How sensitive are feedforward Neural Network to weight changes?
you are asking for the condition I would say.
If you skim through the formulae, the german explanation is more
detailed.
In particular, the absolute condition at $x$ is defined as  $\kappa_{\text{abs}}:= \lim \sup _{\tilde{x} \rightarrow x} \frac{||f(x) - f(\tilde{x})||}{||x - \tilde{x}||}$, which means $\kappa_{\text{abs}} \geq 0 $ is the smallest number such that
there is a $\delta &gt;0 $ so that all $\tilde{x}$ with $||\tilde{x}-x|| &lt; \delta $ it holds that $|| f(\tilde{x})-f(x) || \leq \kappa_\text{abs} || \tilde{x} - x ||.$
The relative condition $\kappa_{\text{rel}} \geq 0 $ at $x$ is the smallest number such that there is a $\delta &gt; 0 $ so that all $\tilde{x}$ with $||\tilde{x}-x|| &lt; \delta $ satisfy:
$ \frac{|| f(\tilde x)-f(x) ||}{||f(x)||} \leq \kappa_\text{rel} \frac{|| \tilde{x} - x ||}{||x||}.$
The difference is thus, that the $\kappa_{\text{rel}}$ compares the relative change of the output with the relative change of the input.
In general, let $\tilde{f}$ denote an approximation of the real function $f$, $\tilde{x}$ the input with some noise, then there are 4 categories in numerics:

condition: Analyze $||f(x)-f(\tilde{x})||$
stability: Analyze $||\tilde{f}(x)-\tilde{f}(\tilde{x})||$
consistence: Analyze $||\tilde{f}(x)-f(x)||$
convergence: Analyze $||\tilde{f}(\tilde{x})-f(x)||$.

Your question is also related to adverserial attacks. You can have a look into the literature.
Note also that $\kappa_{\text{rel}} = \frac{||Df(x)||||x||}{||f(x)||}$, so that you could compute the condition number for any given neural network.