Paper:
Embeddings are a fundamental component of many modern machine learning and natural language processing models. Understanding them and visualizing them is essential for gathering insights about the information they capture and the behavior of the models. State of the art in analyzing embeddings consists in projecting them in two-dimensional planes without any interpretable semantics associated to the axes of the projection, which makes detailed analyses and comparison among multiple sets of embeddings challenging. In this work, we propose to use explicit axes defined as algebraic formulae over embeddings to project them into a lower dimensional, but semantically meaningful subspace, as a simple yet effective analysis and visualization methodology. This methodology assigns an interpretable semantics to the measures of variability and the axes of visualizations, allowing for both comparisons among different sets of embeddings and fine-grained inspection of the embedding spaces. We demonstrate the power of the proposed methodology through a series of case studies that make use of visualizations constructed around the underlying methodology and through a user study. The results show how the methodology is effective at providing more profound insights than classical projection methods and how it is widely applicable to many other use cases.

Review:
The idea of analyzing embedding spaces in a non-parametric (example-based) way is well-motivated. However, the main technical contribution of this paper is otherwise not clear - the methodology section covers a very broad set of techniques but doesn't provide a clear picture of what is novel; furthermore, it makes a strong assumption about linear structure in the embedding space that may not hold. (It's worth noting that t-SNE does not make this assumption.)
The visualization strategies presented don't appear to be particularly novel. In particular, projection onto a linear subspace defined by particular attributes was done in the original word2vec and GloVe papers for the analogy task. There's also a lot of other literature on interpreting deeper models using locally-linear predictors, see for example LIME (Ribeiro et al. 2016) or TCAV (Kim at el. 2018).
Evaluations are exclusively qualitative, which is disappointing because there are quantitative ways of evaluating a projection - for example, how well do the reduced dimensions predict a particular attribute relative to the entire vector. Five-axis polar plots can pack in more information than a 2-dimensional plot in some ways, but quickly become cluttered. The authors might consider using heatmaps or bar plots, as are commonly used elsewhere in the literature (e.g. for visualizing activation maps or attention vectors).
User study is hard to evaluate. What were the specific formulae used in the comparison? Did subjects just see a list of nearest-neighbors, or did they see the 2D projection? If the latter, I'd imagine it would be easy to tell which was the t-SNE plot, since most researchers are familiar with how these look.