Reading Group Thread: The Simple Essence of Automatic Differentiation

[srush]

I plan to work my way through this paper The Simple Essence of Automatic Differentiation http://conal.net/papers/essence-of-ad/essence-of-ad-icfp.pdf over the next couple weeks. Feel free to chime in as well.

Based on this thread: #454 (comment)

(I basically have undergrad-level PL depth so it's going to be slow. But I'm going to try to summarize as I go.)

[oxinabox]

I will try to do the same.

[conal]

I recommend this link instead, which will point you to abstract, talks (especially the Microsoft Research version), and related work.

Feel free to ask me questions along the way.

[breandan]

Hi Conal, in the paragraph highlighted above you mention the symmetry of the Hessian. I recently became aware that Hessians can be asymmetric if the second-order partials are not continuous. I was curious, are you only considering smooth functions or do you have an explanation for why Schwarz' theorem does not apply in your setting? Thank you!

[conal]

Hi Breandan. The point I was getting at in this paragraph is that multilinear maps are subsumed by curried linear maps. I don't think I have any insight on your question about Hessians and symmetry.