## 4 Discussion  
In this study, we proposed a novel RNN-based model to detect the SO timing automatically from EOG signals alone. The histogram of the differences between the predicted SO timing using the proposed method and that determined using the VD method indicated that the proposed model learned the SO timing determined by the VD method. This result, together with the observation of clear EFRP responses with the SO timing predicted by the proposed method, demonstrates that the proposed model can automatically detect the SO timing for observing EFRPs. The detection process needs to be automated, especially when using a large dataset (2500 trials per person \(\times\) 50 participants = 125,000 trials in total), as in this study. Furthermore, automated detection allows the response to be measured online in a real-world environment. Thus, our proposed automated determination of EFRPs will expand the availability of EFRP responses for mental state estimation in real environments. The mean amplitude of the lambda response based on the proposed method was significantly larger than that based on either the PV or VD method. As the lambda response was obtained by averaging across trials that were time-locked to the SO timing, an increase in the consistency of the SO timing prediction across trials theoretically increases the amplitude of the lambda response in the EFRP waveform. That is, as the consistency of the SO timing decreases, the mean amplitude decreases [10]. Such inconsistent decisions probably occur owing to the fatigue caused by many hours of determination by visual inspection. The enhanced mean amplitudes of the lambda responses based on the proposed method indicate that it provides more consistent prediction results across trials than the VD method, which is susceptible to operator fatigue during the decision process, and thus, automatic detection by our proposed model enables the EFRP amplitudes to be calculated more reliably. The most consistent prediction may have benefited from the more complex model architecture of the proposed RNN-based method compared to the PV method. Conversely, as a positive correlation generally exists between the model complexity and the required volume of training data, a very large quantity of data is required for training NN models because of the many model parameters that are required to realize the model complexity [21]. This study used a biometric dataset of 54,177 trials, which is relatively large. This large data  
Figure 4: Comparison of the mean amplitude of the lambda response across the three methods. The error bars indicate the standard errors. volume enabled the training of the proposed model, and the more complex model architecture compared to the PV methods may have contributed to more consistent prediction. Moreover, as noted previously, the PV method detects the saccade time based on the peak velocity rather than the SO timing. However, EFRP responses are observed time-locked to the SO timing and not the saccade time. The proposed method offers the advantage of detecting the SO timing, which may allow for more consistent prediction compared to the PV method. It may seem paradoxical that the proposed model that was trained by the SO timing determined by the VD method improved the consistency of the prediction compared to the VD method. However, as mentioned previously, the VD method is likely to be inconsistent in determining the SO timing owing to fatigue. These inconsistent label data can be considered as noise when training the proposed model. We believe that the proposed model is sufficiently generalizable to perform robust predictions against such noise by using a large amount of data including noise, thereby outperforming the VD method. In general, various types of noise tend to contaminate biological data, especially when they are recorded in a real environment [3]. The results of this study suggest that learning the nature of biological data can be facilitated by training the NN model with large quantities of data.