This paper presents the ballistic graph neural network. Ballistic graph neural network tackles the weight distribution from a transportation perspective and has many different properties comparing to the traditional graph neural network pipeline. The filters propagate exponentially faster(
2 ) comparing to traditional graph neural network( 2 ⇠ T ). We use a perturbed coin operator to perturb and optimize the diffusion rate. Our results show that by selecting the diffusion speed, the network can reach a similar accuracy with fewer parameters. We also show the perturbed filters act as better representations comparing to pure ballistic ones. We provide a new perspective of training graph neural network, by adjusting the diffusion rate, the neural network's performance can be improved.
This paper was extremely hard to read or comprehend. It’s riddled with typos, inaccurate notations and undefined variables (see below for a sampling). The authors will need to significantly polish and improve the presentation of the paper. 
After a few forward and backward passes through the paper, I was able to gather the following high level ideas about the paper:
(1) This paper is somewhat related to the Defferard et. al, 2016 in that the authors want to define a propagation filter for graph neural networks.
2) This proposed filter known as “ballistic filter” should have the property of allowing fast diffusion through the network. 
(3) The authors claim that the ballistic kernel diffuses @ O(k) as compared to O(\sqrt k) when compared to traditional GCNs, where k is the number of propagation steps.
(4) The authors additionally claim that their approach needs one-third the number of parameters.
(5) The authors provide some plots to visualize the linear diffusion rate of their proposed filter.
--- Issues and clarifications ---
- Sec 3, Eq 1 seems to have been taken from Eq 1 in Defferard et. al, however there’s no reference to it and the terms g, U, etc. are not defined.
 - Sec 4, Algo 1 contains the main core of the proposed algorithm, but it’s only defined for the 2D grid case. The notation therein is extremely unclear. What is H_space, H_c? How does one sample \hat{O}_coin.? The net result is that algorithm is undefined. Without a clear definition of the algorithm, it’s completely unclear what the proposed method does.
 - Sec 4.2 is completely unparseable. What is problem setting? What is the metric? How have the baselines been implemented? How has data been split for training/testing?
 - Section 5 mentions that one-third params are used to get 97% but no details are provided as to how less params are consumed.
 - How is figure 7 generated?
 - Sec 8, feel totally unrelated to the paper. There are a whole bunch of random, unmotivated diffusion equations  Eq 6, mentions “.. \hat{g}(f) decreases as f increases and thus can be seen as a low pass filter…” . This is not true from the formula.
 
 --- A sampling of typos ---
Sec 4.1, .. consisits …
Sec 5 “REVISIT” -> “REVISITING”
Figure 6, text, “cassical”
Sec 6.2 title, “SUMMAY”
Sec 8  “aggreated”
Sec 8  t=\-tau to -\tau
Several typos with Hardmard, Hadmard instead of Hadamard.
Overall, the major criticisms of this paper:
 - The proposed algorithm is not clear. 
 - The authors need much more experimentation to bolster their claims in the paper. It’s completely unclear if fast diffusion even if it were possible will help GNNs perform better on a diverse set of tasks.
 - The paper needs a lot more polish and proof reading to make this paper presentable.