Which event causes such a kink in gradient descent?

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I'm running gradient descent on a continuous function and I observe this pattern: enter image description here

What can cause such a sudden kink? Why does the Loss keep increasing after it? I understand issues related to a learning rate that is too large, but this does not seem to be the case.

The parameter also turns abruptly (it's a complex-valued parameter, or we can think of it as a pair of parameters): enter image description here

For completeness, here's the norm of the gradient (there's no large jump as if there was a cliff, see fig. 8.3 pag. 285) enter image description here