We talk about gradcheck, the property based testing mechanism that we use to verify the correctness of analytic gradient formulas in PyTorch. I'll talk a bit about testing in general, property based testing and why gradcheck is a particularly useful property based test. There will be some calculus, although I've tried to keep the math mostly to intuitions and pointers on what to read up on elsewhere.

Further reading.

• Gradcheck mechanics, a detailed mathematical explanation of how it works https://pytorch.org/docs/stable/notes/gradcheck.html In particular, it also explains how gradcheck extends to complex numbers
• JAX has a pretty good explanation about vjp and jvp at https://jax.readthedocs.io/en/latest/notebooks/autodiff_cookbook.html
• Fast gradcheck tracking issue https://github.com/pytorch/pytorch/issues/53876