# Does sum of embeddings make sense?

Referring to the LightFM model from paper Metadata Embeddings for User and Item Cold-start Recommendations, the model tries to learn $$d$$-dimensional user and item feature embeddings $$e_f^U$$ and $$e_f^I$$ for each feature $$f$$ ($$U$$ is the set of users, $$I$$ is the set of items).

The latent representation of user $$u$$ is given by the sum of its features' latent vectors: $$\mathbf{q_u} = \sum_{j\in{f_u}}\mathbf{e_j^U}$$

The same holds for item $$i$$: $$\mathbf{p_i} = \sum_{j\in{f_i}}\mathbf{e_j^I}$$

Does it really make sense to sum the latent embeddings to represent a set of features (user or item)?