## 5 Conclusions  
In this study, we developed a novel anomaly detection framework and demonstrated its application using several publicly available multivariate time series datasets. Our proposed framework combines the advantages of an AE and a new variant of LSTM, namely working memory connections. The AE part is responsible for learning the latent  
Figure 11: Comparison of anomaly detection times across multiple models and datasets. Figure 10: Comparison of training times across multiple models and datasets. features of the normal training data to acquire the ability to reconstruct normal data. When anomalous data are input into the trained model during the anomaly detection phase, the reconstruction error increases significantly. The Bi-LSTM-WMCs part is responsible for learning the temporal dependencies of the data. Through comparisons with a series of baseline models, we found that as the time window size (t) increases, the performance advantage of the model we proposed, namely Bi-LSTM-WMCs-AE, becomes increasingly evident. For smaller time windows (t = 5), the bidirectional architectures do not exhibit a significant advantage, likely due to the fact that with smaller time windows, unidirectional LSTM models can already effectively utilize the temporal information within the window. However, models using LSTM-WMCs (LSTM-WMCs-AE and Bi-LSTM-WMCs-AE) almost consistently outperform those without such connections. Therefore, we have reason to believe that our proposed model, incorporating bidirectional architecture and LSTM-WMCs, demonstrates greater robustness under various conditions. The practical significance of our study lies in its ability to address the challenges of anomaly detection in multivariate time series data through a reconstruction-based approach. Central to our contribution is the integration of LSTM-WMCs, which, while not proposed by us, is applied for the first time in the anomaly detection domain in this study. This innovative LSTM variant enhances the model's ability to effectively process time series data by allowing memory cells to influence gate values, leading to more accurate reconstructions and improved anomaly detection reliability. This also demonstrates the feasibility of applying such a novel LSTM variant to other domains. Furthermore, our model significantly reduces the reliance on labeled anomaly data, addressing a critical limitation in real-world applications where such data are often scarce and expensive to obtain. The robust performance of our approach across datasets with varying characteristics, including continuous sensor data and mixed sensor-actuator data, further highlights its scalability and adaptability. These advancements validate the effectiveness of our approach and underscore its potential to provide a reliable and flexible solution for anomaly detection across diverse fields, such as industrial monitoring and space exploration. Our study has some limitations that should be acknowledged. Firstly, while replacing the traditional LSTM units with the LSTM-WMCs has undoubtedly improved performance, this enhancement comes at the cost of increased computational complexity. The more intricate connection mechanism of the LSTM-WMCs demands greater computational resources, especially when combined with a bidirectional structure and integrated into the AE framework. This could pose challenges for deploying the model in resource-constrained environments or real-time applications, where computational efficiency is critical. Secondly, our study is primarily focused on detecting point anomalies, and the model's performance on other types of anomalies remains to be validated. We have demonstrated the exceptional capability of the Working Memory Connections for LSTM in the domain of anomaly detection. However, LSTM has been widely employed in various real-world applications, such as logistics and inventory management, energy management, and intelligent production scheduling.