  This paper presents a new reachability analysis approach to compute interval
over-approximations of the output set of feedforward neural networks with input
uncertainty. We adapt to neural networks an existing mixed-monotonicity method
for the reachability analysis of dynamical systems and apply it to each partial
network within the main network. This ensures that the intersection of the
obtained results is the tightest interval over-approximation of the output of
each layer that can be obtained using mixed-monotonicity on any partial network
decomposition. Unlike other tools in the literature focusing on small classes
of piecewise-affine or monotone activation functions, the main strength of our
approach is its generality: it can handle neural networks with any
Lipschitz-continuous activation function. In addition, the simplicity of our
framework allows users to very easily add unimplemented activation functions,
by simply providing the function, its derivative and the global argmin and
argmax of the derivative. Our algorithm is compared to five other
interval-based tools (Interval Bound Propagation, ReluVal, Neurify, VeriNet,
CROWN) on both existing benchmarks and two sets of small and large randomly
generated networks for four activation functions (ReLU, TanH, ELU, SiLU).
