Fix complex vjps for several unary ops#3766
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Square, Sin, Sinh, Cosh, Tan, Tanh, and Log1p delegated their vjp to their jvp. For a holomorphic f the jvp is f'(z) * t, but the vjp must be cotangent * conj(f'(z)); delegating dropped the conjugate, so the gradient through these ops was wrong for complex inputs (e.g. the grad of Re(z**2) was 2*z instead of 2*conj(z)). Conjugate the cotangent into the jvp and conjugate the result, which yields cotangent * conj(f'(z)) and is a no-op for real inputs.
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Proposed changes
Fixes #3765.
Square,Sin,Sinh,Cosh,Tan,Tanh, andLog1pdelegated theirvjpto theirjvp. For a holomorphicfthe jvp isf'(z) * t, but the vjp must becotangent * conj(f'(z))(the convention already used byExp/Log). Delegating dropped the conjugate, so gradients through these ops were wrong for complex inputs — e.g. the gradient ofRe(z**2)was2*zinstead of2*conj(z).Each vjp now conjugates the cotangent, runs the jvp, and conjugates the result — i.e.
conj(jvp(conj(w)))=w * conj(f'(z))— which is a no-op for real inputs (so real gradients and the jvps are unchanged).Verified each op's complex gradient against finite differences and against the hand-computed
cotangent * conj(f'(z)); real gradients and all jvps are unchanged. Addedtest_complex_unary_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