## 5 Discussion  
The proposed FMTL framework consistently performed well in both sleep staging and SDB severity classification tasks across all three datasets, validating its capacity to generalize under real-world non-IID data distributions. The use of multi-task learning significantly contributed to model performance. Compared with single-task baselines, joint optimization of sleep staging and SDB classification allowed the model to benefit from shared information between the two tasks, which are physiologically correlated. In this study, a deep neural network was constructed based on seven-channel multimodal signals (EEG, EOG, EMG, ECG, respiratory airflow, blood oxygen saturation, snoring) to achieve joint recognition of sleep stages and SDB severity. Compared with traditional single-channel or unimodal models, multimodal input not only improved the expressive power of feature space but also prompts the model to learn shared and specific representations between modalities during encoding. In our shared CNN-GRU backbone structure, early fusion guided the network to establish a unified time-frequency representation at a low level, while task-specific branches further explore task-related modalities. High accuracy and Kappa coefficients were maintained across datasets (SHHS_rest and HMC), indicating that multimodal fusion not only improves task discrimination but also improves the adaptability to individual differences, device differences, and labeling styles to a certain extent. For difficult-to-distinguish states such as N1, REM, and mild-to-moderate SDB, the multimodal model showed significantly better performance than the unimodal baseline, indicating that it indeed captured compensatory cues across modalities. We particularly observed that the classification performance of the N1 stage was significantly improved compared with traditional methods. As is known, the EEG activity of the N1 stage is usually between wakefulness and N2, lacking clear K-complex or spindle events, making it very easy to be confused with wakefulness or N2 in visual annotation [44]. The literature shows that even the consistency of annotation of the N1 stage among clinical sleep experts is only about 40-60%, which is significantly lower than other stages. The model based on the federated multi-task learning framework in this study achieved considerable F1 scores in N1 recognition (such as APPLES: 53.7%, SHHS_rest: 57.8%, HMC: 61.4%), which are significantly improved compared with previous single-task or single-modality methods. We believe that this is due to the information transfer between tasks. In the process of jointly optimizing the sleep staging and SDB classification tasks, the multi-task learning model can learn more abstract and discriminative shared features. In actual training, the model is forced to be sensitive to subtle physiological changes associated with respiratory disorders, which often occur in the N1 stage at the beginning of sleep. For example, when breathing is mildly restricted, individuals are prone to micro-arousals and frequent N1 regressions [45], which imply a certain statistical association between N1 and SDB labels. This cross-task structural information provides additional indirect supervision  
Figure 6: Comparison with different common classification strategies. Transparent colors represent no privacy-preserving capability. (**a**) Single. (**b**) Mix. (**c**) Fedavg. for the N1 stage and enhances its ability to express discriminative boundaries. In addition, we also believe that multimodal fusion to enhance boundary modeling may be helpful. Compared with traditional methods that rely only on EEG signals, we integrate multiple modalities such as EOG, EMG, ECG, and respiratory airflow.