If you're looking for interesting derivative-adjacent ideas, I would also recommend Clarke derivatives [1]. They occasionally show up in ML papers, e.g., [2], [3]. Unrelated bu tangential, another place where you need derivatives but don't have access to them (standard or otherwise) is in the area of black-box optimization. Within this area, Bayesian Optimization (BayesOpt) has picked up quite a bit, which I've successfully used quite a bit in my work - I've an introduction here [4]. There is also a good book available online for free on the topic [5].