## 6 Discussion  
The results of our experiments show that our proposed CoTD-VAE performed better than the baselines. The model can effectively separate static features, long-term trends, and sudden events in human activity data. Furthermore, by adding constraints based on time, the model's ability to capture how things change over time was improved even more.  
CoTD-VAE is better than other VAE versions (like BetaVAE and CVAE) at classifying data while still being good at making copies of the data. This shows that the disentangled latent representations and temporal consistency constraints are important for capturing the essential characteristics of activity data.  
A deeper analysis of the class-specific performance presented in Table 3 reveals significant insights into the architectural biases and capabilities of the evaluated models. Firstly, the near-perfect scores for the LAYING activity across all models suggest that its feature representation is highly distinct and stable. The low signal variance and clear separation from dynamic activities make it an easy class to identify, regardless of the modeling approach. Secondly, the challenge lies in distinguishing between activities with high similarity, such as the two static states SITTING and STANDING, and the three dynamic states (WALKING, WALKING_UPSTAIRS, WALKING_DOWNSTAIRS). Here, the architectural differences become apparent. The Conditional VAE (CVAE) demonstrated exceptional performance in separating SITTING from STANDING. We attribute this to its conditional design, which explicitly uses class labels to learn highly specialized feature distributions for each activity. This makes it powerful for discriminating between classes based on subtle, static differences. However, this same model struggled significantly with WALKING_DOWNSTAIRS, suggesting that its label-conditioned generation may not be robust enough to capture the complex and transient signal patterns of dynamic movements.  
In contrast, our proposed CoTD-VAE, designed for temporal disentanglement, showed strong and more balanced performance across dynamic activities. We posit that its ability to separate a signal into a smooth trend component and a sparse event component is crucial. The trend representation captures the overall rhythm of walking, while the event representation effectively isolates the abrupt, high-frequency signals corresponding to individual steps, which are particularly pronounced during stair descent.  
Nevertheless, this detailed analysis also highlights a potential limitation of CoTD-VAE. Its slightly lower performance compared to CVAE on the SITTING vs. STANDING task suggests that while our model excels at understanding temporal dynamics, its unsupervised disentanglement might be less effective than supervised, label-conditioned methods for resolving fine-grained differences between very similar static states. This presents a clear direction for future work: exploring hybrid models that combine the benefits of temporal disentanglement with label-conditional learning to achieve both dynamic robustness and high-fidelity static-state separation.  
A key limitation of our experimental framework is the two-stage model selection process. By selecting the optimal autoencoder based solely on reconstruction performance, we may have inadvertently favored models that excel at data compression rather than learning the most discriminative features for activity recognition. This likely explains the performance discrepancy of the Transformer-AE model, which achieved the lowest reconstruction error but did not yield the best classification results. Future work should employ an end-to-end hyperparameter optimization strategy guided directly by the downstream task performance to ensure a more holistic model evaluation.