[SR-12156] Make @differentiable attribute on class methods more fine-grained

[dan-zheng]

Previous ID	SR-12156
Radar	None
Original Reporter	@dan-zheng
Type	Sub-task

Additional Detail from JIRA

Votes	0
Component/s
Labels	Sub-task
Assignee	None
Priority	Medium

md5: 5db9c5c7c42530ea5694370955eac541

Issue Description:

@differentiable attribute on class methods currently does two orthogonal things:

• Requests derivative generation for the class method.

• Adds JVP/VJP vtable entries for the class method.

There's currently no way using @differentiable to do only one of the above. There may be use cases for doing only one of the above:

• Adding JVP/VJP vtable entries + custom derivative registration via @derivative attribute (no derivative generation).

• Requesting derivative generation without JVP/VJP vtable entries? Maybe there's no use for this.

Supporting this may require new attribute syntax.

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Note that this issue does not occur for protocol requirements, where @differentiable attribute can only mean one thing: add JVP/VJP witness table entries (and require implementations to specify same @differentiable attribute). This is because they have no function body for derivative generation.