Fix complex vjps for the inverse trig and hyperbolic ops#3779
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ArcCos, ArcCosh, ArcSin, ArcSinh, ArcTan, and ArcTanh delegated their vjp to their jvp, dropping the conjugate for complex inputs. As with the other unary ops, conjugate the cotangent into the jvp and conjugate the result so the vjp is cotangent * conj(f'(z)); this is a no-op for real inputs.
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Proposed changes
Fixes #3778.
ArcCos,ArcCosh,ArcSin,ArcSinh,ArcTan, andArcTanhdelegated theirvjpto theirjvp. For a holomorphicfthe jvp isf'(z) * tbut the vjp must becotangent * conj(f'(z)); delegating dropped the conjugate, so gradients through these ops were wrong for complex inputs. This is the same fix as #3766, applied to the inverse trig / hyperbolic ops.Each vjp now conjugates the cotangent, runs the jvp, and conjugates the result (
conj(jvp(conj(w)))=w * conj(f'(z))), a no-op for real inputs.Verified each op's complex gradient against finite differences and the hand-computed
cotangent * conj(f'(z))(away from the branch cuts); real gradients and jvps are unchanged. Addedtest_complex_inverse_trig_vjps.Checklist
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xin the boxes that apply.pre-commit run --all-filesto format my code / installed pre-commit prior to committing changes