Rewrite sigmoid gradient into numerically stable form#2041
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ricardoV94 wants to merge 1 commit intopymc-devs:v3from
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Rewrite sigmoid gradient into numerically stable form#2041ricardoV94 wants to merge 1 commit intopymc-devs:v3from
ricardoV94 wants to merge 1 commit intopymc-devs:v3from
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Enable allow_multiple_clients on the 1-sigmoid(x)->sigmoid(-x) rewrite so it fires even when sigmoid(x) has other consumers. This stabilizes expressions like sigmoid(x) * (1 - sigmoid(x)) which suffer catastrophic cancellation for large |x|. The sigmoid pullback is kept in naive form to preserve algebraic cancellation in composed expressions like log(1 - sigmoid(x)).
ricardoV94
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Replace sigmoid(x) * (1 - sigmoid(x)) with sigmoid(x) * sigmoid(-x) in the Sigmoid pullback. The naive form suffers catastrophic cancellation for large |x| because (1 - expit(x)) rounds to zero.Instead of doing that (which we may want to). I left as is but let the stabilize rewrite be more aggressive and rewrite 1-sigmoid(x) -> sigmoid(-x), even if sigmoid(x) is used elsewhere. (Users who don't care about this can exclude "stabilize" then)
This may be too much tip-toeing. Maybe we want the rewrite to always be eager (and in this case implement the pullback already in this format). There was one test that checked whether the grad of a naive
log(1 - sigmoid(x))simplified (to not have a sum), and that one ended up cancelling a sigmoid(x) / sigmoid(x), that an eager stable pullback didn't produce. (rewrite ordering is fun).I don't know if sigmoids are expensive enough to worry about duplicating use in the first place.