Large portions of the possible research areas in Automatic Differentiation have broadly defined known solutions; most of which were derived in the 80s and 90s. Compute vector jacobian products: use reverse mode. Compute jacobian vector products: use forwards mode. (other things are a bit less solved, but still, we have a solid idea of what the solution space is e.g. computing whole jacobians using mixed-mode, and computing single partial derivatives using cross-country) There is a lot of work and refinements and tweaks to those ideas that are still active research today, and also a lot of implementations and innovations there. But the core of the ideas is well-established.

Is this also the case for automatically computing subgradients? Is current work variations on existing ideas, or is current work proposing whole new ideas?


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