Most algorithms for representation learning and link prediction in relational data have been designed for static data. However, the data they are applied to usually evolves with time, such as friend graphs in social networks or user interactions with items in recommender systems. This is also the case for knowledge bases, which contain facts such as (US, has president, B. Obama, [2009][2010][2011][2012][2013][2014][2015][2016][2017]) that are valid only at certain points in time. For the problem of link prediction under temporal constraints, i.e., answering queries such as (US, has president, ?, 2012), we propose a solution inspired by the canonical decomposition of tensors of order 4. We introduce new regularization schemes and present an extension of ComplEx (Trouillon et al., 2016) that achieves state-of-the-art performance. Additionally, we propose a new dataset for knowledge base completion constructed from Wikidata, larger than previous benchmarks by an order of magnitude, as a new reference for evaluating temporal and non-temporal link prediction methods.
The work in this paper is focused on the task of knowledge base completion, dealing specifically with temporal relations, which is quite important in practice, and also not as well studied in literature. Specifically, the authors have 3 main contributions in this paper:
1. They present an order 4 tensor factorization for dealing with temporal data, which is a nice extension of the work in Lacroix 2018. The authors introduce different forms of regularization to extend to the order 4 tensors. Inspired by previous work, they produce different regularization strategies for order 4 tensor by unfolding the modes to reduce it ot an order 3 formulation. They also describe a regularization term for smoothing the temporal embeddings. 
3. Finally, the authors mine wikidata for temporal relations and contribute a dataset based on wikidata that is much larger than existing datasets for this task.
Overall, I think this paper is  interesting as it provides an incremental extension of ComplEx to the temporal case, and the experiments to support the formulation show improvements in MRR. However, the experiments around standard benchmarks as well as the data produced by the authors do not always support the hypothesis that modeling temporal dimension in the proposed formulation is a win for the KB completion task.  For example, the use of auxiliary losses  for enforcing temporal constraints makes the overall performance worse. This is mentioned in a section, but I think it deserves a more thorough explanation. Also, there is no mention about statistical significance of the results, and so it is hard to judge the claim of these being SOTA as made by the authors. For example, on the wikidata dataset produced, the ComplEx model outperforms the proposed models.
Strengths:
1. The work in this paper is quite well motivated and the modeling formulation is clear and easy to follow. The authors did a great job in citing relevant work and walking through the model formulation as well as the various regularization terms introduced.
2. The authors compare their work to the previous SOTA - the ComplEx models for multiple datasets, including their own released datasets. They present a clear set of experiments to demonstrate the effectiveness of their approach both on non-temporal and temporal relations.
3. There is a dataset being released and also code, which should aid in reproducibility of the results (though I have not tested the code).
Areas to be addressed:
1. The work seems to assume that the time is discretized by year. However, it is unclear how one would deal with a KB where the temporal relations can change on the order of weeks (example popular movies). For that matter, how would the model be modified to deal with heterogenous time scales in the evolution of the relations in the KB? Can the authors add some clarification as well as explanations for how this would be addressed in this formulation?
2. While there is a section devoted to different regularization, from Table 3, the impact of choosing the right regularizer seems minimal in terms of MRR. Also, it seems that the results in Table 3 are comparable to the “ranks multiplied by 10” setting in Table 2. What is the reason for this choice? 
3. For Table 4, why is there a performance difference between static and non-static relations? It would help if the authors could provide some more error analyses to dive into this performance difference - is it just data imbalance or inherent difficulty in the task for temporal relations. 
4. Section 6 talks about enforcing another auxiliary loss, however, these results are not part of the table. I would urge the authors to add this to Table 4. Also, the loss in MRR mentioned is it the average loss or does enforcing this auxiliary loss also influence performance on T-MRR as well? If so, might it be that the auxiliary loss is too strong and might need to be penalized? Did the authors try penalizing the auxiliary loss? Finally, the graph in Figure 2 is hard to follow when printed in black and white. What would the plot look like in comparison to a model that does not enforce the auxiliary function for the same example? I would recommend re-working Section 6 to provide some more details about the performance of the models both across the various datasets as well as error analyses of a few examples compared across TNTComplex, TNTComplex + auxiliary loss + Baseline Complex. Having some representative examples would make it easy to understand where these models differ in their performance.
5. In the results, can the authors include metrics like filtered MRR as well as Hits@10, similar to the one suggested by Bordes 2013? This would make it easier to compare against previous literature results which all seem to be reporting on these metrics.