We study the application of the factor graph framework for symbol detection on linear inter-symbol interference channels. Cyclic factor graphs have the potential to yield low-complexity symbol detectors, but are suboptimal if the ubiquitous sum-product algorithm is applied. In this paper, we present and evaluate strategies to improve the performance of cyclic factor graph-based symbol detection algorithms by means of neural enhancement. In particular, we apply neural belief propagation as an effective way to counteract the effect of cycles within the factor graph. We further propose the application and optimization of a linear preprocessor of the channel output. By modifying the observation model, the preprocessing can effectively change the underlying factor graph, thereby significantly improving the detection performance as well as reducing the complexity.