# How to measure smoothness of inputs over outputs?

I know similar questions have been asked for time series data. But my question is a little bit different.

Consider that we have input dataset $$X \in R^{N \times M}$$, where $$M$$ is the dimension of inputs and $$N$$ is the number of samples. The output can be more than one dimension. Therefore, the output of our dataset is $$Y \in R^{N \times T}$$, where $$T$$ is the dimension of outputs. The problem refers to multitarget regression in the literature.

My question: Is there any criteria to measure the smoothness or the roughness of this dataset?

My definition for smoothness: Small change on inputs does not change outputs significantly.

Also, if there is a method for just $$T=1$$, I would like to know.