PyTorch Developer Podcast

Conjugate views

Episode Summary

What are complex numbers? What is conjugation? Why is conjugation so common in linear algebra? Why would we like conjugation to behave similarly to transposition (and why is matrix multiply with a transposed input so fast?) What is a conjugate view? How is it implemented? What's the relationship between views, laziness and call-by-name evaluation?

Episode Notes

What are complex numbers? What is conjugation? Why is conjugation so common in linear algebra? Why would we like conjugation to behave similarly to transposition (and why is matrix multiply with a transposed input so fast?) What is a conjugate view? How is it implemented? What's the relationship between views, laziness and call-by-name evaluation?

Further reading.

• Pull request that adds conjugate views https://github.com/pytorch/pytorch/pull/54987
• The idea of conjugate views originally came up when we were deciding which complex autograd convention to use in https://github.com/pytorch/pytorch/issues/41857 . PyTorch uses the conjugate Wirtinger derivative which, true to its name, involves a lot of conjugations in its formulas.
• Conjugate views are a form of bidirectional lens. This nice presentation explains what the concept is https://www.cis.upenn.edu/~bcpierce/papers/lenses-etapsslides.pdf