This paper proposes a neural-network-based decoder architecture binary linear block codes with constant-degree variable nodes. It is based on message passing on the unfolded Tanner graph but replaces the variable-node operation in each iteration with a neural network g, whose parameters are provided by another neural network f which takes the absolute values of the messages as its input. (The check-node operation is also approximated via the Taylor expansion of arctanh as in (8).) Experimental results are provided to demonstrate that the proposed scheme performs well for various different types of codes. Although the review scores were around the acceptance threshold in the initial round of review, after the authors' rebuttal two reviewers have raised their scores, so that now all the reviewers are positive. I would thus like to recommend acceptance of this paper. Minor point: Line 81: has a fixed value(d)