Many irregular domains such as social networks, financial transactions, neuron connections, and natural language structures are represented as graphs. In recent years, a variety of graph neural networks (GNNs) have been successfully applied for representation learning and prediction on such graphs. However, in many of the applications, the underlying graph changes over time and existing GNNs are inadequate for handling such dynamic graphs. In this paper we propose a novel technique for learning embeddings of dynamic graphs based on a tensor algebra framework. Our method extends the popular graph convolutional network (GCN) for learning representations of dynamic graphs using the recently proposed tensor M-product technique. Theoretical results that establish the connection between the proposed tensor approach and spectral convolution of tensors are developed. Numerical experiments on real datasets demonstrate the usefulness of the proposed method for an edge classification task on dynamic graphs.
This paper presents a M-product based temporal GCNs to handle dynamic graphs. Experiments on four real datasets are performed to verify the effectiveness of the proposed model.
Overall, I think this paper make a few contributions to advocate tensor M-product. However, there are several big issues as listed below. Given the current status, I could not accept the paper.
Pros:
1, The generalization brought by M-product seems to be general as it includes quite a few graph convolution elements for 3D tensors in a natural way.
2, The experimental setup is reasonable. Datasets are collected from practical problems and of moderately large scale.
3, The paper is clearly written and easy to follow.
Cons & Questions: 
1, My first concern is that M-product formulation does not bring any new insights as people have already used some of the key elements in practice for a long time. For example, the M-transform is just applying 1x1 convolution to multi-channel image. Slice-wise matrix multiplication is also common in practice.
2, Moreover, I think there are several challenges in the M-product formulation which prevent the technique from being practical.
(1) Sharing M such that frontal slices of the transformed signal are the same, i.e., each row of M share the same vector, limits the model capacity significantly. If there is no sharing mechanism, then the model learned on one sequence of graphs could not be applied to another sequence of graphs given two sequences have different lengths. 
(2) If you learn M from data, how could you ensure that M is invertible? In the paragraph before section 4.1, an edge classification formulation is proposed where the inverse M-transform is abandoned. However, if in practice, you do not need the inverse transform, then do those theoretical properties still hold and what is the meaning of introducing such M-product formulation?
3, A few temporal GCN baselines are neither compared or discussed, e.g., [1]. 
4, Could you explain why all the other GCN variants performs significantly worse with a symmetrized adjacency matrix compared to using the asymmetric one? 
[1] Li, Y., Yu, R., Shahabi, C. and Liu, Y., 2017. Diffusion convolutional recurrent neural network: Data-driven traffic forecasting. arXiv preprint arXiv:1707.01926.
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After I read authors' reply and other reviewers' comments, I would like to keep my original rating as the issues have not been properly addressed. I agree with the Reviewer #4 that the theoretical results are a bit artificial and trivial.