> everything which makes programs useful is impure device access and state change, discretely sequenced over time
I haven't heard about this before actually. I'd love to hear more about this!
"Impure," here, is PL terminology for functions that affect global state/arguments when you run them. right? So, brainstorming a bit, what this means is that making a diff. programming language that treats a NN module as a pure function won't actually be beneficial? I'm not sure if I'm drawing the correct conclusion but this is a really interesting point. Don't have an answer for this (yet!).
> grad. desc. et al. do not learn discrete constraints
Great Point! To push back a little on this. You're right that any discrete constraint will always mess up the smoothness of the function (eg: less-than-g is not smooth at x=g). However, we can engineer our way around this by relaxing a discrete constraint to its closest smooth approximation! So, we can implement the less-than-g function as a sigmoid that is shifted by +/-g. This introduces a parameter to control the slope of the sigmoid. In practice, I haven't had much difficulty learning programs even with a really steep slope for the sigmoid.
I haven't heard about this before actually. I'd love to hear more about this! "Impure," here, is PL terminology for functions that affect global state/arguments when you run them. right? So, brainstorming a bit, what this means is that making a diff. programming language that treats a NN module as a pure function won't actually be beneficial? I'm not sure if I'm drawing the correct conclusion but this is a really interesting point. Don't have an answer for this (yet!).
> grad. desc. et al. do not learn discrete constraints
Great Point! To push back a little on this. You're right that any discrete constraint will always mess up the smoothness of the function (eg: less-than-g is not smooth at x=g). However, we can engineer our way around this by relaxing a discrete constraint to its closest smooth approximation! So, we can implement the less-than-g function as a sigmoid that is shifted by +/-g. This introduces a parameter to control the slope of the sigmoid. In practice, I haven't had much difficulty learning programs even with a really steep slope for the sigmoid.