Denoising Cosine Similarity: A Theory-Driven Approach for Efficient Representation Learning

Abstract: Representation learning has been increasing its impact on the research and practice of machine learning, since it enables to learn representations that can apply to various downstream tasks efficiently. However, recent works pay little attention to the fact that real-world datasets used during the stage of representation learning are commonly contaminated by noise, which can degrade the quality of learned representations. This paper tackles the problem to learn robust representations against noise in a raw dataset. To this end, inspired by recent works on denoising and the success of the cosine-similarity-based objective functions in representation learning, we propose the denoising Cosine-Similarity (dCS) loss. The dCS loss is a modified cosine-similarity loss and incorporates a denoising property, which is supported by both our theoretical and empirical findings. To make the dCS loss implementable, we also construct the estimators of the dCS loss with statistical guarantees. Finally, we empirically show the efficiency of the dCS loss over the baseline objective functions in vision and speech domains.