The chain rule has always been about composability 
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Yeah but who knew you could take concepts from math and repurpose them for software...
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Maybe programming *is* math after all.
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Only somewhat-relatedly, non-probabilistic computing has a bunch of primitives that are used everywhere because they're "pseudo-linear", like sorting, hashing, etc. I've always wondered what the analogs are for probabilistic computing.
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sigmoids are maybe similarly ubiquitous to hashing?
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The nice thing about hashing is that it's so efficient and convenient that you can build really nice data structures and algorithms out of it. What I'd really like to know is whether there are efficient primitives you can use to build prob. algorithms/ data structures.
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The chain rule is the only definition that type-checks for the derivative of a composition. That seems pretty natural in the context of software and composability.
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All this time I should’ve been bragging in job interviews about the 106 I got in high school calculus
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