The progress made in the field of neuroscience, along with the advancement of deep learning (DL), has led to notable achievements with wearable biomedical sensors. However, the large amount of data generated by wearable sensors poses a significant challenge for data transmission due to the limited resource capacity of wearable and implantable devices. We present in this paper presents a task-aware signal compression framework, dubbed task-aware compression (TAC), for wearable sensor data that considers the specific task being performed and the data reconstruction process. The proposed algorithm uses a learnable compression matrix that is trained by a neural network to extract task-related features to reduce the dimension of the data. The compressed data is utilized for task-related analysis and high-fidelity reconstruction. The proposed methodology is evaluated with the task of seizure prediction using electroencephalogram (EEG) data, and experimental results illustrate that with a compression ratio of 1/16, the method is able to reduce maximum transmission and data analysis related power by more than 90%, and the prediction accuracy degradation is below 3%.