Non-contact remote photoplethysmography can be used in a variety of medical and healthcare fields by measuring vital signs continuously and unobtrusively. Recently, end-to-end deep learning methods have been proposed to replace the existing handcrafted features. However, since the existing deep learning methods are known as black box models, the problem of interpretability has been raised, and the same problem exists in the remote photoplethysmography (rPPG) network. In this study, we propose a method to visualize temporal and spectral representations for hidden layers, deeply supervise the spectral representation of intermediate layers through the depth of networks and optimize it for a lightweight model. The optimized network improves performance and enables fast training and inference times. The proposed spectral deep supervision helps to achieve not only high performance but also fast convergence speed through the regularization of the intermediate layers. The effect of the proposed methods was confirmed through a thorough ablation study on public datasets. As a result, similar or outperforming results were obtained in comparison to state-of-the-art models. In particular, our model achieved an RMSE of 1 bpm on the PURE dataset, demonstrating its high accuracy. Moreover, it excelled on the V4V dataset with an impressive RMSE of 6.65 bpm, outperforming other methods. We observe that our model began converging from the very first epoch, a significant improvement over other models in terms of learning efficiency. Our approach is expected to be generally applicable to models that learn spectral domain information as well as to the applications of regression that require the representations of periodicity.