Just as a general response to the objections to this: The goal was to use XOR and PARITY as simple tasks and formal languages that exhibit a larger problem wit

Just as a general response to the objections to this: The goal was to use XOR and PARITY as simple tasks and formal languages that exhibit a larger problem with the architecture. The unfortunate side-effect of this is that the most straightforward thing to relate them to are human reasoning tasks like arithmetic, for which the most straightforward thing to say is then: "We use calculators too!". Or worse, over-focusing on the PARITY problem, specifically. The PARITY problem requires a kind of circuit that flips a bit on and off alternatively whenever we see a '1'/ signal. Is there a subconscious process that we employ in our brains that implements this circuit? Might some aspects of linguistic processing require this? (Michael Hahn brings up 'iterated negation' here: https://direct.mit.edu/tacl/article/doi/10.1162/tacl_a_00306/43545/Theoretical-Limitations-of-Self-Attention-in https://direct.mit.edu/tacl/article/doi/10.1162/tacl_a_00306...) All this to say, maintaining and updating latent state may be an implicit requirement for certain tasks, and that would be more likely learned from data than from an explicit prompt or outsourcing to a calculator.