Task: Language Identification
Input (Spanish, English): This paper introduces a polynomial linear model for supervised classification tasks. The model is based on a combination of the Tensor Train (TT) tensor decomposition method and a form of stochastic Riemannian  optimization. A few empirical experiments are performed that demonstrate the good performance of the proposed model relative to appropriate baselines.  From a theoretical standpoint, I think the approach is interesting and elegant. The main machinery underlying this work are the TT decomposition and the geometric structure of the manifold of tensors with fixed TT-rank, which have been established in prior work. The novelty of this paper is in the combination of this machinery to form an efficient polynomial linear model. As such, I would have hoped that the paper mainly focused on the efficacy of this combination and how it is superior to obvious alternatives. For example, I would have really appreciated seeing how FMs performed when optimized over the manifold of positive definite matrices, as another reviewer mentioned. Instead, there is a bit too much effort devoted to explaining prior work.  I think the empirical analysis could be substantially improved. I am particularly puzzled by the significant performance boost obtained from initializing with the ordinary logistic regression solution. I would have liked some further analysis of this effect, especially whether or not it is possible to obtain a similar performance boost with other models. Regarding the synthetic data, I think an important baseline would be against a vanilla feed forward neural network, which would help readers understand how complicated the interactions are and how difficult the dataset is to model. I agree with the previous reviewer regarding a variety of other possible improvements to the experimental section.  A few typos: 'Bernoulli distrbution', 'reproduce the experiemnts', 'generilize better'.  Overall, I am on the fence regarding this paper. The main idea is quite good, but insufficient attention was devoted to analyzing the aspects of the model that make it interesting and novel.
Output (English): en