Many types of relations in physical, biological, social and information systems can be modeled as homogeneous or heterogeneous concept graphs. Hence, learning from and with graph embeddings has drawn a great deal of research interest recently, but only ad hoc solutions have been obtained this far. In this paper, we conjecture that the one-shot supervised learning mechanism is a bottleneck in improving the performance of the graph embedding learning algorithms, and propose to extend this by introducing a multi-shot unsupervised learning framework. Empirical results on several real-world data set show that the proposed model consistently and significantly outperforms existing state-of-the-art approaches on knowledge base completion and graph based multi-label classification tasks.
The paper proposes a new method to compute embeddings of multirelational graphs. In particular, the paper proposes so-called E-Cells and R-Cells to answer queries of the form (h,r,?), (?,r,t), and(h,?,t). The proposed method (GEN), is evaluated on standard datasets for link prediction as well as datasets for node classification.
The paper tackles an interesting problem, as learning from graphs via embedding methods has become increasingly important. The experimental results of the proposed model, especially for the node classification tasks, look promising. Unfortunately, the paper makes a number of claims which are not justified or seem to result from misconceptions about related methods. For instance, the abstract labels prior work as "ad hoc solutions" and claims to propose a principled approach. However, I do not see how the proposed method is a more principled than previously proposed methods. For instance, methods such as RESCAL, TransE, HolE or ComplEx can be motivated as compositional models that reflect the compositional structure of relational data. Furthermore, RESCAL-like models can be linked to prior research in cognitive science on relational memory [3]. HolE explicitly motivates its modeling through its relation to models for associative memory. 
Furthermore, due to their compositional nature, these model are all able to answer the queries considered in the paper (i.e, (h,r,?), (h,?,t), (?,r,t)) and are implicitly trained to do so. The HolE paper discusses this for instance when relating the model to associative memory. For RESCAL, [4] shows how even more complicated queries involving logical connectives and quantification can be answered. It is therefore not clear how to proposed method improves over these models.
With regard to the evaluation: It is nice that the authors provided an evaluation which compares to several SOTA methods. However, it is unclear under which setting these results where obtained. In particular, how were the hyperparameter for each model chosen and which parameters ranges were considered in the grid search. Appendix B.2 in the supplementary seems to specify the parameter setting for GEN, but it is unclear whether the same parameters where chosen for the competing models and whether they were trained with similar methods (e.g., dropout, learning rate decay etc.). The big difference in performance of HolE and ComplEx is also surprising, as they are essentially the same model (e.g. see [1,2]). It is therefore not clear to me which conclusions we can draw from the reported numbers.
Further comments:
- p.3: The statement "This is the actual way we humans learn the meaning of concepts expressed by a statement" requires justification
- p.4: The authors state that the model is trained unsupervised, but eq. 10 clearly uses supervised information in form of labels.
- p.4: In 3.1, E-cells are responsible to answer queries of the form (h,r,?) and (?, r, t), while Section 3.2 says E-Cells are used to answer (h, ?, t). I assume in the later case, the task is actually to answer (h,r,?)?
- p.2: Making a closed-world assumption is quite problematic in this context, especially when taking a principled approach. Many graphs such as Freebase are very incomplete and make an explicit open-world assumption. 
- The paper uses a unusual definition of one-shot/multi-shot learning, which makes it confusing to read at first. The authors might consider using different terms to improve readability.
- Paper would benefit if the model is presented earlier. GEN Cells are defined only in Section 3.2, but the model is discussed earlier. Reversing the order might improve presentation.
[1] K. Hayashi et al: "On the Equivalence of Holographic and Complex Embeddings for Link Prediction", 2017
[2] T.Trouillon et al: "Complex and holographic embeddings of knowledge graphs: a comparison", 2017
[3] G. Halford et al: "Processing capacity defined by relational complexity: Implications for comparative, developmental, and cognitive psychology", 1998.
[4] D. Krompaß et al: "Querying factorized probabilistic triple databases", 2014