Behavior of tanh IIR filters If we insert a tanh function (or any other activation function) between the feedback summation and the unit delays, how will such an IIR filter behave for values of $|a| &lt; $1 and $a &gt; ±1$ ?



The filter becomes stable for all values of $a$ but what happens to the frequency response of the filter?
A transfer function is only defined for linear time variant systems. Since your proposed structure is non-linear, the concept of a transfer function doesn't apply any more. You could make approximations for certain special cases and assumptions, but overall the answer to "what happens to the frequency response" is "undefined".