Abstract: Piecewise linear neural networks (PLNNs) are proven universal approximators for continuous functions on the compact domain. For multiple PLNNs (mPLNNs) differing from each other in suffering ...

The pursuit of differentiability in functions is a cornerstone of calculus, demanding a delicate balance of smoothness and continuity. When tasked with finding specific parameters that ensure a ...

A piecewise relation, at its core, is a relation that is defined by multiple sub-relations, each applying to a certain interval of the domain. These sub-relations are essentially different equations ...

We review the methods and applications of automatic differentiation, a research and development activity, which has evolved in various computational fields since the mid 1950's. Starting from very ...

I just noticed that the textbook lacks an example relevant to this exercise group, which is a type of problem we frequently assess: Given a piecewise-defined function, we want to know if it is ...

When business owners think about creating a business continuity plan, many tend to limit the scope of their plans to simple IT recovery and emergency preparedness without considering all critical ...

For many Apple fans, it can be difficult to express what exactly about the ecosystem keeps us coming back. Some people will claim that it's because of the sleek designs that stand the test of time.

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