## 5 Conclusions  
In this paper, we introduced G-CTRNN, a novel gradient-based training framework for Continuous-Time Recurrent Neural Networks (CTRNNs), designed to enable efficient learning on hardware-constrained platforms such as MEMS-based or analog signal processors. Unlike conventional RNNs or heuristic-based CTRNNs, G-CTRNN leverages differentiable programming and constraint-aware optimization to train both synaptic weights and neuron time constants in a biologically inspired, real-time-compatible fashion.  
We evaluated G-CTRNN on the WISDM dataset, a widely used benchmark for human activity recognition (HAR) from wearable sensor data. The results demonstrate that G-CTRNN outperforms traditional RNNs in terms of accuracy, convergence stability, and parameter efficiency--qualities that are particularly important for healthcare applications such as elderly monitoring, activity-based diagnosis, and remote rehabilitation support. G-CTRNN also shows strong promise for low-power operation, making it well-suited for edge deployment in wearable or mobile health systems.  
These results suggest that G-CTRNN is a promising model for real-time embedded AI, assuming physical implementations (e.g., MEMS or analog hardware) that can passively solve the differential dynamics without iterative digital computation. While the current simulation uses Euler integration, which incurs computational overhead, such constraints must be mitigated in native hardware where time dynamics unfold naturally.  
Future work will focus on hardware-software co-design for analog and MEMS implementation of G-CTRNN, robustness to sensor noise, and clinical validation in healthcare environments. Overall, this work contributes a significant step toward enabling real-time embedded AI in next-generation healthcare monitoring systems through the integration of machine learning, edge computing, and analog signal processing. Finally, while this work constrains model parameters to remain hardware-compatible, future research will incorporate direct optimization for energy consumption, fabrication variability, and real-world MEMS dynamics during training, enabling even tighter integration between model behavior and physical implementation.  
Methodology, J.R.; formal analysis, A.A.; investigation, A.A.; resources, D.L. and F.A.; writing--review and editing, F.A.; project administration, F.A.; funding acquisition, D.L. All authors have read and agreed to the published version of the manuscript.  
This research is based upon work supported in part by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via [2022-211002100011].  
**Data Availability Statement:** Publicly available datasets were analyzed in this study. This data can be found here: [[https://www.cis.fordham.edu/wisdm/dataset.php](https://www.cis.fordham.edu/wisdm/dataset.php)]([https://www.cis.fordham.edu/wisdm/dataset.php](https://www.cis.fordham.edu/wisdm/dataset.php)).  
**Acknowledgments:** The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of ODNI, IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein.  
Authors [PERSON] and [PERSON] were employed by the company GE Aerospace Research. The remaining author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.