arXiv:2510.24058v1 Announce Type: cross Abstract: Electrodermal activity (EDA), the primary signal for stress detection, requires costly hardware often unavailable in real-world wearables. In this paper, we propose PULSE, a framework that utilizes EDA exclusively during self-supervised pretraining, while enabling inference without EDA but with more readily available modalities such as ECG, BVP, ACC, and TEMP. Our approach separates encoder outputs into shared and private embeddings. We align shared embeddings across modalities and fuse them into a modality-invariant representation. The private embeddings carry modality-specific information to support the reconstruction objective. Pretraining is followed by knowledge transfer where a frozen EDA teacher transfers sympathetic-arousal representations into student encoders. On WESAD, our method achieves strong stress-detection performance, showing that representations of privileged EDA can be transferred to low-cost sensors to improve accuracy while reducing hardware cost.