functions with bad regularity

Question

I need some bad functions for neural networks and deep learning. So could you give me some explicit functions with bad regularity?

Answer 1

We can prove an even more powerful statement $\sum_{k=1}^{n}{\frac{1}{\sqrt{k}}\leq \2sqrt{n-1}$. We shall prove this as follows using the subsums of the integral $\int_{0}^{n-1}{\frac{1}{sqrt{x}}}=\frac{1}{2}sqrt{n-1}$. Somit ist sogar $\sum_{k=1}^{n}{\frac{1}{\sqrt{k}}\leq\frac{1}{2}sqrt{n-1}$