A More Discussions for Permutation-Invariant Property of Embedding Layers

In Section 2.1, we mentioned that the embedding layer in the backbone network can be equivalently seen as a combination of embedding lookup and a sum aggregation which is permutation-invariant w.r.t. the order of input features. We provide an illustration for this in Figure 1. To support the remark argument in Section 2.1, we next illustrate the equivalence between concatenation of features' embeddings and sum aggregation/pooling over features' embeddings. This observation indicates that our reasoning in the maintext can be applied to general neural network-based models for attribute features and enable them to handle input vectors with variable-length features. We present the training algorithms for our model in Alg. 1 where the model is trained end-to-end via self-supervised learning or inductive learning approaches. We provide a complete discussion and proof for analysis on generalization error of our approach. Some notations are repeatedly defined in order for a self-contained presentation in this section.