## 4 Discussion
TRGC outperformed the ANNs in terms of Sensitivity, but in the case of Ground Truth 1, questions arose surrounding its Precision in the Far-Superficial dipole condition (although its Precision was significantly better in Ground Truth 2, without any indication of possible differences between dipole conditions). While all connections were discovered, two false positives were detected relatively consistently, indicating that even with time-reversal there is, in certain circumstances, an over-detection of connections. The lack of performance of TCDF and Conv2D in Ground Truth 2 cannot be due to the location of the two fixed dipoles since they were located at the exact same location as in Ground Truth 1. Hence, we suspect that the moving nature of the sending dipole explains (at least partly) the lack of Sensitivity in TCDF and Conv2D. Taking the results from both Ground Truths together, both LSTM-NUE and TRGC are clearly more sensitive, but they both still tend towards over-detection. With regard to the score strength rankings, not much can be said about TCDF given that the mean attention scores were significant only for two time series in the Far-Superficial dipole condition, from which one was a falsely detected connectivity (i.e., a false positive). In contrast to TCDF, with LSTM-NUE, for two out of three targets, correct column-wise rankings were obtained for Ground Truth 1. For Conv2D (with TS = 2), correct rankings for predictor pair were found in terms of R\({}^{2}\)-scores, also for two out of three targets. When looking closer to the contributions of individual time series, it was found that predicting, for instance, X1, with itself and another time series works better than predicting it without the past of X1, which is logical. The fact that adding more predictors (i.e., Conv2D with TS = 3) did not work out is obviously the most problematic aspect of Conv2D. Once a third predictor was added, performance dropped substantially, and it was hypothesized that this could be due to the fact that it was convolving rather uncorrelated or only slightly correlated time series together confuses the two-dimensional network to the extent that no proper prediction can be made. The fact that channels are not kept separate such as in a depthwise-separable architecture, may play an important role in this aspect. Finally, with regard to runtimes (time needed to train a model), LSTM-NUE was together with Conv2D, TS = 3 the most time-consuming method, which calls for a trade-off between accuracy and Time Complexity. It is especially the non-uniform embedding strategy (NUE) that is responsible for the high Time Complexity. However, in [15], it was shown that the current LSTM-model could also produce reasonable results without implementation of the NUE strategy, thereby lowering its Time Complexity drastically. Moreover, in [15], it was shown that LSTM-NUE could cope with different types of ground truths (linear, non-linear and non-linear with varying length lags), as confirmed in our work. Contrary to [15], we, in addition, had Ground Truth 2 with a moving dipole (i.e., the \"Sender\") which worked relatively well for LSTM-NUE. Hence, the latter can cope not only with time-varying parameters but also, to some extent, with changing dipole locations. Both TCDF and Conv2D cope far less well with a moving sender, probably (or at least partly) because of the occurrence of both closeness and deepness in the same setting, which has an impact on how signals are transformed by source reconstruction. TCDF and Conv2D are, in contrast to LSTM-NUE, not a part of the family of Recurrent Neural Networks and therefore do not contain feedback loops. The LSTM is particularly known for its excellent memory properties by virtue of its gates that help to remember versus forget certain time samples. In general, the better memory properties of an LSTMin combination with the NUE approach probably play an important role in dealing with variations over time.