How does tf.gradients manages complex functions?

Question

I am working with complex-valued neural networks.

For Complex-valued neural networks Wirtinger calculus is normally used. The definition of the derivate is then (take into acount that functions are non-Holomorphic because of Liouville's theorem):

If you take Akira Hirose book "Complex-Valued Neural Networks: Advances and Applications", Chapter 4 equation 4.9 defines:

Where the partial derivative is also calculated using Wirtinger calculus of course.

Is this the case for tensorflow? or is it defined in some other way? I cannot find any good reference on the topic.

Answer 1

好的，所以我在github/tensorflow的现有线程中讨论了这个问题，@charmasaur 找到了响应，Tensorflow 用于梯度的方程是：

当使用 z 和 z* 的偏导数的定义时，它使用 Wirtinger 微积分。

对于一个或多个复变量的实值标量函数的情况，该定义变为：

这确实是复值神经网络（CVNN）应用程序中使用的定义（在此应用程序中，该函数是损失/误差函数，它确实是真实的）。