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Comment by amelius | Hacker News Reader

Would this be useful for general applications, or just numerical ones?

Your program takes various inputs, does processing and gives you results. To quote the book this applies to programs "including those with control flows and data structures" and are not entirely numerical in the most common sense. Broadly speaking, with AD you can modify the results and the program will spit out the required inputs to get those results.

So if a program's result is "no access", then AD can figure out how you can get access. Sounds like an important hacker tool.

I mean, “differential cryptanalysis” doesn’t go through AD, but I would be surprised if it’s not possible to get pretty close to a discrete analogue to AD using bit flips instead of differential and abstract interpretation.

Cryptography functions, I'd assume, are purposely non-differentiable.

Yes, these are “adversarial patches” in image classification, like https://arxiv.org/abs/1712.09665 . Similarly you can take these adversaries and add them to your own larger model, in an arms race.

> Broadly speaking, with AD you can modify the results and the program will spit out the required inputs to get those results.

I assume you're trying to phrase it in a non-technical way for accessibility, but I wonder if that might have lost some precision. What you describe sounds more like (logically) reversible programming (https://en.wikipedia.org/wiki/Reversible_computing). Differentiability doesn't imply reversibility; for example, the program that takes in an input and returns 1 is as differentiable as they come, but there's nothing that differentiation, automatic or otherwise, can do to tell you an input that will make it return 2.

But it can immediately return "no".

Good point! (And it brings back memories of fun with Prolog, although I guess that's `false`.)

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