciousness at the hardware level.
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Gary -- Yann wants to numerify everything. By doing that there is a significant semantic information loss.
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