  The least-squares ReLU neural network (LSNN) method was introduced and
studied for solving linear advection-reaction equation with discontinuous
solution in \cite{Cai2021linear,cai2023least}. The method is based on an
equivalent least-squares formulation and \cite{cai2023least} employs ReLU
neural network (NN) functions with $\lceil \log_2(d+1)\rceil+1$-layer
representations for approximating solutions. In this paper, we show
theoretically that the method is also capable of accurately approximating
non-constant jumps along discontinuous interfaces that are not necessarily
straight lines. Theoretical results are confirmed through multiple numerical
examples with $d=2,3$ and various non-constant jumps and interface shapes,
showing that the LSNN method with $\lceil \log_2(d+1)\rceil+1$ layers
approximates solutions accurately with degrees of freedom less than that of
mesh-based methods and without the common Gibbs phenomena along discontinuous
interfaces having non-constant jumps.
