Neural networks have proven to be effective at solving
machine learning tasks but it is unclear whether they learn any relevant causal relationships, while their black-box nature makes it difficult for modellers to understand and debug them. We propose a novel
method overcoming these issues by allowing a two-way interaction
whereby neural-network-empowered machines can expose the underpinning learnt causal graphs and humans can contest the machines
by modifying the causal graphs before re-injecting them into the machines, so that the learnt models are guaranteed to conform to the
graphs and adhere to expert knowledge (some of which can also be
given up-front). By building a window into the model behaviour and
enabling knowledge injection, our method allows practitioners to debug networks based on the causal structure discovered from the data
and underpinning the predictions. Experiments with real and synthetic tabular data show that our method improves predictive performance up to 2.4x while producing parsimonious networks, up to 7x
smaller in the input layer, compared to SOTA regularised networks.