Modulate Your Spectrum in Self-Supervised Learning

Whitening loss provides theoretical guarantee in avoiding feature collapse for self-supervised learning (SSL) using joint embedding architectures. One typical implementation of whitening loss is hard whitening that designs whitening transformation over embedding and imposes the loss on the whitened output. In this paper, we propose spectral transformation (ST) framework to map the spectrum of embedding to a desired distribution during forward pass, and to modulate the spectrum of embedding by implicit gradient update during backward pass. We show that whitening transformation is a special instance of ST by definition, and there exist other instances that can avoid collapse by our empirical investigation. Furthermore, we propose a new instance of ST, called IterNorm with trace loss (INTL). We theoretically prove that INTL can avoid collapse and modulate the spectrum of embedding towards an equal-eigenvalue distribution during the course of optimization. Moreover, INTL achieves 76.6% top-1 accuracy in linear evaluation on ImageNet using ResNet-50, which exceeds the performance of the supervised baseline, and this result is obtained by using a batch size of only 256. Comprehensive experiments show that INTL is a promising SSL method in practice. The code is available at https://github.com/winci-ai/intl.

Rot-Pro: Modeling Transitivity by Projection in Knowledge Graph Embedding

Knowledge graph embedding models learn the representations of entities and relations in the knowledge graphs for predicting missing links (relations) between entities. Their effectiveness are deeply affected by the ability of modeling and inferring different relation patterns such as symmetry, asymmetry, inversion, composition and transitivity. Although existing models are already able to model many of these relations patterns, transitivity, a very common relation pattern, is still not been fully supported. In this paper, we first theoretically show that the transitive relations can be modeled with projections. We then propose the Rot-Pro model which combines the projection and relational rotation together. We prove that Rot-Pro can infer all the above relation patterns. Experimental results show that the proposed Rot-Pro model effectively learns the transitivity pattern and achieves the state-of-the-art results on the link prediction task in the datasets containing transitive relations.