  Negative sampling is essential for implicit collaborative filtering to
provide proper negative training signals so as to achieve desirable
performance. We experimentally unveil a common limitation of all existing
negative sampling methods that they can only select negative samples of a fixed
hardness level, leading to the false positive problem (FPP) and false negative
problem (FNP). We then propose a new paradigm called adaptive hardness negative
sampling (AHNS) and discuss its three key criteria. By adaptively selecting
negative samples with appropriate hardnesses during the training process, AHNS
can well mitigate the impacts of FPP and FNP. Next, we present a concrete
instantiation of AHNS called AHNS_{p<0}, and theoretically demonstrate that
AHNS_{p<0} can fit the three criteria of AHNS well and achieve a larger lower
bound of normalized discounted cumulative gain. Besides, we note that existing
negative sampling methods can be regarded as more relaxed cases of AHNS.
Finally, we conduct comprehensive experiments, and the results show that
AHNS_{p<0} can consistently and substantially outperform several
state-of-the-art competitors on multiple datasets.
