# What is the expression for derivative of the signum function one should use in the BP training method

The back propagation learning method requires knowing of derivatives of activation functions. But what expression one should use for signum activation function $$\mathrm{Signum}( x ) = \begin{cases} 1, &x \geq \gamma\\ 0, &x < \gamma \end{cases}$$

The function you wrote is completely flat, except at $x=\gamma$ where the step occurs. So, its derivative w.r.t. $x$ is zero everywhere, except at $x=\gamma$, where the derivative doesn't exist. This means gradients (whenever they exist) will always be zero, and gradient-based learning rules (e.g. backprop) won't work. If you want learning to happen, you'd have to use a non-flat activation function or a learning rule that isn't based on gradients.