There were many algorithms to substitute the back-propagation (BP) in the deep neural network (DNN) training. However, they could not become popular because their training accuracy and the computational efficiency were worse than BP. One of them was direct feedback alignment (DFA), but it showed low training performance especially for the convolutional neural network (CNN). In this paper, we overcome the limitation of the DFA algorithm by combining with the conventional BP during the CNN training. To improve the training stability, we also suggest the feedback weight initialization method by analyzing the patterns of the fixed random matrices in the DFA. Finally, we propose the new training algorithm, binary direct feedback alignment (BDFA) to minimize the computational cost while maintaining the training accuracy compared with the DFA. In our experiments, we use the CIFAR-10 and CIFAR-100 dataset to simulate the CNN learning from the scratch and apply the BDFA to the online learning based object tracking application to examine the training in the small dataset environment. Our proposed algorithms show better performance than conventional BP in both two different training tasks especially when the dataset is small.
The paper propses to use a combination of Direct Feedback Allignment (DFA) and BackPropagation (BP) to improve upon standard back propagation.
To understand what is done, consider the following: Feedback Alignment is +- equal to back propagation when using random but fixed weights in the backwards pass. Direct feedback alignment uses random backprojections directly to the layer of interest. 
The advantage of DFA is that It bypasses the normal computational graph. The advantage of this is that if compute is infinite, all of these updates can be computed in parallel instead of pipelining them as is done in standard BP.
In the current paper, the use of DFA for dense layers and BP for conv layers which is named CDFA is proposed.
In addition the paper also proposes a binarized version of BDFA to limit memory consumption and communication. It is claimed that the proposed techniques improve upon standard back propagation.
Overall, the paper is easy to understand, but I lean towards rejecting this paper because I am not convinced by the experimental evidence. As outlined below, the key issue is that the baseline appears to be weak. Additionally, the main limitation of the proposed approach can only benefit a very limited set of architectures. 
Positive points:
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The authors did an excellent job of introducing BP, FA and DFA in the paper. This makes the core concepts and ideas accessable without having to delve through prior work.
The own contributions and the key idea is easy to understand. 
Limitations and possible improvements
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A core limitation is that recent networks do not have a combination of dense layers and convolutional layers. In many cases the networks are fully convolutional, this limits the applicability of the proposed combination of DFA and BP. The use of additional networks would benefit the paper. Currently only VGG 16 on Cifar 10 is used. Also, the data augmentation strategy is not discussed. Of course, it would be nice if additional datasets could be included as well, but this of course depends on the computational resources the authors have available. 
The key issue to me is that performance improvements for CIFAR are reported, but I fear that the baseline accuracy for VGG16 might be a bit low. If I memory serves me well, it should be able to achieve around 90% at least on CIFAR 10 using VGG style networks. I did a quick search and found http://torch.ch/blog/2015/07/30/cifar.html corroborating this but I did not verify this directly. 
Related to the previous point, since this is an empirical paper, describing the hyper-parameter optimizations and final settings in detail  can convince the reader that the study is exectued correctly. Much of the information is missing now.
Similarly, I have trouble understanding section 4.1 and section 4.2 since I do not know the exact details of the experiments. This can be fixed easily however.
Provide complexity estimates of the potential speedup or provide actual timing information. (Although this might not be that meaningful without much additional work given that gpu kernels are often heavily optimized).
Last year there was a submission to ICLR about fixing the final output layer and only learning the convolutional layers. If we consider that random projections work remarkably well and can be considered approximations of kernels, it could be interesting to add a baseline where the fully connected layers are fixed and only the convolutional layers are trained. The error signal can be propagated using standard BP, FA or DFA methods but it would shed light on whether learning in the higher layers is actually needed or BP in the conv layers is sufficient.
Minor possible improvements
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Finally, I would strongly suggest that the authors perform some additional proofreading. There are quite a few strange formulations and spelling mistakes. That being said, it did not prevent me from understanding the manuscript so this remark DID NOT factor into my judgement.
In addition to remark above, I would suggest removing the second paragraph from the introduction. It feels out of place to me, and the vanishing gradient effects are not discussed in the remainder of the manuscript.
The list of possible optimizers before the selection for SGD+Momentum is not needed. Simply stating that SGD with momentum is used should be sufficient. 
“Training from scratch” instead of “Training from the scratch”