###### Abstract  
Continuous-time Recurrent Neural Networks (CTRNNs) are well-suited for modeling temporal dynamics in low-power neuromorphic and analog computing systems, making them promising candidates for edge-based human activity recognition (HAR) in healthcare. However, training CTRNNs remains challenging due to their continuous-time nature and the need to respect physical hardware constraints. In this work, we propose G-CTRNN, a novel gradient-based training framework for analog-friendly CTRNNs designed for embedded healthcare applications. Our method extends Backpropagation Through Time (BPTT) to continuous domains using TensorFlow's automatic differentiation, while enforcing constraints on time constants and synaptic weights to ensure hardware compatibility. We validate G-CTRNN on the WISDM human activity dataset, which simulates realistic wearable sensor data for healthcare monitoring. Compared to conventional RNNs, G-CTRNN achieves superior classification accuracy with fewer parameters and greater stability--enabling continuous, real-time HAR on low-power platforms such as MEMS computing networks. The proposed framework provides a pathway toward on-device AI for remote patient monitoring, elderly care, and personalized healthcare in resource-constrained environments.  
Real-time, on-device human activity recognition using low-power MEMS-based wearables for remote patient monitoring, fall detection and personalized healthcare in resource-constrained edge environments.  
202520  
Continuous-Time Recurrent Neural Networks (CTRNNs) offer an analog-friendly, biologically inspired framework for modeling temporal dynamics in continuous data streams [3; 4], such as acceleration signals from wearable healthcare devices. Their formulation using differential equations allows direct mapping onto low-power embedded hardware like mixed-signal processors [5] and MEMS sensors [6; 7; 8]. However, a persistent barrier to their practical adoption is the difficulty of training such systems using gradient-based methods, especially when time constants and other physical parameters must remain bounded and interpretable [9].  
Traditional training techniques for recurrent networks, such as Backpropagation Through Time (BPTT), are typically applied in discrete time and do not directly extend to physical systems governed by continuous dynamics. Moreover, existing approaches often fail to account for hardware constraints, including energy efficiency, device variability, and limited tunability of analog parameters. In this paper, we introduce G-CTRNN, a gradient-based training framework for analog-friendly CTRNNs, tailored specifically for low-power healthcare-focused HAR applications. Implemented in TensorFlow, our approach extends BPTT to continuous-time networks while enforcing parameter constraints that reflect real-world hardware requirements. This makes it uniquely suited for real-time HAR on low-power embedded systems such as MEMS sensors used in wearables. We validate G-CTRNN using the WISDM dataset, which contains smartphone-based activity data commonly used in healthcare applications. The results show that G-CTRNN provides superior accuracy and efficiency compared to traditional RNNs while significantly reducing the number of parameters and resource consumption.