Paper:
Many works have been proposed in the literature to capture the dynamics of diffusion in networks. While some of them define graphical markovian models to extract temporal relationships between node infections in networks, others consider diffusion episodes as sequences of infections via recurrent neural models. In this paper we propose a model at the crossroads of these two extremes, which embeds the history of diffusion in infected nodes as hidden continuous states. Depending on the trajectory followed by the content before reaching a given node, the distribution of influence probabilities may vary. However, content trajectories are usually hidden in the data, which induces challenging learning problems. We propose a topological recurrent neural model which exhibits good experimental performances for diffusion modelling and prediction.

Review:
The authors of this paper are proposing a neural network approach for learning diffusion dynamics in networks. The authors argue that the main advantage of their framework is that it incorporates the structure of independent cascades into the model which predicts the diffusion process.
The primary difficulty in reviewing this paper is the poor presentation of the paper. There are many typos and mistakes (e.g., the last paragraph of the paper starts with a sentence that does not make any sense), missing references (e.g., there is an empty parenthesis at the end of the second paragraph on the second page) and in at least two cases, there are references to a formula that is not in the manuscript (e.g., reference to formula 15 on line 3 of page 5). This issues makes reviewing this paper very difficult.
In the modeling section, authors use p(I|D) as q^D(.) in the Eq. 12, where p(I|D) is the conditional probability that a particular node infected an observed infected node first. Plugging p(I|D) in Eq. 12 and using decomposition of p(D ,I) used in Eq. 10, we arrive at a formulation which drops all p(I|D) terms. This results in an objective function which only involves infected nodes (and no term associated with the parent node), weighted by likelihood of each node j infecting the node at step i. This should make the training more simplified than what is discussed in Algorithm 2. Beyond this simplification, I am not clear if that is actually intended by the authors.
The experiments demonstrate a superior performance of the proposed model compared to alternative benchmarks. The authors explain how they trained their own model but there is no mention on how they trained benchmark models. However, given that the datasets used in the experiments were not used in the associated benchmark papers, it is necessary for authors to explain how they trained competing models.
Due to several shortcomings of the paper, most important of which is on presentation of the paper, this manuscript requires a significant revision by the authors to reach the necessary standards for publication, moreover it would be helpful to clarify the modeling choices and consequences of these choices more clearly.