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At least at first glance, the "downside" to automatic differentiation seems pretty trivial. Are there any major programming languages that have features to take care of this programming challenge automatically-- like an option to interpret all variables as derivative tuples, or just having this be the default?


It looks like this slide describes the forward approach to automatic differentiation where you operate on value/derivative pairs, which is different from the backward approach that many automatic differentiation frameworks seem to take (for example in machine learning). Are there any tradeoffs between forward and backward automatic differentiation? For example, in backward automatic differentiation I believe you'd need to store all the intermediate values of gradients but in forward automatic differentiation you can discard previous gradients once you've used them in your calculation